On a stochastic model of epidemic spread with an application to competing infections

TL;DR

This paper analyzes a stochastic epidemic model in large populations, examining the different phases of spread, the interaction of competing strains, and the final epidemic outcomes using branching processes and differential equations.

Contribution

It introduces a comprehensive analysis of epidemic phases and models the interaction of competing strains with immunity, providing insights into final infection proportions.

Findings

Initial epidemic approximated by branching process

Differential equations describe later epidemic phases

Interaction of strains affects final infection distribution

Abstract

A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the process is approximated by a branching process. It is discussed for how long time this approximation is valid. When a non-negligible proportion of the population is already infected the process can be studied using differential equations. In a final phase the spread will fade out. The results are used to investigate what happens if two strains of infectious agents, with different potential for spread, are simultaneously introduced in a totally susceptible population. It is assumed that an infection causes immunity, and that a person can only be infected by one strain. The two epidemics will initially develop approximately as independent branching processes. However, if both strains causes large epidemics they will, due to immunity, eventually interact. We will mainly be interested in the final outcome of the spread, i.e., how large proportion of the population is infected by the different strains.