Multiplicity of Endemic Equilibria for a Diffusive SIS Epidemic Model with Mass-Action

SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 732-755, April 2024.
Abstract. We study a diffusive Susceptible-Infected-Susceptible (SIS) epidemic model with the mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria (EE). Our results answer some open questions on previous studies related to disease extinction or persistence when [math] and the multiplicity of EE solutions when [math]. Interestingly, even with such a simple nonlinearity induced by the mass-action, we show that the diffusive epidemic model may have an S-shaped or backward bifurcation curve of EE solutions. This strongly highlights the impacts of environmental heterogeneity on the spread of infectious diseases as the basic reproduction number alone is insufficient as a threshold quantity to predict its extinction. Our results also shed some light on the significance of disease transmission mechanisms.