### Major changes:

1. Bugfix in initial condition setting for MCMC and prediction.

2. Rationalised data import.  Now uses a load_data function in the covid.model module.

3. Updated model doc to reflect loss of background infectious pressure, implementation of commuting frequency.

4. Fixes in covid_ode.py reflecting updated model interface.
parent e315c086
 %% LyX 2.2.4 created this file. For more info, see http://www.lyx.org/. % LyX 2.2.4 created this file. For more info, see http://www.lyx.org/. %% Do not edit unless you really know what you are doing. \documentclass[english]{article} \usepackage[T1]{fontenc} ... ... @@ -94,30 +94,65 @@ number of individual in each age-group-LAD combination at time $t$ by the vectors $\vec{S}(t),\vec{E}(t),\vec{I}(t),\vec{R}(t)$. We therefore have \begin{align*} \frac{\mathrm{d\vec{S}(t)}}{dt} & =-\beta_{1}\left[M^{\star}\vec{I}(t)+\beta_{2}\bar{M}C^{\star}\frac{{\vec{I}(t)}}{N}\right]\frac{\vec{S}(t)}{N}\\ \frac{\mathrm{d}\vec{E}(t)}{dt} & =\beta_{1}\left[M^{\star}\vec{I}(t)+\beta_{2}\bar{M}C^{\star}\frac{{\vec{I}(t)}}{N}\right]\frac{\vec{S}(t)}{N}-\nu\vec{E}(t)\\ \frac{\mathrm{d\vec{S}(t)}}{dt} & =-\epsilon\frac{\vec{S}(t)}{N}-\beta_{t}\left[M^{\star}\vec{I}(t)+\beta_{2}w_{t}\bar{M}C^{\star}\frac{{\vec{I}(t)}}{N}\right]\frac{\vec{S}(t)}{N}\\ \frac{\mathrm{d}\vec{E}(t)}{dt} & =\epsilon\frac{\vec{S}(t)}{N}+\beta_{t}\left[M^{\star}\vec{I}(t)+\beta_{2}w_{t}\bar{M}C^{\star}\frac{{\vec{I}(t)}}{N}\right]\frac{\vec{S}(t)}{N}-\nu\vec{E}(t)\\ \frac{\mathrm{d}\vec{I}(t)}{dt} & =\nu\vec{E}(t)-\gamma\vec{I}(t)\\ \frac{\mathrm{d}\vec{R}(t)}{dt} & =\gamma\vec{I}(t) \end{align*} where $\bar{M}$ is the global mean person-person contact rate. Parameters are: baseline infection rate $\beta_{1}$, commuting infection ratio $\beta_{2}$, latent period $\frac{1}{\nu}$, and infectious period $\frac{1}{\gamma}$. Typically, we assume that contact with commuters is $\beta_{2}=\frac{1}{3}$ of that between members of the same age-LAD combination assuming an 8 hour working day. where $\bar{M}$ is the global mean person-person contact rate, and $w_{t}$ is the total rail ticket sales in the UK expressed as a fraction of the 2019 mean (a proxy for reduction in travel). Parameters are: \subsection{Noise model (under construction)} \[ \epsilon_{t}=\begin{cases} \epsilon_{0} & \mbox{if}t