Dynamics and Persistence of a Generalized Multi-strain SIS Model

by Scott Greenhalgh, Tabitha Henriquez, Michael Frutschy, and Rebecah Leonard

Non-autonomous differential equation compartmental models are powerful tools for predicting trajectories of recurrent epidemics. However, using these models can complicate solution analysis compared to their autonomous counterparts, as the criteria for understanding long-term behavior are often only computable numerically. Our work presents a simple, yet general, non-autonomous SIS model with algebraic expressions for the stability and coexistence criteria of multi-strain periodic solutions, as well as a single-strain asymptotically periodic solution in terms of elementary functions. To illustrate our model’s utility, we fit it to US syphilis data, assessing its ability to match past trends and its predictive accuracy for future outbreaks.

A non-autonomous multi-strain SIS model: persistence of periodic solutions, co-existence, and an asymptotically periodic single-strain solution in terms of elementary functions.