# SIRModel

class SIRModel = MarkovModel<SIRState, SIRParameter>

SIR (susceptible-infectious-recovered) model for infectious disease outbreaks in epidemiology.

### Usage

Run with:

birch sample \
--model SIRModel \
--input-file input/russian_influenza.json \
--output-file output/russian_influenza.json \
--ncheckpoints 14 \
--nparticles 100 \
--nsamples 10


The data set is of an outbreak of Russian influenza at a boy's boarding school in northern England (Anonymous, 1978). The model on which this is based is described in Murray et. al. (2018).

Any of the parameters and the initial conditions can be clamped by modifying the input file, input/russian_influenza.json.

### Details

The parameter model is given by: where $\lambda$ is a rate of interaction in the population, $\delta$ the probability of infection when a susceptible individual interacts with an infectious individual, and $\gamma$ the daily recovery probability.

The initial model for time $t = 0$ is:

The transition model for time $t$ is: where $\tau_t$ is the number of interactions between infectious and susceptible individuals, $\Delta i_t$ the number of newly infected individuals, and $\Delta r_t$ the number of newly recovered individuals.

Population counts are then updated: