On the Analysis and Observability of a Networked Competitive Multi-Virus SIR Model
Ciyuan Zhang, Sebin Gracy, Tamer Başar, and Philip E. Paré
This work proposes a novel discrete-time multi-virus SIR (susceptible-infected-recovered) model that captures the spread of competing SIR virus over a computer network. First, we provide a sufficient condition for the infected proportion of all the computer viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses' infected proportions in each node, which represents the computers which are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be locally observable. We propose a Luenberger observer for the system state estimation and show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.