Predator-induced and mating limitation-induced Allee effects in a discrete-time [formula omitted] epidemic model

Abstract

We use a Susceptible–Infected–Immune–Susceptible (SIMS) discrete-time epidemic model that incorporates both predator-induced and mating limitation-induced Allee effects in the demographic dynamics to study the impact of an infectious disease on population persistence or extinction. When the Allee effect is strong, with or without the disease, the total population goes extinct whenever the initial total population size is smaller than the Allee threshold. However, when the Allee effect is weak or the initial population sizes are high and the total population is either asymptotically constant or under geometric growth, we use the next generation method to compute the basic reproductive number, ℜ0, and use it to predict the (uniform) persistence or extinction of the infective and immune populations.