Analysis of a Competitive Bivirus SIS Epidemic Model with Game Theoretic Social Distancing

Abstract

We propose a competitive bi-virus model with dynamic social distancing behavior. Our model illustrates how public perception of different viruses changes the conditions for their eradication, their coexistence, or the dominance of one over the other. We show that our model is not monotone, in contrast to the classic bi-virus model. We detail how social distancing behavior produces different sets of equilibria than the classic bi-virus model and changes the criteria for their stability. In particular, we detail the set of disease free equilibria (DFE) present in our model and identify necessary and sufficient conditions for almost global exponential stability of the same. We prove similar global results for all but one non-DFE isolated (unilateral) equilibria and local stability results for the remainder. We also consider coexistence equilibria; we show such equilibria, when they exist, take the form of lines of equilibria and give local conditions for their stability. Finally, we illustrate our theoretical findings with numerical examples.