Modeling and analyzing competitive epidemic diseases with partial and waning virus-specific and cross-immunity

In this paper, we consider a novel mathematical modeling framework for the spread of two competitive diseases in a well-mixed population. The proposed framework, which we term a bivirus SIRIS model, encapsulates key real-world features of natural immunity, accounting for different levels of (partial and waning) virus-specific and cross protection acquired after recovery. Formally, the proposed framework consists of a system of coupled nonlinear ordinary differential equations that builds on a classical bivirus susceptible-infected-susceptible model by means of the addition of further states to account for (temporarily) protected individuals. Through the analysis of the proposed framework and of two specializations, we offer analytical insight into how natural immunity can shape a wide range of complex emergent behaviors, including eradication of both diseases, survival of the fittest one, or even steady-state co-existence of the two diseases.