Mathematical models for the spread of multiple pathogens with cross-reactivity and waning of immunity

Abstract

Using several mathematical models for multi-strain epidemics, we study both theoretically and with stochastic simulations, how waning of overall immunity and cross-immunity impact the coexistence of multiple pathogen strains. The focus lies on one specific multi-strain model with individual-based continuous waning (cross-)immunity. For that model, we observe and study three immunity regimes: (1) short-term immunity, (2) long-term immunity and short-term cross immunity, and (3) long-term immunity and long-term cross-immunity, which differ in the observed number of coexisting strains. Equilibria densities are derived using a compartmentalised model. The short-term immunity coexistence regime is also studied through compartmental models, with analysis being conducted to: (i) influence of cross-immunity on strain density, and (ii) the densities of total infecteds and susceptibles, in addition to the chance of invasion of a new strain into an existing equilibrium. For the long-term immunity non-coexistence parameter regime, we obtain explicit approximations for the expected time between outbreaks.