Mutating Epidemic Processes Over Time-Varying Networks in Discrete-Time

Sebin Gracy, Philip. E. Pare, Henrik Sandberg, Karl Henrik Johansson

Published 2019-11-20Version 1

This paper studies epidemic processes over discrete-time periodic time-varying networks. Our objective is to find necessary and sufficient conditions for asymptotic convergence to the disease-free equilibrium (DFE). We provide, in terms of the joint spectral radius of a set of matrices, a sufficient condition for global asymptotic stability (GAS) of the DFE. Subsequently, we provide, in terms of the spectral radius of the product of matrices over an interval of size $p$, a necessary and sufficient condition for GAS of the DFE.