# lawmurray/SIR

SIR package for LibBi.
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Latest commit 6260164 Aug 18, 2014
 Failed to load latest commit information. data May 15, 2014 oct May 16, 2014 .gitignore Apr 11, 2014 LICENSE Mar 18, 2014 MANIFEST Apr 29, 2014 META.yml Apr 29, 2014 README.md Aug 18, 2014 SIR.bi May 15, 2014 VERSION.md Mar 18, 2014 config.conf May 16, 2014 filter.conf Apr 29, 2014 init.sh Apr 29, 2014 posterior.conf May 16, 2014 qsub_run_bootstrap.sh Apr 15, 2014 qsub_run_bridge.sh Apr 15, 2014 run.sh May 16, 2014 run_bootstrap.sh May 15, 2014 run_bridge.sh May 15, 2014

# 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]