Stochastic Model of SIR Epidemic Modelling

TL;DR

This paper compares deterministic and stochastic SIR epidemic models with demography, highlighting their similar behavior when R0 ≤ 1 and differences when R0 > 1 through simulations.

Contribution

It provides a comparative analysis of deterministic and stochastic SIR models with demography, emphasizing their differing interpretations for R0 > 1.

Findings

Models behave similarly when R0 ≤ 1.

Differences emerge in model interpretations when R0 > 1.

Simulations support the comparative analysis.

Abstract

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.