Stability analysis of an epidemic model with two competing variants and cross-infections

Abstract The competition between pathogens is an essential issue in epidemiology. As the COVID-19 pandemic persists, new variants mutate resulting in further waves of infections. In this work, we propose a simple two-variant susceptible-infected-removed-susceptible (SIRS) model for studying the competitive epidemic processes. We obtain the global basic reproduction number of our proposed model and show that whether the epidemic persists or diminishes depends on the more contagious of the two variants. Furthermore, by studying the stability of the endemic equilibria, given a specific choice of parameters, we can predict \textcolor{red}{whether either variant will eventually dominate the competitive epidemic process, or if both variants will persist.}Numerical results show that periodic solutions become viable if the two variants’ cross-infectivities are unequal, i.e., recovery from one variant offers unequal protection against the other. In other words, reducing the infectivity of a variant via non-pharmaceutical interventions may trigger periodic or even chaotic behavior and paradoxically cause healthcare demand to increase. Note that our model is sufficiently general so as to be used for studying competitive behavior in other areas of science.