[MAT3300 Final Project, 2021] Mathematical Modeling of COVID-19

This repository contains codes for MAT3300 final project, Mathematical Modeling of COVID-19. If you have any question regarding this project, feel free to contact me at [email protected].

Requirement

Python3
numpy
pandas

Data

Data from John Hoopkins Univerisity is used. The downloaded data has been placed under data folder. Note: since recovery data after Aug 4, 2021 is not available, only data before Aug 4, 2021 (include) is used.

The data has been processed to recover active cases. If you wish to process it again, run

python data_preprocess.py

Models (Simulators)

The four models are in simulator.py. To run a simulation with a model, consult the following example

from simulator import  DTMCSEIR, CTMCSEIR, ApproxSEIR, ExactSEIR

param = {
    'ae': 1e-8,
    'ai': 1e-8,
    'gamma': 0.01,
    'kappa': 0.1,
    'beta': 0.1,
    'rho': 0.01,
    'mu': 0.01,
    's': 5e7,
    'e': 1e3,
    'max_e': 1e3,
    'max_i': 1e3
}
init_state = {
    'i': 2,
    'r': 3,
    'p': 0,
    'cr': 3
}
model = DTMC(param, init_state)  # can be one of the four model
# run simulation for 100 days
for i in range(100):
    model.step()
# access the result
result = model.history
# visualize the result
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
model.plot(ax)
plt.show()

Note: the DTMC model is strongly recommended for its speed. Plus, NEVER use the CTMC model in real world setting. It is SUPER SLOW in large problems.

Fit the model

To obtain the fitting result in the report, run

python fit_predict_dtmc.py

Note: slight differences are expected due to randomness in the DTMC model.

To fit the model to another time period, change line 156 to

# original
evaluate('2021-03-01', '2021-05-31', '2021-05-01',
# change to
evaluate('start date', 'end date', 'date to split the fitting and predicting period',

Please note that the fitting will last for a few hours because simulated annealing is slow.

Outbreak analysis

First extract the outbreak periods (pre-extracted periods are in data). If you wish to extract it again using your standard of selecting a outbreak period, run

python extract_explode_date.py

To obtain the result in the report, run

python fit_explode.py