Benjamin Catalano | Searcharxiv

arXiv2026

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

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.

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arXiv2025

Game-theoretic Social Distancing in Competitive Bi-Virus SIS Epidemics

Numerous elements drive the spread of infectious diseases in complex real-world networks. Of particular interest is social behaviors that evolve in tandem with the spread of disease. Moreover, recent studies highlight the importance of understanding how multiple strains spread simultaneously through a population (e.g. Delta and Omicron variants of SARS-CoV-2). In this paper, we propose a bi-virus SIS epidemic model coupled with a game-theoretic social distancing behavior model. The behaviors are governed by replicator equations from evolutionary game theory. The prevalence of each strain impacts the choice of an individual to social distance, and, in turn, their behavior affects the spread of each virus in the SIS model. Our analysis identifies equilibria of the system and their local stability properties, which reveal several isolated fixed points with varying levels of social distancing. We find that endemic co-existence is possible only when the reproduction numbers of both strains are equal. Assuming the reproduction number for each virus is the same, we identify suitable parameter regimes that give rise to lines of coexistence equilibria. Moreover, we also identify conditions for local exponential stability of said lines of equilibria. We illustrate our findings with several numerical simulations.

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