Mitigation of Discrete‐Time SIS Networked Epidemics: A Local State Feedback Approach

ABSTRACT The paper deals with a discrete‐time susceptible‐infected susceptible (SIS) networked epidemic model. In the model, nodes represent populations and the network links possible transmission pathways of the disease between populations. Our aim is to design a feedback controller so that the fraction of infected in each population node remains below a prespecified value for all time instants. To this end, we introduce a distributed control law at the node level. This control law can be realized by the population following announcements made by local policymakers to enhance nonpharmaceutical interventions such as hand‐washing, mask‐wearing, and social distancing. We show that with the controller in place not only do the fraction of infected in each population node stay below the prespecified level but also the state of the disease dynamics converges either to the disease‐free equilibrium or to a unique endemic equilibrium. It turns out that the endemic equilibrium is (element‐wise) smaller than the unique endemic equilibrium of the uncontrolled system. The theoretical findings are illustrated by numerical examples.