add citation

vignettes/estimate_infections.Rmd

@@ -43,19 +43,19 @@ The model is initialised before the first observed data point by assuming consta
 
 where $I_{t}$ is the number of latent infections on day $t$, $r$ is an estimate of the initial growth rate, $\xi$ is the proportion reported (see [Delays and scaling]), \iota is a scaling factor and $C_\mathrm{init}$ is the mean of the first 7 days of cases (or all cases if fewer than 7 days of data are available).
 
-The initial growth rate $r$ is estimated from the first estimated value of the reproduction number $R_t$ by solving the linear system
+The initial growth rate $r$ is estimated from the first estimated value of the reproduction number $R_t$ by solving the linear system [wallinga2006how]
 
 $$
-G(r) - 1 / R_0 = 0.
+M(-r) - 1 / R_0 = 0.
 $$
 
 where
 
 $$
-G(r) = \sum_{i=1}^n g_i e^{-r i}.
+M(r) = \sum_{i=1}^n g_i e^{r i}.
 $$
 
-is the negative moment generating function (MGF) of the discretised generation interval distribution (see [Infections]).
+is the moment generating function of the discretised generation time distribution (see  [Infections]).
 
 ### Infections
 
@@ -65,7 +65,7 @@ For the time window of the observed data and beyond infections are then modelled
   I_t = R_t \sum_{\tau = 1}^{g_\mathrm{max}} g(\tau | \theta_g) I_{t - \tau}
 \end{equation}
 
-where $g(\tau | \theta_g)$ is the discretised distribution of generation times with parameters $\theta_g$ and maximum $g_\mathrm{max}$.
+where $g_\tau = g(\tau | \theta_g)$ is the discretised distribution of generation times with parameters $\theta_g$ and maximum $g_\mathrm{max}$.
 Generation times can be specified as coming from a distribution with uncertainty by giving mean and standard deviations of normal priors of the distributional parameters.
 By default this prior is weighted by default by the number of observations although this can be changed by the user.
 It is truncated to be positive where relevant for the given distribution.

vignettes/library.bib

@@ -33,3 +33,19 @@ @article{renewal
     pages = {1-12},
     number = {8},
 }
+
+@Article{wallinga2006how,
+  author          = {Wallinga, J and Lipsitch, M},
+  title           = {How generation intervals shape the relationship between
+                  growth rates and reproductive numbers},
+  journal         = {Proceedings of the Royal Society B: Biological Sciences},
+  year            = 2006,
+  volume          = 274,
+  number          = 1609,
+  month           = nov,
+  pages           = {599–604},
+  issn            = {1471-2954},
+  doi             = {10.1098/rspb.2006.3754},
+  url             = {http://dx.doi.org/10.1098/rspb.2006.3754},
+  publisher       = {The Royal Society}
+}