Analysis, state estimation, and control for the networked competitive multi-virus SIR model

This paper proposes a novel discrete-time multi-virus susceptible–infected–recovered (SIR) model that captures the spread of competing epidemics over a population network. First, we provide sufficient conditions for the infection levels of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model that captures the summation of all the viruses’ infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. Third, we present a sufficient, but not necessary, condition for the model to be strongly locally observable, and, assuming that the network has only infected or recovered individuals, a necessary and sufficient condition for the model to be strongly locally observable. We prove that the estimation error of our proposed estimator converges to zero asymptotically with the observer gain. Finally, we present a distributed feedback controller which guarantees that each virus dies out at an exponential rate. We then show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.