Time-dependent non-homogeneous stochastic epidemic model of SIR type

TL;DR

This paper extends a stochastic SIR epidemic model to include time-dependent encounters and quarantine effects, providing analytical insights and simulations on disease spread dynamics.

Contribution

It introduces a time-dependent stochastic SIR model with quarantine parameters and derives analytical descriptions and the basic reproduction number.

Findings

Disease spread is significantly affected by daily encounter distribution.

Time dependence influences epidemic dynamics.

Quarantine measures impact the basic reproduction number.

Abstract

To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a possible quarantine of the infectious individuals. We provide an analytic description of this Markovian model and investigate its dynamics. Both a diffusion approximation and the basic reproduction number are derived. Through several simulations, we show how the evolution of a disease is affected by the distribution of the number of daily encounters and its dependence on time.