The time to extinction for an SIS-household-epidemic model

TL;DR

This paper investigates how population size and household transmission influence the time until an SIS epidemic dies out, using stochastic models and approximations validated by simulations.

Contribution

It introduces two novel approximations for the time to extinction in household-structured SIS models, applicable across different transmission levels.

Findings

Mean time to extinction is minimized at moderate within-household transmission levels.

Two approximation methods effectively predict extinction times across transmission intensities.

Simulation results support the accuracy of the proposed models.

Abstract

We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission.