Past Event: Center for Autonomy Seminar

Networked Competitive Bivirus SIS spread with Higher Order Interactions

Sebin Gracy, Assistant Professor, South Dakota School of Mines and Technology

Abstract

This talk explores the problem of the simultaneous spread of two competing viruses over a network of population nodes by also accounting for the possibility of higher-order interactions (HOI). To this end, we consider a continuous-time time-invariant competitive bivirus networked susceptible-infected-susceptible (SIS) HOI system. First, we show that, under the assumption that the hypergraph associated with the system is strongly connected, the model is strongly monotone. Subsequently, we show that, for generic parameter choices, the system admits only a finite number of equilibria, and that the Jacobian, evaluated at any equilibrium, is a nonsingular matrix. The aforementioned two findings together guarantee that the typical behavior of the model is convergence to some stable equilibrium point. The equilibria of this system are i) the disease-free equilibrium (DFE), ii) single-virus endemic equilibria, and iii) coexistence equilibria (where both viruses are present in separate fractions of a population node). We identify a parameter regime that admits the possibility of three equilibria (namely, the DFE, and two single-virus endemic equilibria) being simultaneously stable. We then provide sufficient conditions for the existence of a coexistence equilibrium, both for the same parameter regime as mentioned above, and for a different one. Thereafter, we identify a necessary condition for the existence of a coexistence equilibrium.

Biography

Sebin Gracy is an Assistant Professor in the department of Electrical Engineering and Computer Science at South Dakota School of Mines and Technology. Previously, he was a Post-Doctoral Associate in the Department of Electrical and Computer Engineering at Rice University, and even prior to that he was a Post-Doctoral Researcher in the Division of Decision and Control Systems in the School of Electrical Engineering and Computer Science at KTH Royal Institute of Technology. He obtained his Ph.D. degree at Universite Grenoble-Alpes in November, 2018. Prior to that, he obtained his M.S. and B.E. degrees in Electrical Engineering from the University of Colorado at Boulder and the University of Mumbai, in December, 2013 and June 2010, respectively. His research interests are in the realm of networked control systems. He is a member of the IEEE Control Systems Society.