LibBi package: SIR

Synopsis

./init.sh

This fits the bridge weight function. GNU Octave and GPML are required. Running it is optional, as the included files already have this set up.

./run.sh

This samples from the posterior distribution using a Russian influenza data set.

octave --path oct/ --eval "plot_and_print"

This plots the results.

Description

This package includes a stochastic SIR (susceptible/infectious/recovered) epidemiological compartmental model of the form

$$\begin{eqnarray} dS(t) &=& -\beta(t)S(t)I(t), dt \\\ dI(t) &=& \left(\beta(t)S(t)I(t)-\nu(t)I(t)\right), dt \\\ dR(t) &=& \nu(t)I(t), dt \\\ d\log\beta(t) &=& \left(\theta_{\beta,1}-\theta_{\beta,2}\log\beta(t)\right), dt+\theta_{\beta,3}, dW_{\beta}(t) \\\ d\log\nu(t) &=& \left(\theta_{\nu,1}-\theta_{\nu,2}\log\nu(t)\right), dt+\theta_{\nu,3}, dW_{\nu}(t). \end{eqnarray}$$

It also includes an observational data set of an epidemic of Russian influenza at a boys boarding school (Anonymous 1978). As this is a closed system the observations are considered exact, and the task is to simulate diffusion bridges between the observed values, and to estimate parameters.

The model and data set were used as a test case in Del Moral & Murray (2014). The package may be used to reproduce the results in that paper.

References

Anonymous. Influenza in a boarding school. British Medical Journal, 1978, 1, 587.

Del Moral, P. & Murray, L. M. Sequential Monte Carlo with Highly Informative Observations, 2014. [arXiv]