notebooks/sir/julia.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SIR model in Julia using DifferentialEquations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Author*: Simon Frost @sdwfrost\n",
    "*Editor*: Chris Rackauckas @ChrisRackauckas\n",
    "\n",
    "*Date*: 2018-07-12\n",
    "\n",
    "### Using the Macro DSL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using DifferentialEquations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: Symbolic calculations could not initiate. Likely there's a function which is not differentiable by SymEngine.\n",
      "└ @ ParameterizedFunctions /home/simon/.julia/packages/ParameterizedFunctions/ozDxQ/src/ode_def_opts.jl:244\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(::SIRModel{getfield(Main, Symbol(\"##3#4\")),Nothing,Nothing,Nothing,Nothing,Nothing,Any,Any}) (generic function with 2 methods)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sir_ode = @ode_def SIRModel begin\n",
    "    dS = -β*S*I\n",
    "    dI = β*S*I-γ*I\n",
    "    dR = γ*I\n",
    "    end β γ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 200.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parms = [0.1,0.05]\n",
    "init = [0.99,0.01,0.0]\n",
    "tspan = (0.0,200.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mODEProblem\u001b[0m with uType \u001b[36mArray{Float64,1}\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mtrue\u001b[0m\n",
       "timespan: (0.0, 200.0)\n",
       "u0: [0.99, 0.01, 0.0]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sir_prob = ODEProblem(sir_ode,init,tspan,parms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sir_sol = solve(sir_prob,saveat = 0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "  613.418,198.295 614.453,198.894 615.488,199.495 616.523,200.098 617.558,200.704 618.593,201.311 619.628,201.921 620.663,202.532 621.698,203.146 622.733,203.762 \n",
       "  623.769,204.38 624.804,205.001 625.839,205.623 626.874,206.248 627.909,206.875 628.944,207.504 629.979,208.135 631.014,208.768 632.049,209.404 633.084,210.042 \n",
       "  634.119,210.682 635.154,211.324 636.189,211.968 637.224,212.615 638.259,213.263 639.294,213.914 640.329,214.568 641.364,215.223 642.4,215.88 643.435,216.54 \n",
       "  644.47,217.202 645.505,217.867 646.54,218.533 647.575,219.202 648.61,219.873 649.645,220.546 650.68,221.221 651.715,221.899 652.75,222.579 653.785,223.261 \n",
       "  654.82,223.946 655.855,224.632 656.89,225.321 657.925,226.012 658.96,226.706 659.995,227.402 661.031,228.1 662.066,228.8 663.101,229.502 664.136,230.207 \n",
       "  665.171,230.914 666.206,231.623 667.241,232.335 668.276,233.049 669.311,233.765 670.346,234.483 671.381,235.204 672.416,235.927 673.451,236.652 674.486,237.38 \n",
       "  675.521,238.11 676.556,238.842 677.591,239.576 678.626,240.313 679.662,241.052 680.697,241.793 681.732,242.537 682.767,243.282 683.802,244.031 684.837,244.781 \n",
       "  685.872,245.534 686.907,246.289 687.942,247.046 688.977,247.806 690.012,248.568 691.047,249.332 692.082,250.099 693.117,250.868 694.152,251.639 695.187,252.413 \n",
       "  696.222,253.188 697.257,253.966 698.293,254.747 699.328,255.53 700.363,256.315 701.398,257.102 702.433,257.892 703.468,258.684 704.503,259.478 705.538,260.275 \n",
       "  706.573,261.074 707.608,261.875 708.643,262.678 709.678,263.484 710.713,264.293 711.748,265.103 712.783,265.916 713.818,266.731 714.853,267.548 715.888,268.368 \n",
       "  716.924,269.19 717.959,270.014 718.994,270.841 720.029,271.67 721.064,272.501 722.099,273.335 723.134,274.17 724.169,275.009 725.204,275.849 726.239,276.692 \n",
       "  727.274,277.537 728.309,278.384 729.344,279.234 730.379,280.085 731.414,280.94 732.449,281.796 733.484,282.655 734.52,283.516 735.555,284.379 736.59,285.245 \n",
       "  737.625,286.113 738.66,286.983 739.695,287.855 740.73,288.73 741.765,289.607 742.8,290.486 743.835,291.367 744.87,292.251 745.905,293.137 746.94,294.025 \n",
       "  747.975,294.916 749.01,295.809 750.045,296.704 751.08,297.601 752.115,298.5 753.151,299.402 754.186,300.306 755.221,301.212 756.256,302.121 757.291,303.031 \n",
       "  758.326,303.944 759.361,304.859 760.396,305.777 761.431,306.696 762.466,307.618 763.501,308.542 764.536,309.468 765.571,310.396 766.606,311.327 767.641,312.259 \n",
       "  768.676,313.194 769.711,314.131 770.746,315.071 771.782,316.012 772.817,316.956 773.852,317.901 774.887,318.849 775.922,319.799 776.957,320.751 777.992,321.706 \n",
       "  779.027,322.662 780.062,323.621 781.097,324.582 782.132,325.545 783.167,326.51 784.202,327.477 785.237,328.446 786.272,329.418 787.307,330.391 788.342,331.367 \n",
       "  789.377,332.344 790.413,333.324 791.448,334.306 792.483,335.29 793.518,336.276 794.553,337.264 795.588,338.254 796.623,339.246 797.658,340.24 798.693,341.237 \n",
       "  799.728,342.235 800.763,343.235 801.798,344.238 802.833,345.242 803.868,346.248 804.903,347.257 805.938,348.267 806.973,349.28 808.008,350.294 809.044,351.31 \n",
       "  810.079,352.329 811.114,353.349 812.149,354.371 813.184,355.396 814.219,356.422 815.254,357.45 816.289,358.48 817.324,359.512 818.359,360.546 819.394,361.582 \n",
       "  820.429,362.62 821.464,363.66 822.499,364.702 823.534,365.745 824.569,366.791 825.604,367.838 826.639,368.887 827.675,369.938 828.71,370.991 829.745,372.046 \n",
       "  830.78,373.102 831.815,374.16 832.85,375.22 833.885,376.282 834.92,377.346 835.955,378.412 836.99,379.479 838.025,380.548 839.06,381.619 840.095,382.691 \n",
       "  841.13,383.765 842.165,384.841 843.2,385.919 844.235,386.998 845.27,388.079 846.306,389.162 847.341,390.247 848.376,391.333 849.411,392.42 850.446,393.51 \n",
       "  851.481,394.601 852.516,395.693 853.551,396.788 854.586,397.884 855.621,398.981 856.656,400.08 857.691,401.181 858.726,402.283 859.761,403.387 860.796,404.492 \n",
       "  861.831,405.599 862.866,406.707 863.901,407.817 864.937,408.928 865.972,410.041 867.007,411.155 868.042,412.271 869.077,413.388 870.112,414.507 871.147,415.627 \n",
       "  872.182,416.749 873.217,417.872 874.252,418.996 875.287,420.122 876.322,421.249 877.357,422.378 878.392,423.508 879.427,424.639 880.462,425.772 881.497,426.906 \n",
       "  882.532,428.041 883.568,429.178 884.603,430.316 885.638,431.455 886.673,432.595 887.708,433.737 888.743,434.88 889.778,436.024 890.813,437.17 891.848,438.316 \n",
       "  892.883,439.464 893.918,440.613 894.953,441.764 895.988,442.915 897.023,444.068 898.058,445.221 899.093,446.376 900.128,447.532 901.163,448.69 902.199,449.848 \n",
       "  903.234,451.007 904.269,452.168 905.304,453.329 906.339,454.492 907.374,455.655 908.409,456.82 909.444,457.986 910.479,459.152 911.514,460.32 912.549,461.489 \n",
       "  913.584,462.659 914.619,463.829 915.654,465.001 916.689,466.173 917.724,467.347 918.759,468.521 919.794,469.696 920.83,470.872 921.865,472.049 922.9,473.227 \n",
       "  923.935,474.406 924.97,475.586 926.005,476.766 927.04,477.947 928.075,479.129 929.11,480.312 930.145,481.496 931.18,482.68 932.215,483.865 933.25,485.051 \n",
       "  934.285,486.237 935.32,487.425 936.355,488.613 937.39,489.801 938.425,490.991 939.461,492.181 940.496,493.371 941.531,494.563 942.566,495.754 943.601,496.947 \n",
       "  944.636,498.14 945.671,499.334 946.706,500.528 947.741,501.723 948.776,502.918 949.811,504.114 950.846,505.31 951.881,506.507 952.916,507.704 953.951,508.902 \n",
       "  954.986,510.101 956.021,511.299 957.056,512.498 958.092,513.698 959.127,514.898 960.162,516.098 961.197,517.299 962.232,518.5 963.267,519.702 964.302,520.904 \n",
       "  965.337,522.106 966.372,523.308 967.407,524.511 968.442,525.714 969.477,526.917 970.512,528.121 971.547,529.324 972.582,530.528 973.617,531.733 974.652,532.937 \n",
       "  975.687,534.141 976.723,535.346 977.758,536.551 978.793,537.756 979.828,538.961 980.863,540.166 981.898,541.372 982.933,542.577 983.968,543.783 985.003,544.988 \n",
       "  986.038,546.194 987.073,547.399 988.108,548.605 989.143,549.81 990.178,551.016 991.213,552.222 992.248,553.427 993.283,554.633 994.318,555.839 995.354,557.044 \n",
       "  996.389,558.25 997.424,559.455 998.459,560.66 999.494,561.865 1000.53,563.07 1001.56,564.275 1002.6,565.48 1003.63,566.685 1004.67,567.889 1005.7,569.093 \n",
       "  1006.74,570.297 1007.77,571.501 1008.81,572.704 1009.84,573.908 1010.88,575.111 1011.91,576.313 1012.95,577.516 1013.98,578.718 1015.02,579.92 1016.05,581.121 \n",
       "  1017.09,582.322 1018.12,583.523 1019.16,584.723 1020.19,585.923 1021.23,587.123 1022.26,588.322 1023.3,589.521 1024.34,590.719 1025.37,591.917 1026.41,593.114 \n",
       "  1027.44,594.311 1028.48,595.507 1029.51,596.703 1030.55,597.899 1031.58,599.093 1032.62,600.288 1033.65,601.482 1034.69,602.675 1035.72,603.867 1036.76,605.059 \n",
       "  1037.79,606.251 1038.83,607.441 1039.86,608.632 1040.9,609.821 1041.93,611.01 1042.97,612.198 1044,613.386 1045.04,614.572 1046.07,615.759 1047.11,616.944 \n",
       "  1048.14,618.129 1049.18,619.313 1050.21,620.496 1051.25,621.678 1052.28,622.86 1053.32,624.041 1054.35,625.221 1055.39,626.4 1056.42,627.579 1057.46,628.756 \n",
       "  1058.49,629.933 1059.53,631.109 1060.56,632.284 1061.6,633.458 1062.63,634.632 1063.67,635.804 1064.7,636.975 1065.74,638.146 1066.77,639.316 1067.81,640.484 \n",
       "  1068.84,641.652 1069.88,642.819 1070.91,643.985 1071.95,645.15 1072.98,646.314 1074.02,647.477 1075.05,648.638 1076.09,649.799 1077.12,650.959 1078.16,652.118 \n",
       "  1079.19,653.276 1080.23,654.432 1081.26,655.588 1082.3,656.742 1083.33,657.896 1084.37,659.048 1085.4,660.199 1086.44,661.349 1087.47,662.498 1088.51,663.646 \n",
       "  1089.54,664.793 1090.58,665.938 1091.61,667.083 1092.65,668.226 1093.68,669.368 1094.72,670.509 1095.75,671.648 1096.79,672.786 1097.82,673.924 1098.86,675.059 \n",
       "  1099.89,676.194 1100.93,677.327 1101.96,678.46 1103,679.59 1104.03,680.72 1105.07,681.848 1106.1,682.975 1107.14,684.101 1108.17,685.225 1109.21,686.348 \n",
       "  1110.24,687.47 1111.28,688.591 1112.31,689.71 1113.35,690.827 1114.38,691.944 1115.42,693.059 1116.46,694.172 1117.49,695.284 1118.53,696.395 1119.56,697.504 \n",
       "  1120.6,698.612 1121.63,699.719 1122.67,700.824 1123.7,701.928 1124.74,703.03 1125.77,704.131 1126.81,705.23 1127.84,706.328 1128.88,707.424 1129.91,708.519 \n",
       "  1130.95,709.613 1131.98,710.705 1133.02,711.795 1134.05,712.884 1135.09,713.971 1136.12,715.057 1137.16,716.142 1138.19,717.224 1139.23,718.306 1140.26,719.385 \n",
       "  1141.3,720.463 1142.33,721.54 1143.37,722.615 1144.4,723.688 1145.44,724.76 1146.47,725.831 1147.51,726.899 1148.54,727.966 1149.58,729.032 1150.61,730.096 \n",
       "  1151.65,731.158 1152.68,732.218 1153.72,733.277 1154.75,734.335 1155.79,735.39 1156.82,736.444 1157.86,737.496 1158.89,738.547 1159.93,739.596 1160.96,740.643 \n",
       "  1162,741.689 1163.03,742.733 1164.07,743.775 1165.1,744.816 1166.14,745.855 1167.17,746.892 1168.21,747.927 1169.24,748.961 1170.28,749.993 1171.31,751.023 \n",
       "  1172.35,752.051 1173.38,753.078 1174.42,754.103 1175.45,755.126 1176.49,756.148 1177.52,757.168 1178.56,758.185 1179.59,759.202 1180.63,760.216 1181.66,761.229 \n",
       "  1182.7,762.239 1183.73,763.249 1184.77,764.256 1185.8,765.261 1186.84,766.265 1187.87,767.267 1188.91,768.267 1189.94,769.265 1190.98,770.261 1192.01,771.256 \n",
       "  1193.05,772.248 1194.08,773.239 1195.12,774.228 1196.15,775.215 1197.19,776.2 1198.22,777.184 1199.26,778.165 1200.29,779.145 1201.33,780.123 1202.36,781.099 \n",
       "  1203.4,782.073 1204.43,783.045 1205.47,784.016 1206.5,784.984 1207.54,785.951 1208.57,786.916 1209.61,787.879 1210.65,788.84 1211.68,789.799 1212.72,790.756 \n",
       "  1213.75,791.711 1214.79,792.665 1215.82,793.616 1216.86,794.566 1217.89,795.514 1218.93,796.46 1219.96,797.404 1221,798.346 1222.03,799.286 1223.07,800.225 \n",
       "  1224.1,801.161 1225.14,802.095 1226.17,803.028 1227.21,803.959 1228.24,804.888 1229.28,805.814 1230.31,806.739 1231.35,807.662 1232.38,808.584 1233.42,809.503 \n",
       "  1234.45,810.42 1235.49,811.335 1236.52,812.249 1237.56,813.16 1238.59,814.07 1239.63,814.978 1240.66,815.883 1241.7,816.787 1242.73,817.689 1243.77,818.589 \n",
       "  1244.8,819.487 1245.84,820.383 1246.87,821.277 1247.91,822.17 1248.94,823.06 1249.98,823.948 1251.01,824.835 1252.05,825.719 1253.08,826.602 1254.12,827.482 \n",
       "  1255.15,828.361 1256.19,829.238 1257.22,830.113 1258.26,830.985 1259.29,831.856 1260.33,832.725 1261.36,833.592 1262.4,834.457 1263.43,835.321 1264.47,836.182 \n",
       "  1265.5,837.041 1266.54,837.898 1267.57,838.754 1268.61,839.607 1269.64,840.459 1270.68,841.308 1271.71,842.156 1272.75,843.001 1273.78,843.845 1274.82,844.687 \n",
       "  1275.85,845.527 1276.89,846.364 1277.92,847.2 1278.96,848.034 1279.99,848.866 1281.03,849.696 1282.06,850.525 1283.1,851.351 1284.13,852.175 1285.17,852.997 \n",
       "  1286.2,853.818 1287.24,854.636 1288.27,855.452 1289.31,856.267 1290.34,857.08 1291.38,857.89 1292.41,858.699 1293.45,859.506 1294.48,860.31 1295.52,861.113 \n",
       "  1296.55,861.914 1297.59,862.713 1298.62,863.51 1299.66,864.305 1300.69,865.099 1301.73,865.89 1302.77,866.679 1303.8,867.467 1304.84,868.252 1305.87,869.036 \n",
       "  1306.91,869.817 1307.94,870.597 1308.98,871.375 1310.01,872.15 1311.05,872.924 1312.08,873.696 1313.12,874.466 1314.15,875.234 1315.19,876.001 1316.22,876.765 \n",
       "  1317.26,877.527 1318.29,878.288 1319.33,879.046 1320.36,879.803 1321.4,880.558 1322.43,881.31 1323.47,882.061 1324.5,882.81 1325.54,883.557 1326.57,884.302 \n",
       "  1327.61,885.046 1328.64,885.787 1329.68,886.527 1330.71,887.264 1331.75,888 1332.78,888.734 1333.82,889.466 1334.85,890.196 1335.89,890.924 1336.92,891.65 \n",
       "  1337.96,892.374 1338.99,893.097 1340.03,893.817 1341.06,894.536 1342.1,895.253 1343.13,895.968 1344.17,896.681 1345.2,897.392 1346.24,898.101 1347.27,898.809 \n",
       "  1348.31,899.514 1349.34,900.218 1350.38,900.92 1351.41,901.62 1352.45,902.318 1353.48,903.015 1354.52,903.709 1355.55,904.402 1356.59,905.093 1357.62,905.782 \n",
       "  1358.66,906.469 1359.69,907.154 1360.73,907.838 1361.76,908.519 1362.8,909.199 1363.83,909.877 1364.87,910.553 1365.9,911.228 1366.94,911.9 1367.97,912.571 \n",
       "  1369.01,913.24 1370.04,913.907 1371.08,914.573 1372.11,915.236 1373.15,915.898 1374.18,916.558 1375.22,917.216 1376.25,917.872 1377.29,918.527 1378.32,919.18 \n",
       "  1379.36,919.831 1380.39,920.48 1381.43,921.128 1382.46,921.774 1383.5,922.418 1384.53,923.06 1385.57,923.7 1386.6,924.339 1387.64,924.976 1388.67,925.611 \n",
       "  1389.71,926.245 1390.74,926.877 1391.78,927.507 1392.81,928.135 1393.85,928.762 1394.89,929.387 1395.92,930.01 1396.96,930.631 1397.99,931.251 1399.03,931.869 \n",
       "  1400.06,932.485 1401.1,933.1 1402.13,933.713 1403.17,934.324 1404.2,934.933 1405.24,935.541 1406.27,936.147 1407.31,936.751 1408.34,937.353 1409.38,937.954 \n",
       "  1410.41,938.553 1411.45,939.151 1412.48,939.747 1413.52,940.341 1414.55,940.933 1415.59,941.524 1416.62,942.113 1417.66,942.7 1418.69,943.286 1419.73,943.87 \n",
       "  1420.76,944.452 1421.8,945.033 1422.83,945.612 1423.87,946.189 1424.9,946.765 1425.94,947.339 1426.97,947.912 1428.01,948.483 1429.04,949.052 1430.08,949.619 \n",
       "  1431.11,950.185 1432.15,950.75 1433.18,951.312 1434.22,951.874 1435.25,952.433 1436.29,952.991 1437.32,953.547 1438.36,954.102 1439.39,954.655 1440.43,955.207 \n",
       "  1441.46,955.757 1442.5,956.305 1443.53,956.852 1444.57,957.397 1445.6,957.941 1446.64,958.483 1447.67,959.023 1448.71,959.562 1449.74,960.1 1450.78,960.636 \n",
       "  1451.81,961.17 1452.85,961.703 1453.88,962.234 1454.92,962.764 1455.95,963.292 1456.99,963.818 1458.02,964.344 1459.06,964.867 1460.09,965.389 1461.13,965.91 \n",
       "  1462.16,966.429 1463.2,966.946 1464.23,967.462 1465.27,967.977 1466.3,968.49 1467.34,969.001 1468.37,969.511 1469.41,970.02 1470.44,970.527 1471.48,971.033 \n",
       "  1472.51,971.537 1473.55,972.04 1474.58,972.541 1475.62,973.04 1476.65,973.539 1477.69,974.035 1478.72,974.531 1479.76,975.025 1480.79,975.517 1481.83,976.008 \n",
       "  1482.86,976.498 1483.9,976.986 1484.93,977.473 1485.97,977.958 1487,978.442 1488.04,978.924 1489.08,979.405 1490.11,979.885 1491.15,980.363 1492.18,980.84 \n",
       "  1493.22,981.315 1494.25,981.789 1495.29,982.261 1496.32,982.733 1497.36,983.202 1498.39,983.671 1499.43,984.138 1500.46,984.603 1501.5,985.068 1502.53,985.53 \n",
       "  1503.57,985.992 1504.6,986.452 1505.64,986.911 1506.67,987.368 1507.71,987.824 1508.74,988.279 1509.78,988.732 1510.81,989.184 1511.85,989.635 1512.88,990.084 \n",
       "  1513.92,990.532 1514.95,990.979 1515.99,991.424 1517.02,991.868 1518.06,992.311 1519.09,992.752 1520.13,993.192 1521.16,993.631 1522.2,994.068 1523.23,994.504 \n",
       "  1524.27,994.939 1525.3,995.373 1526.34,995.805 1527.37,996.236 1528.41,996.665 1529.44,997.094 1530.48,997.521 1531.51,997.946 1532.55,998.371 1533.58,998.794 \n",
       "  1534.62,999.216 1535.65,999.637 1536.69,1000.06 1537.72,1000.47 1538.76,1000.89 1539.79,1001.31 1540.83,1001.72 1541.86,1002.13 1542.9,1002.55 1543.93,1002.96 \n",
       "  1544.97,1003.37 1546,1003.77 1547.04,1004.18 1548.07,1004.59 1549.11,1004.99 1550.14,1005.39 1551.18,1005.8 1552.21,1006.2 1553.25,1006.6 1554.28,1007 \n",
       "  1555.32,1007.39 1556.35,1007.79 1557.39,1008.18 1558.42,1008.58 1559.46,1008.97 1560.49,1009.36 1561.53,1009.75 1562.56,1010.14 1563.6,1010.53 1564.63,1010.91 \n",
       "  1565.67,1011.3 1566.7,1011.68 1567.74,1012.07 1568.77,1012.45 1569.81,1012.83 1570.84,1013.21 1571.88,1013.59 1572.91,1013.96 1573.95,1014.34 1574.98,1014.71 \n",
       "  1576.02,1015.09 1577.05,1015.46 1578.09,1015.83 1579.12,1016.2 1580.16,1016.57 1581.2,1016.94 1582.23,1017.31 1583.27,1017.67 1584.3,1018.04 1585.34,1018.4 \n",
       "  1586.37,1018.76 1587.41,1019.13 1588.44,1019.49 1589.48,1019.84 1590.51,1020.2 1591.55,1020.56 1592.58,1020.92 1593.62,1021.27 1594.65,1021.62 1595.69,1021.98 \n",
       "  1596.72,1022.33 1597.76,1022.68 1598.79,1023.03 1599.83,1023.38 1600.86,1023.72 1601.9,1024.07 1602.93,1024.41 1603.97,1024.76 1605,1025.1 1606.04,1025.44 \n",
       "  1607.07,1025.78 1608.11,1026.12 1609.14,1026.46 1610.18,1026.8 1611.21,1027.14 1612.25,1027.47 1613.28,1027.81 1614.32,1028.14 1615.35,1028.47 1616.39,1028.81 \n",
       "  1617.42,1029.14 1618.46,1029.47 1619.49,1029.79 1620.53,1030.12 1621.56,1030.45 1622.6,1030.77 1623.63,1031.1 1624.67,1031.42 1625.7,1031.74 1626.74,1032.06 \n",
       "  1627.77,1032.38 1628.81,1032.7 1629.84,1033.02 1630.88,1033.34 1631.91,1033.66 1632.95,1033.97 1633.98,1034.29 1635.02,1034.6 1636.05,1034.91 1637.09,1035.22 \n",
       "  1638.12,1035.53 1639.16,1035.84 1640.19,1036.15 1641.23,1036.46 1642.26,1036.77 1643.3,1037.07 1644.33,1037.38 1645.37,1037.68 1646.4,1037.99 1647.44,1038.29 \n",
       "  1648.47,1038.59 1649.51,1038.89 1650.54,1039.19 1651.58,1039.49 1652.61,1039.78 1653.65,1040.08 1654.68,1040.38 1655.72,1040.67 1656.75,1040.96 1657.79,1041.26 \n",
       "  1658.82,1041.55 1659.86,1041.84 1660.89,1042.13 1661.93,1042.42 1662.96,1042.71 1664,1042.99 1665.03,1043.28 1666.07,1043.57 1667.1,1043.85 1668.14,1044.13 \n",
       "  1669.17,1044.42 1670.21,1044.7 1671.24,1044.98 1672.28,1045.26 1673.31,1045.54 1674.35,1045.82 1675.39,1046.1 1676.42,1046.37 1677.46,1046.65 1678.49,1046.92 \n",
       "  1679.53,1047.2 1680.56,1047.47 1681.6,1047.74 1682.63,1048.02 1683.67,1048.29 1684.7,1048.56 1685.74,1048.83 1686.77,1049.09 1687.81,1049.36 1688.84,1049.63 \n",
       "  1689.88,1049.89 1690.91,1050.16 1691.95,1050.42 1692.98,1050.69 1694.02,1050.95 1695.05,1051.21 1696.09,1051.47 1697.12,1051.73 1698.16,1051.99 1699.19,1052.25 \n",
       "  1700.23,1052.51 1701.26,1052.76 1702.3,1053.02 1703.33,1053.28 1704.37,1053.53 1705.4,1053.78 1706.44,1054.04 1707.47,1054.29 1708.51,1054.54 1709.54,1054.79 \n",
       "  1710.58,1055.04 1711.61,1055.29 1712.65,1055.54 1713.68,1055.79 1714.72,1056.03 1715.75,1056.28 1716.79,1056.52 1717.82,1056.77 1718.86,1057.01 1719.89,1057.25 \n",
       "  1720.93,1057.5 1721.96,1057.74 1723,1057.98 1724.03,1058.22 1725.07,1058.46 1726.1,1058.7 1727.14,1058.93 1728.17,1059.17 1729.21,1059.41 1730.24,1059.64 \n",
       "  1731.28,1059.88 1732.31,1060.11 1733.35,1060.34 1734.38,1060.58 1735.42,1060.81 1736.45,1061.04 1737.49,1061.27 1738.52,1061.5 1739.56,1061.73 1740.59,1061.96 \n",
       "  1741.63,1062.18 1742.66,1062.41 1743.7,1062.64 1744.73,1062.86 1745.77,1063.09 1746.8,1063.31 1747.84,1063.53 1748.87,1063.76 1749.91,1063.98 1750.94,1064.2 \n",
       "  1751.98,1064.42 1753.01,1064.64 1754.05,1064.86 1755.08,1065.08 1756.12,1065.29 1757.15,1065.51 1758.19,1065.73 1759.22,1065.94 1760.26,1066.16 1761.29,1066.37 \n",
       "  1762.33,1066.59 1763.36,1066.8 1764.4,1067.01 1765.43,1067.22 1766.47,1067.44 1767.51,1067.65 1768.54,1067.86 1769.58,1068.06 1770.61,1068.27 1771.65,1068.48 \n",
       "  1772.68,1068.69 1773.72,1068.89 1774.75,1069.1 1775.79,1069.31 1776.82,1069.51 1777.86,1069.71 1778.89,1069.92 1779.93,1070.12 1780.96,1070.32 1782,1070.52 \n",
       "  1783.03,1070.72 1784.07,1070.92 1785.1,1071.12 1786.14,1071.32 1787.17,1071.52 1788.21,1071.72 1789.24,1071.92 1790.28,1072.11 1791.31,1072.31 1792.35,1072.5 \n",
       "  1793.38,1072.7 1794.42,1072.89 1795.45,1073.09 1796.49,1073.28 1797.52,1073.47 1798.56,1073.66 1799.59,1073.85 1800.63,1074.04 1801.66,1074.23 1802.7,1074.42 \n",
       "  1803.73,1074.61 1804.77,1074.8 1805.8,1074.99 1806.84,1075.17 1807.87,1075.36 1808.91,1075.55 1809.94,1075.73 1810.98,1075.92 1812.01,1076.1 1813.05,1076.28 \n",
       "  1814.08,1076.47 1815.12,1076.65 1816.15,1076.83 1817.19,1077.01 1818.22,1077.19 1819.26,1077.37 1820.29,1077.55 1821.33,1077.73 1822.36,1077.91 1823.4,1078.09 \n",
       "  1824.43,1078.26 1825.47,1078.44 1826.5,1078.62 1827.54,1078.79 1828.57,1078.97 1829.61,1079.14 1830.64,1079.31 1831.68,1079.49 1832.71,1079.66 1833.75,1079.83 \n",
       "  1834.78,1080.01 1835.82,1080.18 1836.85,1080.35 1837.89,1080.52 1838.92,1080.69 1839.96,1080.86 1840.99,1081.03 1842.03,1081.19 1843.06,1081.36 1844.1,1081.53 \n",
       "  1845.13,1081.69 1846.17,1081.86 1847.2,1082.03 1848.24,1082.19 1849.27,1082.36 1850.31,1082.52 1851.34,1082.68 1852.38,1082.85 1853.41,1083.01 1854.45,1083.17 \n",
       "  1855.48,1083.33 1856.52,1083.49 1857.55,1083.65 1858.59,1083.81 1859.63,1083.97 1860.66,1084.13 1861.7,1084.29 1862.73,1084.45 1863.77,1084.6 1864.8,1084.76 \n",
       "  1865.84,1084.92 1866.87,1085.07 1867.91,1085.23 1868.94,1085.38 1869.98,1085.54 1871.01,1085.69 1872.05,1085.85 1873.08,1086 1874.12,1086.15 1875.15,1086.31 \n",
       "  1876.19,1086.46 1877.22,1086.61 1878.26,1086.76 1879.29,1086.91 1880.33,1087.06 1881.36,1087.21 1882.4,1087.36 1883.43,1087.51 1884.47,1087.65 1885.5,1087.8 \n",
       "  1886.54,1087.95 1887.57,1088.09 1888.61,1088.24 1889.64,1088.39 1890.68,1088.53 1891.71,1088.68 1892.75,1088.82 1893.78,1088.96 1894.82,1089.11 1895.85,1089.25 \n",
       "  1896.89,1089.39 1897.92,1089.54 1898.96,1089.68 1899.99,1089.82 1901.03,1089.96 1902.06,1090.1 1903.1,1090.24 1904.13,1090.38 1905.17,1090.52 1906.2,1090.66 \n",
       "  1907.24,1090.8 1908.27,1090.93 1909.31,1091.07 1910.34,1091.21 1911.38,1091.34 1912.41,1091.48 1913.45,1091.62 1914.48,1091.75 1915.52,1091.89 1916.55,1092.02 \n",
       "  1917.59,1092.15 1918.62,1092.29 1919.66,1092.42 1920.69,1092.55 1921.73,1092.69 1922.76,1092.82 1923.8,1092.95 1924.83,1093.08 1925.87,1093.21 1926.9,1093.34 \n",
       "  1927.94,1093.47 1928.97,1093.6 1930.01,1093.73 1931.04,1093.86 1932.08,1093.99 1933.11,1094.12 1934.15,1094.24 1935.18,1094.37 1936.22,1094.5 1937.25,1094.62 \n",
       "  1938.29,1094.75 1939.32,1094.87 1940.36,1095 1941.39,1095.13 1942.43,1095.25 1943.46,1095.37 1944.5,1095.5 1945.53,1095.62 1946.57,1095.74 1947.6,1095.87 \n",
       "  1948.64,1095.99 1949.67,1096.11 1950.71,1096.23 1951.74,1096.35 1952.78,1096.47 1953.82,1096.59 1954.85,1096.71 1955.89,1096.83 1956.92,1096.95 1957.96,1097.07 \n",
       "  1958.99,1097.19 1960.03,1097.31 1961.06,1097.43 1962.1,1097.54 1963.13,1097.66 1964.17,1097.78 1965.2,1097.89 1966.24,1098.01 1967.27,1098.13 1968.31,1098.24 \n",
       "  1969.34,1098.36 1970.38,1098.47 1971.41,1098.58 1972.45,1098.7 1973.48,1098.81 1974.52,1098.92 1975.55,1099.04 1976.59,1099.15 1977.62,1099.26 1978.66,1099.37 \n",
       "  1979.69,1099.48 1980.73,1099.6 1981.76,1099.71 1982.8,1099.82 1983.83,1099.93 1984.87,1100.04 1985.9,1100.15 1986.94,1100.25 1987.97,1100.36 1989.01,1100.47 \n",
       "  1990.04,1100.58 1991.08,1100.69 1992.11,1100.79 1993.15,1100.9 1994.18,1101.01 1995.22,1101.11 1996.25,1101.22 1997.29,1101.33 1998.32,1101.43 1999.36,1101.54 \n",
       "  2000.39,1101.64 2001.43,1101.75 2002.46,1101.85 2003.5,1101.95 2004.53,1102.06 2005.57,1102.16 2006.6,1102.26 2007.64,1102.36 2008.67,1102.47 2009.71,1102.57 \n",
       "  2010.74,1102.67 2011.78,1102.77 2012.81,1102.87 2013.85,1102.97 2014.88,1103.07 2015.92,1103.17 2016.95,1103.27 2017.99,1103.37 2019.02,1103.47 2020.06,1103.57 \n",
       "  2021.09,1103.67 2022.13,1103.77 2023.16,1103.86 2024.2,1103.96 2025.23,1104.06 2026.27,1104.15 2027.3,1104.25 2028.34,1104.35 2029.37,1104.44 2030.41,1104.54 \n",
       "  2031.44,1104.63 2032.48,1104.73 2033.51,1104.82 2034.55,1104.92 2035.58,1105.01 2036.62,1105.11 2037.65,1105.2 2038.69,1105.29 2039.72,1105.39 2040.76,1105.48 \n",
       "  2041.79,1105.57 2042.83,1105.66 2043.86,1105.75 2044.9,1105.85 2045.94,1105.94 2046.97,1106.03 2048.01,1106.12 2049.04,1106.21 2050.08,1106.3 2051.11,1106.39 \n",
       "  2052.15,1106.48 2053.18,1106.57 2054.22,1106.66 2055.25,1106.75 2056.29,1106.83 2057.32,1106.92 2058.36,1107.01 2059.39,1107.1 2060.43,1107.19 2061.46,1107.27 \n",
       "  2062.5,1107.36 2063.53,1107.45 2064.57,1107.53 2065.6,1107.62 2066.64,1107.7 2067.67,1107.79 2068.71,1107.87 2069.74,1107.96 2070.78,1108.04 2071.81,1108.13 \n",
       "  2072.85,1108.21 2073.88,1108.3 2074.92,1108.38 2075.95,1108.46 2076.99,1108.55 2078.02,1108.63 2079.06,1108.71 2080.09,1108.79 2081.13,1108.88 2082.16,1108.96 \n",
       "  2083.2,1109.04 2084.23,1109.12 2085.27,1109.2 2086.3,1109.28 2087.34,1109.36 2088.37,1109.44 2089.41,1109.52 2090.44,1109.6 2091.48,1109.68 2092.51,1109.76 \n",
       "  2093.55,1109.84 2094.58,1109.92 2095.62,1110 2096.65,1110.08 2097.69,1110.15 2098.72,1110.23 2099.76,1110.31 2100.79,1110.39 2101.83,1110.46 2102.86,1110.54 \n",
       "  2103.9,1110.62 2104.93,1110.69 2105.97,1110.77 2107,1110.85 2108.04,1110.92 2109.07,1111 2110.11,1111.07 2111.14,1111.15 2112.18,1111.22 2113.21,1111.3 \n",
       "  2114.25,1111.37 2115.28,1111.44 2116.32,1111.52 2117.35,1111.59 2118.39,1111.66 2119.42,1111.74 2120.46,1111.81 2121.49,1111.88 2122.53,1111.96 2123.56,1112.03 \n",
       "  2124.6,1112.1 2125.63,1112.17 2126.67,1112.24 2127.7,1112.31 2128.74,1112.39 2129.77,1112.46 2130.81,1112.53 2131.84,1112.6 2132.88,1112.67 2133.91,1112.74 \n",
       "  2134.95,1112.81 2135.98,1112.88 2137.02,1112.95 2138.05,1113.02 2139.09,1113.08 2140.13,1113.15 2141.16,1113.22 2142.2,1113.29 2143.23,1113.36 2144.27,1113.43 \n",
       "  2145.3,1113.49 2146.34,1113.56 2147.37,1113.63 2148.41,1113.69 2149.44,1113.76 2150.48,1113.83 2151.51,1113.89 2152.55,1113.96 2153.58,1114.03 2154.62,1114.09 \n",
       "  2155.65,1114.16 2156.69,1114.22 2157.72,1114.29 2158.76,1114.35 2159.79,1114.42 2160.83,1114.48 2161.86,1114.55 2162.9,1114.61 2163.93,1114.68 2164.97,1114.74 \n",
       "  2166,1114.8 2167.04,1114.87 2168.07,1114.93 2169.11,1114.99 2170.14,1115.06 2171.18,1115.12 2172.21,1115.18 2173.25,1115.24 2174.28,1115.3 2175.32,1115.37 \n",
       "  2176.35,1115.43 2177.39,1115.49 2178.42,1115.55 2179.46,1115.61 2180.49,1115.67 2181.53,1115.73 2182.56,1115.79 2183.6,1115.85 2184.63,1115.92 2185.67,1115.98 \n",
       "  2186.7,1116.03 2187.74,1116.09 2188.77,1116.15 2189.81,1116.21 2190.84,1116.27 2191.88,1116.33 2192.91,1116.39 2193.95,1116.45 2194.98,1116.51 2196.02,1116.57 \n",
       "  2197.05,1116.62 2198.09,1116.68 2199.12,1116.74 2200.16,1116.8 2201.19,1116.85 2202.23,1116.91 2203.26,1116.97 2204.3,1117.02 2205.33,1117.08 2206.37,1117.14 \n",
       "  2207.4,1117.19 2208.44,1117.25 2209.47,1117.31 2210.51,1117.36 2211.54,1117.42 2212.58,1117.47 2213.61,1117.53 2214.65,1117.58 2215.68,1117.64 2216.72,1117.69 \n",
       "  2217.75,1117.75 2218.79,1117.8 2219.82,1117.86 2220.86,1117.91 2221.89,1117.96 2222.93,1118.02 2223.96,1118.07 2225,1118.12 2226.03,1118.18 2227.07,1118.23 \n",
       "  2228.1,1118.28 2229.14,1118.34 2230.17,1118.39 2231.21,1118.44 2232.25,1118.49 2233.28,1118.55 2234.32,1118.6 2235.35,1118.65 2236.39,1118.7 2237.42,1118.75 \n",
       "  2238.46,1118.81 2239.49,1118.86 2240.53,1118.91 2241.56,1118.96 2242.6,1119.01 2243.63,1119.06 2244.67,1119.11 2245.7,1119.16 2246.74,1119.21 2247.77,1119.26 \n",
       "  2248.81,1119.31 2249.84,1119.36 2250.88,1119.41 2251.91,1119.46 2252.95,1119.51 2253.98,1119.56 2255.02,1119.61 2256.05,1119.66 2257.09,1119.71 2258.12,1119.75 \n",
       "  2259.16,1119.8 2260.19,1119.85 2261.23,1119.9 2262.26,1119.95 2263.3,1119.99 2264.33,1120.04 2265.37,1120.09 2266.4,1120.14 2267.44,1120.18 2268.47,1120.23 \n",
       "  2269.51,1120.28 2270.54,1120.33 2271.58,1120.37 2272.61,1120.42 2273.65,1120.47 2274.68,1120.51 2275.72,1120.56 2276.75,1120.6 2277.79,1120.65 2278.82,1120.7 \n",
       "  2279.86,1120.74 2280.89,1120.79 2281.93,1120.83 2282.96,1120.88 2284,1120.92 2285.03,1120.97 2286.07,1121.01 2287.1,1121.06 2288.14,1121.1 2289.17,1121.15 \n",
       "  2290.21,1121.19 2291.24,1121.23 2292.28,1121.28 2293.31,1121.32 2294.35,1121.37 2295.38,1121.41 2296.42,1121.45 2297.45,1121.5 2298.49,1121.54 2299.52,1121.58 \n",
       "  2300.56,1121.63 2301.59,1121.67 2302.63,1121.71 2303.66,1121.75 2304.7,1121.8 2305.73,1121.84 2306.77,1121.88 2307.8,1121.92 2308.84,1121.96 2309.87,1122.01 \n",
       "  2310.91,1122.05 2311.94,1122.09 2312.98,1122.13 2314.01,1122.17 2315.05,1122.21 2316.08,1122.25 2317.12,1122.29 2318.15,1122.34 2319.19,1122.38 2320.22,1122.42 \n",
       "  2321.26,1122.46 \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip6703)\" style=\"stroke:#e26f46; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
       "  251.149,1387.77 252.184,1387.71 253.219,1387.64 254.254,1387.58 255.289,1387.51 256.324,1387.45 257.359,1387.38 258.394,1387.31 259.429,1387.24 260.464,1387.18 \n",
       "  261.499,1387.11 262.534,1387.04 263.569,1386.97 264.604,1386.9 265.639,1386.83 266.674,1386.76 267.709,1386.69 268.744,1386.62 269.78,1386.55 270.815,1386.48 \n",
       "  271.85,1386.41 272.885,1386.34 273.92,1386.27 274.955,1386.19 275.99,1386.12 277.025,1386.05 278.06,1385.98 279.095,1385.9 280.13,1385.83 281.165,1385.75 \n",
       "  282.2,1385.68 283.235,1385.6 284.27,1385.53 285.305,1385.45 286.34,1385.38 287.375,1385.3 288.411,1385.22 289.446,1385.15 290.481,1385.07 291.516,1384.99 \n",
       "  292.551,1384.91 293.586,1384.84 294.621,1384.76 295.656,1384.68 296.691,1384.6 297.726,1384.52 298.761,1384.44 299.796,1384.36 300.831,1384.28 301.866,1384.19 \n",
       "  302.901,1384.11 303.936,1384.03 304.971,1383.95 306.006,1383.86 307.042,1383.78 308.077,1383.7 309.112,1383.61 310.147,1383.53 311.182,1383.44 312.217,1383.36 \n",
       "  313.252,1383.27 314.287,1383.19 315.322,1383.1 316.357,1383.01 317.392,1382.93 318.427,1382.84 319.462,1382.75 320.497,1382.66 321.532,1382.57 322.567,1382.48 \n",
       "  323.602,1382.39 324.637,1382.3 325.673,1382.21 326.708,1382.12 327.743,1382.03 328.778,1381.94 329.813,1381.85 330.848,1381.75 331.883,1381.66 332.918,1381.57 \n",
       "  333.953,1381.47 334.988,1381.38 336.023,1381.28 337.058,1381.19 338.093,1381.09 339.128,1381 340.163,1380.9 341.198,1380.8 342.233,1380.71 343.268,1380.61 \n",
       "  344.304,1380.51 345.339,1380.41 346.374,1380.31 347.409,1380.21 348.444,1380.11 349.479,1380.01 350.514,1379.91 351.549,1379.81 352.584,1379.71 353.619,1379.61 \n",
       "  354.654,1379.51 355.689,1379.4 356.724,1379.3 357.759,1379.2 358.794,1379.09 359.829,1378.99 360.864,1378.88 361.899,1378.77 362.935,1378.67 363.97,1378.56 \n",
       "  365.005,1378.45 366.04,1378.35 367.075,1378.24 368.11,1378.13 369.145,1378.02 370.18,1377.91 371.215,1377.8 372.25,1377.69 373.285,1377.58 374.32,1377.47 \n",
       "  375.355,1377.36 376.39,1377.24 377.425,1377.13 378.46,1377.02 379.495,1376.9 380.53,1376.79 381.566,1376.67 382.601,1376.56 383.636,1376.44 384.671,1376.32 \n",
       "  385.706,1376.21 386.741,1376.09 387.776,1375.97 388.811,1375.85 389.846,1375.73 390.881,1375.61 391.916,1375.49 392.951,1375.37 393.986,1375.25 395.021,1375.13 \n",
       "  396.056,1375.01 397.091,1374.89 398.126,1374.76 399.161,1374.64 400.197,1374.51 401.232,1374.39 402.267,1374.26 403.302,1374.14 404.337,1374.01 405.372,1373.88 \n",
       "  406.407,1373.76 407.442,1373.63 408.477,1373.5 409.512,1373.37 410.547,1373.24 411.582,1373.11 412.617,1372.98 413.652,1372.85 414.687,1372.72 415.722,1372.58 \n",
       "  416.757,1372.45 417.792,1372.32 418.828,1372.18 419.863,1372.05 420.898,1371.91 421.933,1371.78 422.968,1371.64 424.003,1371.5 425.038,1371.37 426.073,1371.23 \n",
       "  427.108,1371.09 428.143,1370.95 429.178,1370.81 430.213,1370.67 431.248,1370.53 432.283,1370.39 433.318,1370.24 434.353,1370.1 435.388,1369.96 436.423,1369.81 \n",
       "  437.459,1369.67 438.494,1369.52 439.529,1369.38 440.564,1369.23 441.599,1369.08 442.634,1368.94 443.669,1368.79 444.704,1368.64 445.739,1368.49 446.774,1368.34 \n",
       "  447.809,1368.19 448.844,1368.04 449.879,1367.88 450.914,1367.73 451.949,1367.58 452.984,1367.42 454.019,1367.27 455.054,1367.12 456.09,1366.96 457.125,1366.8 \n",
       "  458.16,1366.65 459.195,1366.49 460.23,1366.33 461.265,1366.17 462.3,1366.01 463.335,1365.85 464.37,1365.69 465.405,1365.53 466.44,1365.37 467.475,1365.2 \n",
       "  468.51,1365.04 469.545,1364.88 470.58,1364.71 471.615,1364.55 472.65,1364.38 473.685,1364.21 474.721,1364.05 475.756,1363.88 476.791,1363.71 477.826,1363.54 \n",
       "  478.861,1363.37 479.896,1363.2 480.931,1363.03 481.966,1362.86 483.001,1362.68 484.036,1362.51 485.071,1362.34 486.106,1362.16 487.141,1361.99 488.176,1361.81 \n",
       "  489.211,1361.63 490.246,1361.46 491.281,1361.28 492.316,1361.1 493.352,1360.92 494.387,1360.74 495.422,1360.56 496.457,1360.38 497.492,1360.19 498.527,1360.01 \n",
       "  499.562,1359.83 500.597,1359.64 501.632,1359.46 502.667,1359.27 503.702,1359.09 504.737,1358.9 505.772,1358.71 506.807,1358.52 507.842,1358.33 508.877,1358.14 \n",
       "  509.912,1357.95 510.947,1357.76 511.983,1357.57 513.018,1357.37 514.053,1357.18 515.088,1356.99 516.123,1356.79 517.158,1356.6 518.193,1356.4 519.228,1356.2 \n",
       "  520.263,1356 521.298,1355.81 522.333,1355.61 523.368,1355.41 524.403,1355.2 525.438,1355 526.473,1354.8 527.508,1354.6 528.543,1354.39 529.578,1354.19 \n",
       "  530.614,1353.98 531.649,1353.78 532.684,1353.57 533.719,1353.36 534.754,1353.15 535.789,1352.95 536.824,1352.74 537.859,1352.53 538.894,1352.31 539.929,1352.1 \n",
       "  540.964,1351.89 541.999,1351.68 543.034,1351.46 544.069,1351.25 545.104,1351.03 546.139,1350.81 547.174,1350.6 548.209,1350.38 549.245,1350.16 550.28,1349.94 \n",
       "  551.315,1349.72 552.35,1349.5 553.385,1349.28 554.42,1349.05 555.455,1348.83 556.49,1348.61 557.525,1348.38 558.56,1348.15 559.595,1347.93 560.63,1347.7 \n",
       "  561.665,1347.47 562.7,1347.24 563.735,1347.01 564.77,1346.78 565.805,1346.55 566.84,1346.32 567.876,1346.09 568.911,1345.85 569.946,1345.62 570.981,1345.38 \n",
       "  572.016,1345.15 573.051,1344.91 574.086,1344.67 575.121,1344.44 576.156,1344.2 577.191,1343.96 578.226,1343.72 579.261,1343.48 580.296,1343.23 581.331,1342.99 \n",
       "  582.366,1342.75 583.401,1342.5 584.436,1342.26 585.471,1342.01 586.507,1341.76 587.542,1341.52 588.577,1341.27 589.612,1341.02 590.647,1340.77 591.682,1340.52 \n",
       "  592.717,1340.27 593.752,1340.01 594.787,1339.76 595.822,1339.51 596.857,1339.25 597.892,1339 598.927,1338.74 599.962,1338.48 600.997,1338.22 602.032,1337.97 \n",
       "  603.067,1337.71 604.102,1337.45 605.138,1337.18 606.173,1336.92 607.208,1336.66 608.243,1336.4 609.278,1336.13 610.313,1335.87 611.348,1335.6 612.383,1335.33 \n",
       "  613.418,1335.07 614.453,1334.8 615.488,1334.53 616.523,1334.26 617.558,1333.99 618.593,1333.72 619.628,1333.45 620.663,1333.17 621.698,1332.9 622.733,1332.62 \n",
       "  623.769,1332.35 624.804,1332.07 625.839,1331.8 626.874,1331.52 627.909,1331.24 628.944,1330.96 629.979,1330.68 631.014,1330.4 632.049,1330.12 633.084,1329.84 \n",
       "  634.119,1329.55 635.154,1329.27 636.189,1328.98 637.224,1328.7 638.259,1328.41 639.294,1328.12 640.329,1327.84 641.364,1327.55 642.4,1327.26 643.435,1326.97 \n",
       "  644.47,1326.68 645.505,1326.39 646.54,1326.09 647.575,1325.8 648.61,1325.51 649.645,1325.21 650.68,1324.92 651.715,1324.62 652.75,1324.32 653.785,1324.03 \n",
       "  654.82,1323.73 655.855,1323.43 656.89,1323.13 657.925,1322.83 658.96,1322.52 659.995,1322.22 661.031,1321.92 662.066,1321.62 663.101,1321.31 664.136,1321.01 \n",
       "  665.171,1320.7 666.206,1320.39 667.241,1320.09 668.276,1319.78 669.311,1319.47 670.346,1319.16 671.381,1318.85 672.416,1318.54 673.451,1318.22 674.486,1317.91 \n",
       "  675.521,1317.6 676.556,1317.28 677.591,1316.97 678.626,1316.65 679.662,1316.34 680.697,1316.02 681.732,1315.7 682.767,1315.39 683.802,1315.07 684.837,1314.75 \n",
       "  685.872,1314.43 686.907,1314.1 687.942,1313.78 688.977,1313.46 690.012,1313.14 691.047,1312.81 692.082,1312.49 693.117,1312.16 694.152,1311.84 695.187,1311.51 \n",
       "  696.222,1311.18 697.257,1310.86 698.293,1310.53 699.328,1310.2 700.363,1309.87 701.398,1309.54 702.433,1309.21 703.468,1308.87 704.503,1308.54 705.538,1308.21 \n",
       "  706.573,1307.87 707.608,1307.54 708.643,1307.2 709.678,1306.87 710.713,1306.53 711.748,1306.19 712.783,1305.86 713.818,1305.52 714.853,1305.18 715.888,1304.84 \n",
       "  716.924,1304.5 717.959,1304.16 718.994,1303.82 720.029,1303.48 721.064,1303.13 722.099,1302.79 723.134,1302.45 724.169,1302.1 725.204,1301.76 726.239,1301.41 \n",
       "  727.274,1301.07 728.309,1300.72 729.344,1300.37 730.379,1300.03 731.414,1299.68 732.449,1299.33 733.484,1298.98 734.52,1298.63 735.555,1298.28 736.59,1297.93 \n",
       "  737.625,1297.58 738.66,1297.23 739.695,1296.87 740.73,1296.52 741.765,1296.17 742.8,1295.81 743.835,1295.46 744.87,1295.1 745.905,1294.75 746.94,1294.39 \n",
       "  747.975,1294.04 749.01,1293.68 750.045,1293.32 751.08,1292.97 752.115,1292.61 753.151,1292.25 754.186,1291.89 755.221,1291.53 756.256,1291.17 757.291,1290.81 \n",
       "  758.326,1290.45 759.361,1290.09 760.396,1289.73 761.431,1289.36 762.466,1289 763.501,1288.64 764.536,1288.28 765.571,1287.91 766.606,1287.55 767.641,1287.18 \n",
       "  768.676,1286.82 769.711,1286.46 770.746,1286.09 771.782,1285.72 772.817,1285.36 773.852,1284.99 774.887,1284.63 775.922,1284.26 776.957,1283.89 777.992,1283.52 \n",
       "  779.027,1283.16 780.062,1282.79 781.097,1282.42 782.132,1282.05 783.167,1281.68 784.202,1281.31 785.237,1280.94 786.272,1280.57 787.307,1280.2 788.342,1279.83 \n",
       "  789.377,1279.46 790.413,1279.09 791.448,1278.72 792.483,1278.35 793.518,1277.97 794.553,1277.6 795.588,1277.23 796.623,1276.86 797.658,1276.49 798.693,1276.11 \n",
       "  799.728,1275.74 800.763,1275.37 801.798,1275 802.833,1274.62 803.868,1274.25 804.903,1273.88 805.938,1273.5 806.973,1273.13 808.008,1272.75 809.044,1272.38 \n",
       "  810.079,1272.01 811.114,1271.63 812.149,1271.26 813.184,1270.88 814.219,1270.51 815.254,1270.13 816.289,1269.76 817.324,1269.38 818.359,1269.01 819.394,1268.64 \n",
       "  820.429,1268.26 821.464,1267.89 822.499,1267.51 823.534,1267.14 824.569,1266.76 825.604,1266.39 826.639,1266.01 827.675,1265.64 828.71,1265.26 829.745,1264.89 \n",
       "  830.78,1264.51 831.815,1264.14 832.85,1263.76 833.885,1263.39 834.92,1263.01 835.955,1262.64 836.99,1262.27 838.025,1261.89 839.06,1261.52 840.095,1261.14 \n",
       "  841.13,1260.77 842.165,1260.4 843.2,1260.02 844.235,1259.65 845.27,1259.28 846.306,1258.9 847.341,1258.53 848.376,1258.16 849.411,1257.79 850.446,1257.41 \n",
       "  851.481,1257.04 852.516,1256.67 853.551,1256.3 854.586,1255.93 855.621,1255.56 856.656,1255.19 857.691,1254.82 858.726,1254.45 859.761,1254.08 860.796,1253.71 \n",
       "  861.831,1253.34 862.866,1252.97 863.901,1252.6 864.937,1252.23 865.972,1251.86 867.007,1251.5 868.042,1251.13 869.077,1250.76 870.112,1250.4 871.147,1250.03 \n",
       "  872.182,1249.67 873.217,1249.3 874.252,1248.94 875.287,1248.57 876.322,1248.21 877.357,1247.84 878.392,1247.48 879.427,1247.12 880.462,1246.76 881.497,1246.4 \n",
       "  882.532,1246.03 883.568,1245.67 884.603,1245.31 885.638,1244.95 886.673,1244.59 887.708,1244.24 888.743,1243.88 889.778,1243.52 890.813,1243.16 891.848,1242.81 \n",
       "  892.883,1242.45 893.918,1242.1 894.953,1241.74 895.988,1241.39 897.023,1241.03 898.058,1240.68 899.093,1240.33 900.128,1239.98 901.163,1239.63 902.199,1239.28 \n",
       "  903.234,1238.93 904.269,1238.58 905.304,1238.23 906.339,1237.88 907.374,1237.53 908.409,1237.19 909.444,1236.84 910.479,1236.5 911.514,1236.15 912.549,1235.81 \n",
       "  913.584,1235.47 914.619,1235.13 915.654,1234.79 916.689,1234.44 917.724,1234.11 918.759,1233.77 919.794,1233.43 920.83,1233.09 921.865,1232.75 922.9,1232.42 \n",
       "  923.935,1232.08 924.97,1231.75 926.005,1231.42 927.04,1231.09 928.075,1230.75 929.11,1230.42 930.145,1230.09 931.18,1229.77 932.215,1229.44 933.25,1229.11 \n",
       "  934.285,1228.78 935.32,1228.46 936.355,1228.13 937.39,1227.81 938.425,1227.49 939.461,1227.17 940.496,1226.85 941.531,1226.53 942.566,1226.21 943.601,1225.89 \n",
       "  944.636,1225.58 945.671,1225.26 946.706,1224.95 947.741,1224.63 948.776,1224.32 949.811,1224.01 950.846,1223.7 951.881,1223.39 952.916,1223.08 953.951,1222.77 \n",
       "  954.986,1222.47 956.021,1222.16 957.056,1221.86 958.092,1221.55 959.127,1221.25 960.162,1220.95 961.197,1220.65 962.232,1220.35 963.267,1220.06 964.302,1219.76 \n",
       "  965.337,1219.47 966.372,1219.17 967.407,1218.88 968.442,1218.59 969.477,1218.3 970.512,1218.01 971.547,1217.72 972.582,1217.43 973.617,1217.15 974.652,1216.86 \n",
       "  975.687,1216.58 976.723,1216.3 977.758,1216.02 978.793,1215.74 979.828,1215.46 980.863,1215.19 981.898,1214.91 982.933,1214.64 983.968,1214.36 985.003,1214.09 \n",
       "  986.038,1213.82 987.073,1213.55 988.108,1213.29 989.143,1213.02 990.178,1212.76 991.213,1212.49 992.248,1212.23 993.283,1211.97 994.318,1211.71 995.354,1211.45 \n",
       "  996.389,1211.19 997.424,1210.94 998.459,1210.69 999.494,1210.43 1000.53,1210.18 1001.56,1209.93 1002.6,1209.68 1003.63,1209.44 1004.67,1209.19 1005.7,1208.95 \n",
       "  1006.74,1208.7 1007.77,1208.46 1008.81,1208.22 1009.84,1207.99 1010.88,1207.75 1011.91,1207.51 1012.95,1207.28 1013.98,1207.05 1015.02,1206.82 1016.05,1206.59 \n",
       "  1017.09,1206.36 1018.12,1206.13 1019.16,1205.91 1020.19,1205.68 1021.23,1205.46 1022.26,1205.24 1023.3,1205.02 1024.34,1204.8 1025.37,1204.59 1026.41,1204.37 \n",
       "  1027.44,1204.16 1028.48,1203.95 1029.51,1203.74 1030.55,1203.53 1031.58,1203.33 1032.62,1203.12 1033.65,1202.92 1034.69,1202.72 1035.72,1202.52 1036.76,1202.32 \n",
       "  1037.79,1202.12 1038.83,1201.92 1039.86,1201.73 1040.9,1201.54 1041.93,1201.35 1042.97,1201.16 1044,1200.97 1045.04,1200.78 1046.07,1200.6 1047.11,1200.42 \n",
       "  1048.14,1200.24 1049.18,1200.06 1050.21,1199.88 1051.25,1199.7 1052.28,1199.53 1053.32,1199.36 1054.35,1199.18 1055.39,1199.02 1056.42,1198.85 1057.46,1198.68 \n",
       "  1058.49,1198.52 1059.53,1198.35 1060.56,1198.19 1061.6,1198.03 1062.63,1197.87 1063.67,1197.72 1064.7,1197.56 1065.74,1197.41 1066.77,1197.26 1067.81,1197.11 \n",
       "  1068.84,1196.96 1069.88,1196.82 1070.91,1196.67 1071.95,1196.53 1072.98,1196.39 1074.02,1196.25 1075.05,1196.11 1076.09,1195.97 1077.12,1195.84 1078.16,1195.71 \n",
       "  1079.19,1195.58 1080.23,1195.45 1081.26,1195.32 1082.3,1195.19 1083.33,1195.07 1084.37,1194.95 1085.4,1194.83 1086.44,1194.71 1087.47,1194.59 1088.51,1194.48 \n",
       "  1089.54,1194.36 1090.58,1194.25 1091.61,1194.14 1092.65,1194.03 1093.68,1193.92 1094.72,1193.82 1095.75,1193.72 1096.79,1193.61 1097.82,1193.51 1098.86,1193.42 \n",
       "  1099.89,1193.32 1100.93,1193.23 1101.96,1193.13 1103,1193.04 1104.03,1192.95 1105.07,1192.86 1106.1,1192.78 1107.14,1192.69 1108.17,1192.61 1109.21,1192.53 \n",
       "  1110.24,1192.45 1111.28,1192.37 1112.31,1192.3 1113.35,1192.22 1114.38,1192.15 1115.42,1192.08 1116.46,1192.01 1117.49,1191.95 1118.53,1191.88 1119.56,1191.82 \n",
       "  1120.6,1191.76 1121.63,1191.7 1122.67,1191.64 1123.7,1191.58 1124.74,1191.53 1125.77,1191.47 1126.81,1191.42 1127.84,1191.37 1128.88,1191.32 1129.91,1191.28 \n",
       "  1130.95,1191.23 1131.98,1191.19 1133.02,1191.15 1134.05,1191.11 1135.09,1191.07 1136.12,1191.04 1137.16,1191 1138.19,1190.97 1139.23,1190.94 1140.26,1190.91 \n",
       "  1141.3,1190.88 1142.33,1190.86 1143.37,1190.83 1144.4,1190.81 1145.44,1190.79 1146.47,1190.77 1147.51,1190.75 1148.54,1190.74 1149.58,1190.72 1150.61,1190.71 \n",
       "  1151.65,1190.7 1152.68,1190.69 1153.72,1190.69 1154.75,1190.68 1155.79,1190.68 1156.82,1190.68 1157.86,1190.67 1158.89,1190.68 1159.93,1190.68 1160.96,1190.68 \n",
       "  1162,1190.69 1163.03,1190.7 1164.07,1190.71 1165.1,1190.72 1166.14,1190.73 1167.17,1190.75 1168.21,1190.76 1169.24,1190.78 1170.28,1190.8 1171.31,1190.82 \n",
       "  1172.35,1190.84 1173.38,1190.87 1174.42,1190.89 1175.45,1190.92 1176.49,1190.95 1177.52,1190.98 1178.56,1191.01 1179.59,1191.05 1180.63,1191.08 1181.66,1191.12 \n",
       "  1182.7,1191.16 1183.73,1191.2 1184.77,1191.24 1185.8,1191.29 1186.84,1191.33 1187.87,1191.38 1188.91,1191.43 1189.94,1191.48 1190.98,1191.53 1192.01,1191.58 \n",
       "  1193.05,1191.63 1194.08,1191.69 1195.12,1191.75 1196.15,1191.81 1197.19,1191.87 1198.22,1191.93 1199.26,1191.99 1200.29,1192.06 1201.33,1192.13 1202.36,1192.2 \n",
       "  1203.4,1192.27 1204.43,1192.34 1205.47,1192.41 1206.5,1192.48 1207.54,1192.56 1208.57,1192.64 1209.61,1192.72 1210.65,1192.8 1211.68,1192.88 1212.72,1192.96 \n",
       "  1213.75,1193.05 1214.79,1193.13 1215.82,1193.22 1216.86,1193.31 1217.89,1193.4 1218.93,1193.49 1219.96,1193.59 1221,1193.68 1222.03,1193.78 1223.07,1193.88 \n",
       "  1224.1,1193.98 1225.14,1194.08 1226.17,1194.18 1227.21,1194.28 1228.24,1194.39 1229.28,1194.49 1230.31,1194.6 1231.35,1194.71 1232.38,1194.82 1233.42,1194.93 \n",
       "  1234.45,1195.04 1235.49,1195.16 1236.52,1195.27 1237.56,1195.39 1238.59,1195.51 1239.63,1195.63 1240.66,1195.75 1241.7,1195.87 1242.73,1196 1243.77,1196.12 \n",
       "  1244.8,1196.25 1245.84,1196.37 1246.87,1196.5 1247.91,1196.63 1248.94,1196.77 1249.98,1196.9 1251.01,1197.03 1252.05,1197.17 1253.08,1197.3 1254.12,1197.44 \n",
       "  1255.15,1197.58 1256.19,1197.72 1257.22,1197.86 1258.26,1198 1259.29,1198.15 1260.33,1198.29 1261.36,1198.44 1262.4,1198.59 1263.43,1198.74 1264.47,1198.89 \n",
       "  1265.5,1199.04 1266.54,1199.19 1267.57,1199.34 1268.61,1199.5 1269.64,1199.65 1270.68,1199.81 1271.71,1199.97 1272.75,1200.13 1273.78,1200.29 1274.82,1200.45 \n",
       "  1275.85,1200.61 1276.89,1200.78 1277.92,1200.94 1278.96,1201.11 1279.99,1201.28 1281.03,1201.44 1282.06,1201.61 1283.1,1201.78 1284.13,1201.96 1285.17,1202.13 \n",
       "  1286.2,1202.3 1287.24,1202.48 1288.27,1202.65 1289.31,1202.83 1290.34,1203.01 1291.38,1203.19 1292.41,1203.37 1293.45,1203.55 1294.48,1203.73 1295.52,1203.91 \n",
       "  1296.55,1204.1 1297.59,1204.28 1298.62,1204.47 1299.66,1204.66 1300.69,1204.85 1301.73,1205.03 1302.77,1205.22 1303.8,1205.42 1304.84,1205.61 1305.87,1205.8 \n",
       "  1306.91,1206 1307.94,1206.19 1308.98,1206.39 1310.01,1206.58 1311.05,1206.78 1312.08,1206.98 1313.12,1207.18 1314.15,1207.38 1315.19,1207.58 1316.22,1207.79 \n",
       "  1317.26,1207.99 1318.29,1208.19 1319.33,1208.4 1320.36,1208.6 1321.4,1208.81 1322.43,1209.02 1323.47,1209.23 1324.5,1209.44 1325.54,1209.65 1326.57,1209.86 \n",
       "  1327.61,1210.07 1328.64,1210.29 1329.68,1210.5 1330.71,1210.71 1331.75,1210.93 1332.78,1211.15 1333.82,1211.36 1334.85,1211.58 1335.89,1211.8 1336.92,1212.02 \n",
       "  1337.96,1212.24 1338.99,1212.46 1340.03,1212.68 1341.06,1212.9 1342.1,1213.13 1343.13,1213.35 1344.17,1213.58 1345.2,1213.8 1346.24,1214.03 1347.27,1214.26 \n",
       "  1348.31,1214.48 1349.34,1214.71 1350.38,1214.94 1351.41,1215.17 1352.45,1215.4 1353.48,1215.63 1354.52,1215.87 1355.55,1216.1 1356.59,1216.33 1357.62,1216.57 \n",
       "  1358.66,1216.8 1359.69,1217.04 1360.73,1217.27 1361.76,1217.51 1362.8,1217.75 1363.83,1217.98 1364.87,1218.22 1365.9,1218.46 1366.94,1218.7 1367.97,1218.94 \n",
       "  1369.01,1219.18 1370.04,1219.42 1371.08,1219.67 1372.11,1219.91 1373.15,1220.15 1374.18,1220.4 1375.22,1220.64 1376.25,1220.89 1377.29,1221.13 1378.32,1221.38 \n",
       "  1379.36,1221.63 1380.39,1221.87 1381.43,1222.12 1382.46,1222.37 1383.5,1222.62 1384.53,1222.87 1385.57,1223.12 1386.6,1223.37 1387.64,1223.62 1388.67,1223.87 \n",
       "  1389.71,1224.12 1390.74,1224.37 1391.78,1224.63 1392.81,1224.88 1393.85,1225.13 1394.89,1225.39 1395.92,1225.64 1396.96,1225.9 1397.99,1226.15 1399.03,1226.41 \n",
       "  1400.06,1226.66 1401.1,1226.92 1402.13,1227.18 1403.17,1227.43 1404.2,1227.69 1405.24,1227.95 1406.27,1228.21 1407.31,1228.47 1408.34,1228.73 1409.38,1228.99 \n",
       "  1410.41,1229.25 1411.45,1229.51 1412.48,1229.77 1413.52,1230.03 1414.55,1230.29 1415.59,1230.56 1416.62,1230.82 1417.66,1231.08 1418.69,1231.34 1419.73,1231.61 \n",
       "  1420.76,1231.87 1421.8,1232.14 1422.83,1232.4 1423.87,1232.66 1424.9,1232.93 1425.94,1233.19 1426.97,1233.46 1428.01,1233.73 1429.04,1233.99 1430.08,1234.26 \n",
       "  1431.11,1234.53 1432.15,1234.79 1433.18,1235.06 1434.22,1235.33 1435.25,1235.6 1436.29,1235.86 1437.32,1236.13 1438.36,1236.4 1439.39,1236.67 1440.43,1236.94 \n",
       "  1441.46,1237.21 1442.5,1237.48 1443.53,1237.75 1444.57,1238.02 1445.6,1238.29 1446.64,1238.56 1447.67,1238.83 1448.71,1239.1 1449.74,1239.37 1450.78,1239.64 \n",
       "  1451.81,1239.92 1452.85,1240.19 1453.88,1240.46 1454.92,1240.73 1455.95,1241 1456.99,1241.28 1458.02,1241.55 1459.06,1241.82 1460.09,1242.09 1461.13,1242.37 \n",
       "  1462.16,1242.64 1463.2,1242.91 1464.23,1243.19 1465.27,1243.46 1466.3,1243.74 1467.34,1244.01 1468.37,1244.28 1469.41,1244.56 1470.44,1244.83 1471.48,1245.11 \n",
       "  1472.51,1245.38 1473.55,1245.66 1474.58,1245.93 1475.62,1246.21 1476.65,1246.48 1477.69,1246.76 1478.72,1247.03 1479.76,1247.31 1480.79,1247.58 1481.83,1247.86 \n",
       "  1482.86,1248.13 1483.9,1248.41 1484.93,1248.68 1485.97,1248.96 1487,1249.23 1488.04,1249.51 1489.08,1249.79 1490.11,1250.06 1491.15,1250.34 1492.18,1250.61 \n",
       "  1493.22,1250.89 1494.25,1251.17 1495.29,1251.44 1496.32,1251.72 1497.36,1251.99 1498.39,1252.27 1499.43,1252.55 1500.46,1252.82 1501.5,1253.1 1502.53,1253.37 \n",
       "  1503.57,1253.65 1504.6,1253.93 1505.64,1254.2 1506.67,1254.48 1507.71,1254.75 1508.74,1255.03 1509.78,1255.31 1510.81,1255.58 1511.85,1255.86 1512.88,1256.14 \n",
       "  1513.92,1256.41 1514.95,1256.69 1515.99,1256.96 1517.02,1257.24 1518.06,1257.51 1519.09,1257.79 1520.13,1258.07 1521.16,1258.34 1522.2,1258.62 1523.23,1258.89 \n",
       "  1524.27,1259.17 1525.3,1259.44 1526.34,1259.72 1527.37,1259.99 1528.41,1260.27 1529.44,1260.54 1530.48,1260.82 1531.51,1261.09 1532.55,1261.37 1533.58,1261.64 \n",
       "  1534.62,1261.92 1535.65,1262.19 1536.69,1262.47 1537.72,1262.74 1538.76,1263.02 1539.79,1263.29 1540.83,1263.56 1541.86,1263.84 1542.9,1264.11 1543.93,1264.39 \n",
       "  1544.97,1264.66 1546,1264.93 1547.04,1265.21 1548.07,1265.48 1549.11,1265.75 1550.14,1266.02 1551.18,1266.3 1552.21,1266.57 1553.25,1266.84 1554.28,1267.11 \n",
       "  1555.32,1267.39 1556.35,1267.66 1557.39,1267.93 1558.42,1268.2 1559.46,1268.47 1560.49,1268.74 1561.53,1269.02 1562.56,1269.29 1563.6,1269.56 1564.63,1269.83 \n",
       "  1565.67,1270.1 1566.7,1270.37 1567.74,1270.64 1568.77,1270.91 1569.81,1271.18 1570.84,1271.45 1571.88,1271.72 1572.91,1271.99 1573.95,1272.26 1574.98,1272.53 \n",
       "  1576.02,1272.79 1577.05,1273.06 1578.09,1273.33 1579.12,1273.6 1580.16,1273.87 1581.2,1274.13 1582.23,1274.4 1583.27,1274.67 1584.3,1274.93 1585.34,1275.2 \n",
       "  1586.37,1275.47 1587.41,1275.73 1588.44,1276 1589.48,1276.27 1590.51,1276.53 1591.55,1276.8 1592.58,1277.06 1593.62,1277.33 1594.65,1277.59 1595.69,1277.86 \n",
       "  1596.72,1278.12 1597.76,1278.38 1598.79,1278.65 1599.83,1278.91 1600.86,1279.17 1601.9,1279.44 1602.93,1279.7 1603.97,1279.96 1605,1280.22 1606.04,1280.49 \n",
       "  1607.07,1280.75 1608.11,1281.01 1609.14,1281.27 1610.18,1281.53 1611.21,1281.79 1612.25,1282.05 1613.28,1282.31 1614.32,1282.57 1615.35,1282.83 1616.39,1283.09 \n",
       "  1617.42,1283.35 1618.46,1283.61 1619.49,1283.87 1620.53,1284.12 1621.56,1284.38 1622.6,1284.64 1623.63,1284.9 1624.67,1285.15 1625.7,1285.41 1626.74,1285.67 \n",
       "  1627.77,1285.92 1628.81,1286.18 1629.84,1286.43 1630.88,1286.69 1631.91,1286.94 1632.95,1287.2 1633.98,1287.45 1635.02,1287.71 1636.05,1287.96 1637.09,1288.21 \n",
       "  1638.12,1288.47 1639.16,1288.72 1640.19,1288.97 1641.23,1289.22 1642.26,1289.48 1643.3,1289.73 1644.33,1289.98 1645.37,1290.23 1646.4,1290.48 1647.44,1290.73 \n",
       "  1648.47,1290.98 1649.51,1291.23 1650.54,1291.48 1651.58,1291.73 1652.61,1291.98 1653.65,1292.23 1654.68,1292.47 1655.72,1292.72 1656.75,1292.97 1657.79,1293.22 \n",
       "  1658.82,1293.46 1659.86,1293.71 1660.89,1293.96 1661.93,1294.2 1662.96,1294.45 1664,1294.69 1665.03,1294.94 1666.07,1295.18 1667.1,1295.43 1668.14,1295.67 \n",
       "  1669.17,1295.91 1670.21,1296.16 1671.24,1296.4 1672.28,1296.64 1673.31,1296.88 1674.35,1297.12 1675.39,1297.37 1676.42,1297.61 1677.46,1297.85 1678.49,1298.09 \n",
       "  1679.53,1298.33 1680.56,1298.57 1681.6,1298.81 1682.63,1299.05 1683.67,1299.28 1684.7,1299.52 1685.74,1299.76 1686.77,1300 1687.81,1300.24 1688.84,1300.47 \n",
       "  1689.88,1300.71 1690.91,1300.94 1691.95,1301.18 1692.98,1301.42 1694.02,1301.65 1695.05,1301.89 1696.09,1302.12 1697.12,1302.35 1698.16,1302.59 1699.19,1302.82 \n",
       "  1700.23,1303.05 1701.26,1303.29 1702.3,1303.52 1703.33,1303.75 1704.37,1303.98 1705.4,1304.21 1706.44,1304.44 1707.47,1304.67 1708.51,1304.9 1709.54,1305.13 \n",
       "  1710.58,1305.36 1711.61,1305.59 1712.65,1305.82 1713.68,1306.05 1714.72,1306.27 1715.75,1306.5 1716.79,1306.73 1717.82,1306.96 1718.86,1307.18 1719.89,1307.41 \n",
       "  1720.93,1307.63 1721.96,1307.86 1723,1308.08 1724.03,1308.31 1725.07,1308.53 1726.1,1308.76 1727.14,1308.98 1728.17,1309.2 1729.21,1309.42 1730.24,1309.65 \n",
       "  1731.28,1309.87 1732.31,1310.09 1733.35,1310.31 1734.38,1310.53 1735.42,1310.75 1736.45,1310.97 1737.49,1311.19 1738.52,1311.41 1739.56,1311.63 1740.59,1311.85 \n",
       "  1741.63,1312.06 1742.66,1312.28 1743.7,1312.5 1744.73,1312.72 1745.77,1312.93 1746.8,1313.15 1747.84,1313.36 1748.87,1313.58 1749.91,1313.79 1750.94,1314.01 \n",
       "  1751.98,1314.22 1753.01,1314.44 1754.05,1314.65 1755.08,1314.86 1756.12,1315.08 1757.15,1315.29 1758.19,1315.5 1759.22,1315.71 1760.26,1315.92 1761.29,1316.13 \n",
       "  1762.33,1316.34 1763.36,1316.55 1764.4,1316.76 1765.43,1316.97 1766.47,1317.18 1767.51,1317.39 1768.54,1317.6 1769.58,1317.81 1770.61,1318.01 1771.65,1318.22 \n",
       "  1772.68,1318.43 1773.72,1318.63 1774.75,1318.84 1775.79,1319.04 1776.82,1319.25 1777.86,1319.45 1778.89,1319.66 1779.93,1319.86 1780.96,1320.07 1782,1320.27 \n",
       "  1783.03,1320.47 1784.07,1320.67 1785.1,1320.88 1786.14,1321.08 1787.17,1321.28 1788.21,1321.48 1789.24,1321.68 1790.28,1321.88 1791.31,1322.08 1792.35,1322.28 \n",
       "  1793.38,1322.48 1794.42,1322.67 1795.45,1322.87 1796.49,1323.07 1797.52,1323.27 1798.56,1323.46 1799.59,1323.66 1800.63,1323.86 1801.66,1324.05 1802.7,1324.25 \n",
       "  1803.73,1324.44 1804.77,1324.64 1805.8,1324.83 1806.84,1325.03 1807.87,1325.22 1808.91,1325.41 1809.94,1325.6 1810.98,1325.8 1812.01,1325.99 1813.05,1326.18 \n",
       "  1814.08,1326.37 1815.12,1326.56 1816.15,1326.75 1817.19,1326.94 1818.22,1327.13 1819.26,1327.32 1820.29,1327.51 1821.33,1327.7 1822.36,1327.89 1823.4,1328.07 \n",
       "  1824.43,1328.26 1825.47,1328.45 1826.5,1328.63 1827.54,1328.82 1828.57,1329.01 1829.61,1329.19 1830.64,1329.38 1831.68,1329.56 1832.71,1329.74 1833.75,1329.93 \n",
       "  1834.78,1330.11 1835.82,1330.29 1836.85,1330.48 1837.89,1330.66 1838.92,1330.84 1839.96,1331.02 1840.99,1331.2 1842.03,1331.38 1843.06,1331.56 1844.1,1331.74 \n",
       "  1845.13,1331.92 1846.17,1332.1 1847.2,1332.28 1848.24,1332.46 1849.27,1332.64 1850.31,1332.82 1851.34,1332.99 1852.38,1333.17 1853.41,1333.35 1854.45,1333.52 \n",
       "  1855.48,1333.7 1856.52,1333.87 1857.55,1334.05 1858.59,1334.22 1859.63,1334.4 1860.66,1334.57 1861.7,1334.75 1862.73,1334.92 1863.77,1335.09 1864.8,1335.26 \n",
       "  1865.84,1335.44 1866.87,1335.61 1867.91,1335.78 1868.94,1335.95 1869.98,1336.12 1871.01,1336.29 1872.05,1336.46 1873.08,1336.63 1874.12,1336.8 1875.15,1336.97 \n",
       "  1876.19,1337.14 1877.22,1337.3 1878.26,1337.47 1879.29,1337.64 1880.33,1337.8 1881.36,1337.97 1882.4,1338.14 1883.43,1338.3 1884.47,1338.47 1885.5,1338.63 \n",
       "  1886.54,1338.8 1887.57,1338.96 1888.61,1339.13 1889.64,1339.29 1890.68,1339.45 1891.71,1339.62 1892.75,1339.78 1893.78,1339.94 1894.82,1340.1 1895.85,1340.26 \n",
       "  1896.89,1340.42 1897.92,1340.58 1898.96,1340.74 1899.99,1340.9 1901.03,1341.06 1902.06,1341.22 1903.1,1341.38 1904.13,1341.54 1905.17,1341.7 1906.2,1341.86 \n",
       "  1907.24,1342.01 1908.27,1342.17 1909.31,1342.33 1910.34,1342.48 1911.38,1342.64 1912.41,1342.8 1913.45,1342.95 1914.48,1343.11 1915.52,1343.26 1916.55,1343.41 \n",
       "  1917.59,1343.57 1918.62,1343.72 1919.66,1343.88 1920.69,1344.03 1921.73,1344.18 1922.76,1344.33 1923.8,1344.48 1924.83,1344.64 1925.87,1344.79 1926.9,1344.94 \n",
       "  1927.94,1345.09 1928.97,1345.24 1930.01,1345.39 1931.04,1345.54 1932.08,1345.69 1933.11,1345.83 1934.15,1345.98 1935.18,1346.13 1936.22,1346.28 1937.25,1346.43 \n",
       "  1938.29,1346.57 1939.32,1346.72 1940.36,1346.87 1941.39,1347.01 1942.43,1347.16 1943.46,1347.3 1944.5,1347.45 1945.53,1347.59 1946.57,1347.74 1947.6,1347.88 \n",
       "  1948.64,1348.02 1949.67,1348.17 1950.71,1348.31 1951.74,1348.45 1952.78,1348.6 1953.82,1348.74 1954.85,1348.88 1955.89,1349.02 1956.92,1349.16 1957.96,1349.3 \n",
       "  1958.99,1349.44 1960.03,1349.58 1961.06,1349.72 1962.1,1349.86 1963.13,1350 1964.17,1350.14 1965.2,1350.28 1966.24,1350.41 1967.27,1350.55 1968.31,1350.69 \n",
       "  1969.34,1350.83 1970.38,1350.96 1971.41,1351.1 1972.45,1351.24 1973.48,1351.37 1974.52,1351.51 1975.55,1351.64 1976.59,1351.78 1977.62,1351.91 1978.66,1352.04 \n",
       "  1979.69,1352.18 1980.73,1352.31 1981.76,1352.44 1982.8,1352.58 1983.83,1352.71 1984.87,1352.84 1985.9,1352.97 1986.94,1353.11 1987.97,1353.24 1989.01,1353.37 \n",
       "  1990.04,1353.5 1991.08,1353.63 1992.11,1353.76 1993.15,1353.89 1994.18,1354.02 1995.22,1354.15 1996.25,1354.27 1997.29,1354.4 1998.32,1354.53 1999.36,1354.66 \n",
       "  2000.39,1354.79 2001.43,1354.91 2002.46,1355.04 2003.5,1355.17 2004.53,1355.29 2005.57,1355.42 2006.6,1355.54 2007.64,1355.67 2008.67,1355.79 2009.71,1355.92 \n",
       "  2010.74,1356.04 2011.78,1356.17 2012.81,1356.29 2013.85,1356.41 2014.88,1356.54 2015.92,1356.66 2016.95,1356.78 2017.99,1356.9 2019.02,1357.03 2020.06,1357.15 \n",
       "  2021.09,1357.27 2022.13,1357.39 2023.16,1357.51 2024.2,1357.63 2025.23,1357.75 2026.27,1357.87 2027.3,1357.99 2028.34,1358.11 2029.37,1358.23 2030.41,1358.35 \n",
       "  2031.44,1358.47 2032.48,1358.58 2033.51,1358.7 2034.55,1358.82 2035.58,1358.94 2036.62,1359.05 2037.65,1359.17 2038.69,1359.28 2039.72,1359.4 2040.76,1359.52 \n",
       "  2041.79,1359.63 2042.83,1359.75 2043.86,1359.86 2044.9,1359.98 2045.94,1360.09 2046.97,1360.2 2048.01,1360.32 2049.04,1360.43 2050.08,1360.54 2051.11,1360.66 \n",
       "  2052.15,1360.77 2053.18,1360.88 2054.22,1360.99 2055.25,1361.1 2056.29,1361.22 2057.32,1361.33 2058.36,1361.44 2059.39,1361.55 2060.43,1361.66 2061.46,1361.77 \n",
       "  2062.5,1361.88 2063.53,1361.99 2064.57,1362.09 2065.6,1362.2 2066.64,1362.31 2067.67,1362.42 2068.71,1362.53 2069.74,1362.64 2070.78,1362.74 2071.81,1362.85 \n",
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       "  851.481,1223.86 852.516,1223.14 853.551,1222.41 854.586,1221.69 855.621,1220.96 856.656,1220.23 857.691,1219.5 858.726,1218.77 859.761,1218.04 860.796,1217.3 \n",
       "  861.831,1216.56 862.866,1215.83 863.901,1215.08 864.937,1214.34 865.972,1213.6 867.007,1212.85 868.042,1212.1 869.077,1211.35 870.112,1210.6 871.147,1209.84 \n",
       "  872.182,1209.09 873.217,1208.33 874.252,1207.57 875.287,1206.81 876.322,1206.04 877.357,1205.28 878.392,1204.51 879.427,1203.74 880.462,1202.97 881.497,1202.2 \n",
       "  882.532,1201.43 883.568,1200.65 884.603,1199.87 885.638,1199.09 886.673,1198.31 887.708,1197.53 888.743,1196.74 889.778,1195.96 890.813,1195.17 891.848,1194.38 \n",
       "  892.883,1193.59 893.918,1192.79 894.953,1192 895.988,1191.2 897.023,1190.4 898.058,1189.6 899.093,1188.8 900.128,1187.99 901.163,1187.19 902.199,1186.38 \n",
       "  903.234,1185.57 904.269,1184.76 905.304,1183.94 906.339,1183.13 907.374,1182.31 908.409,1181.49 909.444,1180.67 910.479,1179.85 911.514,1179.03 912.549,1178.2 \n",
       "  913.584,1177.37 914.619,1176.55 915.654,1175.72 916.689,1174.88 917.724,1174.05 918.759,1173.21 919.794,1172.38 920.83,1171.54 921.865,1170.7 922.9,1169.85 \n",
       "  923.935,1169.01 924.97,1168.17 926.005,1167.32 927.04,1166.47 928.075,1165.62 929.11,1164.77 930.145,1163.91 931.18,1163.06 932.215,1162.2 933.25,1161.34 \n",
       "  934.285,1160.48 935.32,1159.62 936.355,1158.75 937.39,1157.89 938.425,1157.02 939.461,1156.15 940.496,1155.28 941.531,1154.41 942.566,1153.54 943.601,1152.66 \n",
       "  944.636,1151.79 945.671,1150.91 946.706,1150.03 947.741,1149.15 948.776,1148.26 949.811,1147.38 950.846,1146.49 951.881,1145.61 952.916,1144.72 953.951,1143.83 \n",
       "  954.986,1142.93 956.021,1142.04 957.056,1141.15 958.092,1140.25 959.127,1139.35 960.162,1138.45 961.197,1137.55 962.232,1136.65 963.267,1135.74 964.302,1134.84 \n",
       "  965.337,1133.93 966.372,1133.02 967.407,1132.11 968.442,1131.2 969.477,1130.29 970.512,1129.37 971.547,1128.46 972.582,1127.54 973.617,1126.62 974.652,1125.7 \n",
       "  975.687,1124.78 976.723,1123.86 977.758,1122.93 978.793,1122.01 979.828,1121.08 980.863,1120.15 981.898,1119.22 982.933,1118.29 983.968,1117.36 985.003,1116.42 \n",
       "  986.038,1115.49 987.073,1114.55 988.108,1113.61 989.143,1112.67 990.178,1111.73 991.213,1110.79 992.248,1109.84 993.283,1108.9 994.318,1107.95 995.354,1107.01 \n",
       "  996.389,1106.06 997.424,1105.11 998.459,1104.16 999.494,1103.2 1000.53,1102.25 1001.56,1101.29 1002.6,1100.34 1003.63,1099.38 1004.67,1098.42 1005.7,1097.46 \n",
       "  1006.74,1096.5 1007.77,1095.54 1008.81,1094.57 1009.84,1093.61 1010.88,1092.64 1011.91,1091.67 1012.95,1090.71 1013.98,1089.74 1015.02,1088.77 1016.05,1087.79 \n",
       "  1017.09,1086.82 1018.12,1085.85 1019.16,1084.87 1020.19,1083.89 1021.23,1082.92 1022.26,1081.94 1023.3,1080.96 1024.34,1079.98 1025.37,1079 1026.41,1078.01 \n",
       "  1027.44,1077.03 1028.48,1076.04 1029.51,1075.06 1030.55,1074.07 1031.58,1073.08 1032.62,1072.09 1033.65,1071.1 1034.69,1070.11 1035.72,1069.12 1036.76,1068.13 \n",
       "  1037.79,1067.13 1038.83,1066.14 1039.86,1065.14 1040.9,1064.14 1041.93,1063.14 1042.97,1062.15 1044,1061.15 1045.04,1060.14 1046.07,1059.14 1047.11,1058.14 \n",
       "  1048.14,1057.14 1049.18,1056.13 1050.21,1055.13 1051.25,1054.12 1052.28,1053.11 1053.32,1052.1 1054.35,1051.1 1055.39,1050.09 1056.42,1049.08 1057.46,1048.06 \n",
       "  1058.49,1047.05 1059.53,1046.04 1060.56,1045.03 1061.6,1044.01 1062.63,1043 1063.67,1041.98 1064.7,1040.96 1065.74,1039.94 1066.77,1038.93 1067.81,1037.91 \n",
       "  1068.84,1036.89 1069.88,1035.87 1070.91,1034.85 1071.95,1033.82 1072.98,1032.8 1074.02,1031.78 1075.05,1030.75 1076.09,1029.73 1077.12,1028.7 1078.16,1027.68 \n",
       "  1079.19,1026.65 1080.23,1025.62 1081.26,1024.59 1082.3,1023.56 1083.33,1022.54 1084.37,1021.51 1085.4,1020.47 1086.44,1019.44 1087.47,1018.41 1088.51,1017.38 \n",
       "  1089.54,1016.35 1090.58,1015.31 1091.61,1014.28 1092.65,1013.24 1093.68,1012.21 1094.72,1011.17 1095.75,1010.14 1096.79,1009.1 1097.82,1008.06 1098.86,1007.03 \n",
       "  1099.89,1005.99 1100.93,1004.95 1101.96,1003.91 1103,1002.87 1104.03,1001.83 1105.07,1000.79 1106.1,999.748 1107.14,998.707 1108.17,997.665 1109.21,996.623 \n",
       "  1110.24,995.58 1111.28,994.537 1112.31,993.494 1113.35,992.45 1114.38,991.406 1115.42,990.362 1116.46,989.317 1117.49,988.272 1118.53,987.226 1119.56,986.18 \n",
       "  1120.6,985.134 1121.63,984.087 1122.67,983.041 1123.7,981.993 1124.74,980.946 1125.77,979.898 1126.81,978.851 1127.84,977.802 1128.88,976.754 1129.91,975.705 \n",
       "  1130.95,974.656 1131.98,973.607 1133.02,972.558 1134.05,971.508 1135.09,970.458 1136.12,969.408 1137.16,968.358 1138.19,967.308 1139.23,966.257 1140.26,965.207 \n",
       "  1141.3,964.156 1142.33,963.105 1143.37,962.054 1144.4,961.003 1145.44,959.952 1146.47,958.9 1147.51,957.849 1148.54,956.797 1149.58,955.745 1150.61,954.694 \n",
       "  1151.65,953.642 1152.68,952.59 1153.72,951.538 1154.75,950.486 1155.79,949.434 1156.82,948.382 1157.86,947.33 1158.89,946.278 1159.93,945.226 1160.96,944.174 \n",
       "  1162,943.122 1163.03,942.07 1164.07,941.019 1165.1,939.967 1166.14,938.915 1167.17,937.863 1168.21,936.812 1169.24,935.76 1170.28,934.709 1171.31,933.657 \n",
       "  1172.35,932.606 1173.38,931.555 1174.42,930.504 1175.45,929.453 1176.49,928.403 1177.52,927.352 1178.56,926.302 1179.59,925.252 1180.63,924.202 1181.66,923.152 \n",
       "  1182.7,922.102 1183.73,921.053 1184.77,920.004 1185.8,918.955 1186.84,917.906 1187.87,916.857 1188.91,915.809 1189.94,914.761 1190.98,913.713 1192.01,912.666 \n",
       "  1193.05,911.619 1194.08,910.572 1195.12,909.525 1196.15,908.479 1197.19,907.433 1198.22,906.387 1199.26,905.341 1200.29,904.296 1201.33,903.252 1202.36,902.207 \n",
       "  1203.4,901.163 1204.43,900.119 1205.47,899.076 1206.5,898.033 1207.54,896.99 1208.57,895.948 1209.61,894.906 1210.65,893.865 1211.68,892.824 1212.72,891.783 \n",
       "  1213.75,890.743 1214.79,889.703 1215.82,888.664 1216.86,887.625 1217.89,886.586 1218.93,885.548 1219.96,884.511 1221,883.474 1222.03,882.437 1223.07,881.401 \n",
       "  1224.1,880.365 1225.14,879.33 1226.17,878.296 1227.21,877.261 1228.24,876.228 1229.28,875.195 1230.31,874.162 1231.35,873.13 1232.38,872.099 1233.42,871.068 \n",
       "  1234.45,870.038 1235.49,869.008 1236.52,867.979 1237.56,866.95 1238.59,865.922 1239.63,864.895 1240.66,863.868 1241.7,862.842 1242.73,861.816 1243.77,860.791 \n",
       "  1244.8,859.767 1245.84,858.744 1246.87,857.72 1247.91,856.698 1248.94,855.676 1249.98,854.655 1251.01,853.635 1252.05,852.615 1253.08,851.596 1254.12,850.578 \n",
       "  1255.15,849.56 1256.19,848.543 1257.22,847.527 1258.26,846.511 1259.29,845.496 1260.33,844.482 1261.36,843.469 1262.4,842.456 1263.43,841.444 1264.47,840.433 \n",
       "  1265.5,839.423 1266.54,838.413 1267.57,837.404 1268.61,836.396 1269.64,835.389 1270.68,834.382 1271.71,833.377 1272.75,832.372 1273.78,831.367 1274.82,830.364 \n",
       "  1275.85,829.361 1276.89,828.36 1277.92,827.359 1278.96,826.359 1279.99,825.359 1281.03,824.361 1282.06,823.363 1283.1,822.367 1284.13,821.371 1285.17,820.376 \n",
       "  1286.2,819.382 1287.24,818.388 1288.27,817.396 1289.31,816.404 1290.34,815.414 1291.38,814.424 1292.41,813.435 1293.45,812.447 1294.48,811.46 1295.52,810.474 \n",
       "  1296.55,809.489 1297.59,808.505 1298.62,807.521 1299.66,806.539 1300.69,805.557 1301.73,804.577 1302.77,803.597 1303.8,802.619 1304.84,801.641 1305.87,800.664 \n",
       "  1306.91,799.688 1307.94,798.714 1308.98,797.74 1310.01,796.767 1311.05,795.795 1312.08,794.824 1313.12,793.855 1314.15,792.886 1315.19,791.918 1316.22,790.951 \n",
       "  1317.26,789.985 1318.29,789.02 1319.33,788.057 1320.36,787.094 1321.4,786.132 1322.43,785.171 1323.47,784.212 1324.5,783.253 1325.54,782.296 1326.57,781.339 \n",
       "  1327.61,780.384 1328.64,779.429 1329.68,778.476 1330.71,777.524 1331.75,776.573 1332.78,775.623 1333.82,774.673 1334.85,773.726 1335.89,772.779 1336.92,771.833 \n",
       "  1337.96,770.888 1338.99,769.945 1340.03,769.002 1341.06,768.061 1342.1,767.121 1343.13,766.182 1344.17,765.244 1345.2,764.307 1346.24,763.371 1347.27,762.437 \n",
       "  1348.31,761.503 1349.34,760.571 1350.38,759.64 1351.41,758.71 1352.45,757.781 1353.48,756.853 1354.52,755.927 1355.55,755.001 1356.59,754.077 1357.62,753.154 \n",
       "  1358.66,752.232 1359.69,751.311 1360.73,750.392 1361.76,749.473 1362.8,748.556 1363.83,747.64 1364.87,746.725 1365.9,745.812 1366.94,744.899 1367.97,743.988 \n",
       "  1369.01,743.078 1370.04,742.169 1371.08,741.262 1372.11,740.356 1373.15,739.45 1374.18,738.546 1375.22,737.644 1376.25,736.742 1377.29,735.842 1378.32,734.943 \n",
       "  1379.36,734.045 1380.39,733.149 1381.43,732.253 1382.46,731.359 1383.5,730.466 1384.53,729.575 1385.57,728.685 1386.6,727.795 1387.64,726.908 1388.67,726.021 \n",
       "  1389.71,725.136 1390.74,724.252 1391.78,723.369 1392.81,722.487 1393.85,721.607 1394.89,720.728 1395.92,719.851 1396.96,718.974 1397.99,718.099 1399.03,717.225 \n",
       "  1400.06,716.353 1401.1,715.481 1402.13,714.611 1403.17,713.743 1404.2,712.876 1405.24,712.01 1406.27,711.145 1407.31,710.282 1408.34,709.42 1409.38,708.559 \n",
       "  1410.41,707.699 1411.45,706.841 1412.48,705.985 1413.52,705.129 1414.55,704.275 1415.59,703.422 1416.62,702.571 1417.66,701.721 1418.69,700.872 1419.73,700.024 \n",
       "  1420.76,699.178 1421.8,698.333 1422.83,697.49 1423.87,696.648 1424.9,695.807 1425.94,694.967 1426.97,694.129 1428.01,693.292 1429.04,692.457 1430.08,691.623 \n",
       "  1431.11,690.79 1432.15,689.959 1433.18,689.128 1434.22,688.3 1435.25,687.472 1436.29,686.646 1437.32,685.821 1438.36,684.998 1439.39,684.176 1440.43,683.355 \n",
       "  1441.46,682.536 1442.5,681.718 1443.53,680.901 1444.57,680.086 1445.6,679.272 1446.64,678.459 1447.67,677.648 1448.71,676.838 1449.74,676.029 1450.78,675.222 \n",
       "  1451.81,674.416 1452.85,673.612 1453.88,672.808 1454.92,672.007 1455.95,671.206 1456.99,670.407 1458.02,669.609 1459.06,668.813 1460.09,668.018 1461.13,667.224 \n",
       "  1462.16,666.432 1463.2,665.641 1464.23,664.851 1465.27,664.063 1466.3,663.276 1467.34,662.491 1468.37,661.707 1469.41,660.924 1470.44,660.143 1471.48,659.363 \n",
       "  1472.51,658.584 1473.55,657.807 1474.58,657.031 1475.62,656.256 1476.65,655.483 1477.69,654.711 1478.72,653.94 1479.76,653.171 1480.79,652.404 1481.83,651.637 \n",
       "  1482.86,650.872 1483.9,650.108 1484.93,649.346 1485.97,648.585 1487,647.826 1488.04,647.068 1489.08,646.311 1490.11,645.555 1491.15,644.801 1492.18,644.049 \n",
       "  1493.22,643.297 1494.25,642.547 1495.29,641.799 1496.32,641.051 1497.36,640.306 1498.39,639.561 1499.43,638.818 1500.46,638.076 1501.5,637.336 1502.53,636.597 \n",
       "  1503.57,635.859 1504.6,635.123 1505.64,634.388 1506.67,633.654 1507.71,632.922 1508.74,632.192 1509.78,631.462 1510.81,630.734 1511.85,630.007 1512.88,629.282 \n",
       "  1513.92,628.558 1514.95,627.836 1515.99,627.114 1517.02,626.395 1518.06,625.676 1519.09,624.959 1520.13,624.243 1521.16,623.529 1522.2,622.816 1523.23,622.104 \n",
       "  1524.27,621.394 1525.3,620.685 1526.34,619.978 1527.37,619.272 1528.41,618.567 1529.44,617.864 1530.48,617.162 1531.51,616.461 1532.55,615.762 1533.58,615.064 \n",
       "  1534.62,614.367 1535.65,613.672 1536.69,612.978 1537.72,612.286 1538.76,611.594 1539.79,610.905 1540.83,610.216 1541.86,609.529 1542.9,608.844 1543.93,608.159 \n",
       "  1544.97,607.476 1546,606.795 1547.04,606.115 1548.07,605.436 1549.11,604.758 1550.14,604.082 1551.18,603.408 1552.21,602.734 1553.25,602.062 1554.28,601.391 \n",
       "  1555.32,600.722 1556.35,600.054 1557.39,599.387 1558.42,598.722 1559.46,598.058 1560.49,597.396 1561.53,596.735 1562.56,596.075 1563.6,595.416 1564.63,594.759 \n",
       "  1565.67,594.103 1566.7,593.449 1567.74,592.796 1568.77,592.144 1569.81,591.494 1570.84,590.844 1571.88,590.197 1572.91,589.55 1573.95,588.905 1574.98,588.262 \n",
       "  1576.02,587.619 1577.05,586.978 1578.09,586.339 1579.12,585.7 1580.16,585.063 1581.2,584.428 1582.23,583.794 1583.27,583.161 1584.3,582.529 1585.34,581.899 \n",
       "  1586.37,581.27 1587.41,580.642 1588.44,580.016 1589.48,579.391 1590.51,578.767 1591.55,578.145 1592.58,577.524 1593.62,576.904 1594.65,576.286 1595.69,575.669 \n",
       "  1596.72,575.053 1597.76,574.439 1598.79,573.826 1599.83,573.214 1600.86,572.604 1601.9,571.995 1602.93,571.387 1603.97,570.781 1605,570.176 1606.04,569.572 \n",
       "  1607.07,568.969 1608.11,568.368 1609.14,567.768 1610.18,567.17 1611.21,566.573 1612.25,565.977 1613.28,565.382 1614.32,564.789 1615.35,564.197 1616.39,563.606 \n",
       "  1617.42,563.017 1618.46,562.428 1619.49,561.842 1620.53,561.256 1621.56,560.672 1622.6,560.089 1623.63,559.507 1624.67,558.927 1625.7,558.348 1626.74,557.77 \n",
       "  1627.77,557.194 1628.81,556.618 1629.84,556.044 1630.88,555.472 1631.91,554.901 1632.95,554.33 1633.98,553.762 1635.02,553.194 1636.05,552.628 1637.09,552.063 \n",
       "  1638.12,551.499 1639.16,550.937 1640.19,550.376 1641.23,549.816 1642.26,549.257 1643.3,548.7 1644.33,548.144 1645.37,547.589 1646.4,547.035 1647.44,546.483 \n",
       "  1648.47,545.932 1649.51,545.382 1650.54,544.834 1651.58,544.286 1652.61,543.74 1653.65,543.195 1654.68,542.652 1655.72,542.109 1656.75,541.568 1657.79,541.029 \n",
       "  1658.82,540.49 1659.86,539.953 1660.89,539.417 1661.93,538.882 1662.96,538.348 1664,537.816 1665.03,537.284 1666.07,536.754 1667.1,536.226 1668.14,535.698 \n",
       "  1669.17,535.172 1670.21,534.647 1671.24,534.123 1672.28,533.6 1673.31,533.079 1674.35,532.558 1675.39,532.039 1676.42,531.522 1677.46,531.005 1678.49,530.49 \n",
       "  1679.53,529.975 1680.56,529.462 1681.6,528.951 1682.63,528.44 1683.67,527.931 1684.7,527.422 1685.74,526.915 1686.77,526.41 1687.81,525.905 1688.84,525.402 \n",
       "  1689.88,524.899 1690.91,524.398 1691.95,523.898 1692.98,523.4 1694.02,522.902 1695.05,522.406 1696.09,521.91 1697.12,521.416 1698.16,520.924 1699.19,520.432 \n",
       "  1700.23,519.941 1701.26,519.452 1702.3,518.964 1703.33,518.477 1704.37,517.991 1705.4,517.506 1706.44,517.022 1707.47,516.54 1708.51,516.059 1709.54,515.579 \n",
       "  1710.58,515.1 1711.61,514.622 1712.65,514.145 1713.68,513.67 1714.72,513.195 1715.75,512.722 1716.79,512.25 1717.82,511.779 1718.86,511.309 1719.89,510.84 \n",
       "  1720.93,510.372 1721.96,509.906 1723,509.441 1724.03,508.976 1725.07,508.513 1726.1,508.051 1727.14,507.59 1728.17,507.13 1729.21,506.672 1730.24,506.214 \n",
       "  1731.28,505.758 1732.31,505.302 1733.35,504.848 1734.38,504.395 1735.42,503.943 1736.45,503.492 1737.49,503.042 1738.52,502.593 1739.56,502.146 1740.59,501.699 \n",
       "  1741.63,501.254 1742.66,500.809 1743.7,500.366 1744.73,499.924 1745.77,499.483 1746.8,499.043 1747.84,498.604 1748.87,498.166 1749.91,497.729 1750.94,497.293 \n",
       "  1751.98,496.859 1753.01,496.425 1754.05,495.992 1755.08,495.561 1756.12,495.13 1757.15,494.701 1758.19,494.273 1759.22,493.846 1760.26,493.419 1761.29,492.994 \n",
       "  1762.33,492.57 1763.36,492.147 1764.4,491.725 1765.43,491.304 1766.47,490.884 1767.51,490.465 1768.54,490.048 1769.58,489.631 1770.61,489.215 1771.65,488.8 \n",
       "  1772.68,488.387 1773.72,487.974 1774.75,487.563 1775.79,487.152 1776.82,486.742 1777.86,486.334 1778.89,485.926 1779.93,485.52 1780.96,485.114 1782,484.71 \n",
       "  1783.03,484.306 1784.07,483.904 1785.1,483.503 1786.14,483.102 1787.17,482.703 1788.21,482.304 1789.24,481.907 1790.28,481.511 1791.31,481.115 1792.35,480.721 \n",
       "  1793.38,480.327 1794.42,479.935 1795.45,479.543 1796.49,479.153 1797.52,478.764 1798.56,478.375 1799.59,477.988 1800.63,477.601 1801.66,477.216 1802.7,476.831 \n",
       "  1803.73,476.447 1804.77,476.065 1805.8,475.683 1806.84,475.303 1807.87,474.923 1808.91,474.544 1809.94,474.166 1810.98,473.79 1812.01,473.414 1813.05,473.039 \n",
       "  1814.08,472.665 1815.12,472.292 1816.15,471.92 1817.19,471.549 1818.22,471.179 1819.26,470.81 1820.29,470.442 1821.33,470.074 1822.36,469.708 1823.4,469.343 \n",
       "  1824.43,468.978 1825.47,468.615 1826.5,468.252 1827.54,467.89 1828.57,467.53 1829.61,467.17 1830.64,466.811 1831.68,466.453 1832.71,466.096 1833.75,465.74 \n",
       "  1834.78,465.385 1835.82,465.03 1836.85,464.677 1837.89,464.325 1838.92,463.973 1839.96,463.623 1840.99,463.273 1842.03,462.924 1843.06,462.576 1844.1,462.229 \n",
       "  1845.13,461.883 1846.17,461.538 1847.2,461.194 1848.24,460.85 1849.27,460.508 1850.31,460.166 1851.34,459.825 1852.38,459.485 1853.41,459.146 1854.45,458.808 \n",
       "  1855.48,458.471 1856.52,458.135 1857.55,457.799 1858.59,457.465 1859.63,457.131 1860.66,456.798 1861.7,456.466 1862.73,456.135 1863.77,455.805 1864.8,455.476 \n",
       "  1865.84,455.147 1866.87,454.82 1867.91,454.493 1868.94,454.167 1869.98,453.842 1871.01,453.518 1872.05,453.194 1873.08,452.872 1874.12,452.55 1875.15,452.229 \n",
       "  1876.19,451.909 1877.22,451.59 1878.26,451.272 1879.29,450.954 1880.33,450.638 1881.36,450.322 1882.4,450.007 1883.43,449.693 1884.47,449.38 1885.5,449.067 \n",
       "  1886.54,448.755 1887.57,448.445 1888.61,448.135 1889.64,447.825 1890.68,447.517 1891.71,447.209 1892.75,446.903 1893.78,446.597 1894.82,446.292 1895.85,445.987 \n",
       "  1896.89,445.684 1897.92,445.381 1898.96,445.079 1899.99,444.778 1901.03,444.478 1902.06,444.178 1903.1,443.88 1904.13,443.582 1905.17,443.284 1906.2,442.988 \n",
       "  1907.24,442.693 1908.27,442.398 1909.31,442.104 1910.34,441.81 1911.38,441.518 1912.41,441.226 1913.45,440.935 1914.48,440.645 1915.52,440.356 1916.55,440.067 \n",
       "  1917.59,439.779 1918.62,439.492 1919.66,439.206 1920.69,438.92 1921.73,438.635 1922.76,438.351 1923.8,438.068 1924.83,437.785 1925.87,437.503 1926.9,437.222 \n",
       "  1927.94,436.942 1928.97,436.662 1930.01,436.384 1931.04,436.105 1932.08,435.828 1933.11,435.551 1934.15,435.275 1935.18,435 1936.22,434.726 1937.25,434.452 \n",
       "  1938.29,434.179 1939.32,433.907 1940.36,433.635 1941.39,433.364 1942.43,433.094 1943.46,432.825 1944.5,432.556 1945.53,432.288 1946.57,432.021 1947.6,431.754 \n",
       "  1948.64,431.489 1949.67,431.223 1950.71,430.959 1951.74,430.695 1952.78,430.432 1953.82,430.17 1954.85,429.909 1955.89,429.648 1956.92,429.388 1957.96,429.128 \n",
       "  1958.99,428.869 1960.03,428.611 1961.06,428.354 1962.1,428.097 1963.13,427.841 1964.17,427.586 1965.2,427.331 1966.24,427.077 1967.27,426.824 1968.31,426.572 \n",
       "  1969.34,426.32 1970.38,426.069 1971.41,425.818 1972.45,425.568 1973.48,425.319 1974.52,425.071 1975.55,424.823 1976.59,424.576 1977.62,424.329 1978.66,424.084 \n",
       "  1979.69,423.838 1980.73,423.594 1981.76,423.35 1982.8,423.107 1983.83,422.865 1984.87,422.623 1985.9,422.382 1986.94,422.141 1987.97,421.901 1989.01,421.662 \n",
       "  1990.04,421.424 1991.08,421.186 1992.11,420.949 1993.15,420.712 1994.18,420.476 1995.22,420.241 1996.25,420.006 1997.29,419.772 1998.32,419.539 1999.36,419.306 \n",
       "  2000.39,419.074 2001.43,418.843 2002.46,418.612 2003.5,418.382 2004.53,418.152 2005.57,417.924 2006.6,417.695 2007.64,417.468 2008.67,417.241 2009.71,417.014 \n",
       "  2010.74,416.789 2011.78,416.563 2012.81,416.339 2013.85,416.115 2014.88,415.892 2015.92,415.669 2016.95,415.447 2017.99,415.226 2019.02,415.005 2020.06,414.785 \n",
       "  2021.09,414.565 2022.13,414.346 2023.16,414.128 2024.2,413.91 2025.23,413.693 2026.27,413.476 2027.3,413.26 2028.34,413.045 2029.37,412.83 2030.41,412.616 \n",
       "  2031.44,412.403 2032.48,412.19 2033.51,411.977 2034.55,411.765 2035.58,411.554 2036.62,411.344 2037.65,411.134 2038.69,410.924 2039.72,410.715 2040.76,410.507 \n",
       "  2041.79,410.299 2042.83,410.092 2043.86,409.886 2044.9,409.68 2045.94,409.474 2046.97,409.27 2048.01,409.065 2049.04,408.862 2050.08,408.659 2051.11,408.456 \n",
       "  2052.15,408.254 2053.18,408.053 2054.22,407.852 2055.25,407.652 2056.29,407.452 2057.32,407.253 2058.36,407.054 2059.39,406.856 2060.43,406.659 2061.46,406.462 \n",
       "  2062.5,406.266 2063.53,406.07 2064.57,405.875 2065.6,405.68 2066.64,405.486 2067.67,405.292 2068.71,405.099 2069.74,404.907 2070.78,404.715 2071.81,404.524 \n",
       "  2072.85,404.333 2073.88,404.142 2074.92,403.953 2075.95,403.763 2076.99,403.575 2078.02,403.386 2079.06,403.199 2080.09,403.012 2081.13,402.825 2082.16,402.639 \n",
       "  2083.2,402.453 2084.23,402.268 2085.27,402.084 2086.3,401.9 2087.34,401.716 2088.37,401.534 2089.41,401.351 2090.44,401.169 2091.48,400.988 2092.51,400.807 \n",
       "  2093.55,400.627 2094.58,400.447 2095.62,400.268 2096.65,400.089 2097.69,399.91 2098.72,399.733 2099.76,399.555 2100.79,399.379 2101.83,399.202 2102.86,399.027 \n",
       "  2103.9,398.851 2104.93,398.676 2105.97,398.502 2107,398.328 2108.04,398.155 2109.07,397.982 2110.11,397.81 2111.14,397.638 2112.18,397.467 2113.21,397.296 \n",
       "  2114.25,397.126 2115.28,396.956 2116.32,396.786 2117.35,396.618 2118.39,396.449 2119.42,396.281 2120.46,396.114 2121.49,395.947 2122.53,395.78 2123.56,395.614 \n",
       "  2124.6,395.449 2125.63,395.284 2126.67,395.119 2127.7,394.955 2128.74,394.791 2129.77,394.628 2130.81,394.465 2131.84,394.303 2132.88,394.141 2133.91,393.98 \n",
       "  2134.95,393.819 2135.98,393.659 2137.02,393.499 2138.05,393.339 2139.09,393.18 2140.13,393.022 2141.16,392.864 2142.2,392.706 2143.23,392.549 2144.27,392.392 \n",
       "  2145.3,392.236 2146.34,392.08 2147.37,391.924 2148.41,391.769 2149.44,391.615 2150.48,391.461 2151.51,391.307 2152.55,391.154 2153.58,391.001 2154.62,390.849 \n",
       "  2155.65,390.697 2156.69,390.545 2157.72,390.394 2158.76,390.244 2159.79,390.094 2160.83,389.944 2161.86,389.795 2162.9,389.646 2163.93,389.497 2164.97,389.349 \n",
       "  2166,389.202 2167.04,389.054 2168.07,388.908 2169.11,388.761 2170.14,388.615 2171.18,388.47 2172.21,388.325 2173.25,388.18 2174.28,388.036 2175.32,387.892 \n",
       "  2176.35,387.749 2177.39,387.606 2178.42,387.463 2179.46,387.321 2180.49,387.179 2181.53,387.038 2182.56,386.897 2183.6,386.756 2184.63,386.616 2185.67,386.476 \n",
       "  2186.7,386.337 2187.74,386.198 2188.77,386.059 2189.81,385.921 2190.84,385.783 2191.88,385.646 2192.91,385.509 2193.95,385.372 2194.98,385.236 2196.02,385.1 \n",
       "  2197.05,384.965 2198.09,384.83 2199.12,384.695 2200.16,384.561 2201.19,384.427 2202.23,384.293 2203.26,384.16 2204.3,384.027 2205.33,383.895 2206.37,383.763 \n",
       "  2207.4,383.631 2208.44,383.5 2209.47,383.369 2210.51,383.239 2211.54,383.108 2212.58,382.979 2213.61,382.849 2214.65,382.72 2215.68,382.592 2216.72,382.463 \n",
       "  2217.75,382.335 2218.79,382.208 2219.82,382.081 2220.86,381.954 2221.89,381.827 2222.93,381.701 2223.96,381.575 2225,381.45 2226.03,381.325 2227.07,381.2 \n",
       "  2228.1,381.076 2229.14,380.952 2230.17,380.828 2231.21,380.705 2232.25,380.582 2233.28,380.459 2234.32,380.337 2235.35,380.215 2236.39,380.094 2237.42,379.972 \n",
       "  2238.46,379.851 2239.49,379.731 2240.53,379.611 2241.56,379.491 2242.6,379.371 2243.63,379.252 2244.67,379.133 2245.7,379.015 2246.74,378.896 2247.77,378.779 \n",
       "  2248.81,378.661 2249.84,378.544 2250.88,378.427 2251.91,378.31 2252.95,378.194 2253.98,378.078 2255.02,377.963 2256.05,377.847 2257.09,377.732 2258.12,377.618 \n",
       "  2259.16,377.504 2260.19,377.39 2261.23,377.276 2262.26,377.163 2263.3,377.05 2264.33,376.937 2265.37,376.824 2266.4,376.712 2267.44,376.601 2268.47,376.489 \n",
       "  2269.51,376.378 2270.54,376.267 2271.58,376.156 2272.61,376.046 2273.65,375.936 2274.68,375.827 2275.72,375.717 2276.75,375.608 2277.79,375.5 2278.82,375.391 \n",
       "  2279.86,375.283 2280.89,375.176 2281.93,375.068 2282.96,374.961 2284,374.854 2285.03,374.748 2286.07,374.642 2287.1,374.536 2288.14,374.43 2289.17,374.325 \n",
       "  2290.21,374.22 2291.24,374.115 2292.28,374.011 2293.31,373.907 2294.35,373.803 2295.38,373.7 2296.42,373.597 2297.45,373.494 2298.49,373.391 2299.52,373.289 \n",
       "  2300.56,373.187 2301.59,373.085 2302.63,372.984 2303.66,372.883 2304.7,372.782 2305.73,372.682 2306.77,372.582 2307.8,372.482 2308.84,372.382 2309.87,372.283 \n",
       "  2310.91,372.184 2311.94,372.085 2312.98,371.986 2314.01,371.888 2315.05,371.79 2316.08,371.693 2317.12,371.595 2318.15,371.498 2319.19,371.402 2320.22,371.305 \n",
       "  2321.26,371.209 \n",
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       "  1953.07,191.244 2097.07,191.244 \n",
       "  \"/>\n",
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       "</svg>\n"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sir_sol,xlabel=\"Time\",ylabel=\"Number\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the Function Interface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "retcode: Success\n",
       "Interpolation: 1st order linear\n",
       "t: 2001-element Array{Float64,1}:\n",
       "   0.0\n",
       "   0.1\n",
       "   0.2\n",
       "   0.3\n",
       "   0.4\n",
       "   0.5\n",
       "   0.6\n",
       "   0.7\n",
       "   0.8\n",
       "   0.9\n",
       "   1.0\n",
       "   1.1\n",
       "   1.2\n",
       "   ⋮  \n",
       " 198.9\n",
       " 199.0\n",
       " 199.1\n",
       " 199.2\n",
       " 199.3\n",
       " 199.4\n",
       " 199.5\n",
       " 199.6\n",
       " 199.7\n",
       " 199.8\n",
       " 199.9\n",
       " 200.0\n",
       "u: 2001-element Array{Array{Float64,1},1}:\n",
       " [0.99, 0.01, 0.0]                 \n",
       " [0.989901, 0.0100491, 5.01227e-5] \n",
       " [0.989801, 0.0100985, 0.000100492]\n",
       " [0.989701, 0.010148, 0.000151108] \n",
       " [0.9896, 0.0101979, 0.000201972]  \n",
       " [0.989499, 0.0102479, 0.000253087]\n",
       " [0.989397, 0.0102982, 0.000304452]\n",
       " [0.989295, 0.0103487, 0.000356069]\n",
       " [0.989193, 0.0103995, 0.000407939]\n",
       " [0.989089, 0.0104504, 0.000460064]\n",
       " [0.988986, 0.0105017, 0.000512444]\n",
       " [0.988882, 0.0105531, 0.000565081]\n",
       " [0.988777, 0.0106049, 0.000617976]\n",
       " ⋮                                 \n",
       " [0.21018, 0.0149422, 0.774878]    \n",
       " [0.210148, 0.014899, 0.774953]    \n",
       " [0.210117, 0.0148558, 0.775027]   \n",
       " [0.210086, 0.0148128, 0.775101]   \n",
       " [0.210055, 0.01477, 0.775175]     \n",
       " [0.210024, 0.0147272, 0.775249]   \n",
       " [0.209993, 0.0146845, 0.775322]   \n",
       " [0.209962, 0.014642, 0.775396]    \n",
       " [0.209932, 0.0145996, 0.775469]   \n",
       " [0.209901, 0.0145573, 0.775542]   \n",
       " [0.209871, 0.0145151, 0.775614]   \n",
       " [0.20984, 0.0144731, 0.775687]    "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function sir_ode2(du,u,p,t)\n",
    "    S,I,R = u\n",
    "    b,g = p\n",
    "    du[1] = -b*S*I\n",
    "    du[2] = b*S*I-g*I\n",
    "    du[3] = g*I\n",
    "end\n",
    "parms = [0.1,0.05]\n",
    "init = [0.99,0.01,0.0]\n",
    "tspan = (0.0,200.0)\n",
    "sir_prob2 = ODEProblem(sir_ode2,init,tspan,parms)\n",
    "sir_sol = solve(sir_prob2,saveat = 0.1)"
   ]
  }
 ],
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