Two-strain competition in quasi-neutral stochastic disease dynamics

TL;DR

This paper introduces a new perturbation method to analyze stochastic competition between two strains in epidemic models, revealing how noise influences fixation probabilities and strain dominance.

Contribution

It develops a novel perturbation approach for quasi-neutral stochastic competition, applying it to two epidemic models, including a previously unstudied SIR model with population turnover.

Findings

Shot noise causes one strain to fixate and the other to go extinct.

The slow strain has an advantage for typical initial conditions.

The fast strain is more likely to dominate when few infectives are introduced.

Abstract

We develop a new perturbation method for studying quasi-neutral competition in a broad class of stochastic competition models, and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic Susceptible-Infected-Susceptible (SIS) model. Here we extend previous results due to Parsons and Quince (2007), Parsons et al (2008) and Lin, Kim and Doering (2012). The second model, a two-strain generalization of the stochastic Susceptible-Infected-Recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of sub-population sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the sub-populations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.