Stochastic Model of SIR Epidemic Modelling

Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with demography. The behaviour of the model approached by deteministic and stochastic models will be introduced, mainly using simulations. Furthermore, we will also investigate the dynamic of susceptibles in population in absence of infective. We have successfully showed that both deterministic and stochastic models performed similar results when $R_0 \leq 1$. That is, the disease-free stage in the epidemic. But when $R_0 > 1$, the deterministic and stochastic approaches had different interpretations.