Networked Competitive Bivirus SIS Models: The Discrete-Time Case

Status: Paper under review (IEEE Open Journal of Control Systems) · Collaborators: Sebin J. Gracy, Ji Liu, Tamer Başar, César A. Uribe · Affiliation: Rice University

We analyze a discrete-time, networked, competitive bivirus susceptible–infected–susceptible (SIS) model in which two viruses spread and compete across a meta-population. The system admits three kinds of equilibria — the disease-free equilibrium, single-virus endemic equilibria (one virus persists while the other dies out), and coexistence equilibria (both persist).

We show the model is strongly monotone and, under suitable assumptions, admits no periodic orbits, then establish conditions for the existence of — and, in several cases, convergence to — these equilibria in terms of the two viruses’ reproduction numbers. We give sufficient and necessary conditions for coexistence equilibria, identify parameters yielding a locally exponentially attractive line of coexistence equilibria, and validate the theory with extensive simulations, including on real-world networks such as the Massachusetts county travel graph and New York City taxi data.

Materials

• Paper — Networked Competitive Bivirus SIS Model: Analysis of the Discrete-Time Case (with S. J. Gracy, J. Liu, T. Başar, C. A. Uribe): under review at the IEEE Open Journal of Control Systems.
• Slides — Gulf Coast Undergraduate Research Symposium 2024 (oral presentation): PDF · Google Slides · abstract