Event-triggered control for mitigating SIS spreading processes

Abstract

In this paper, we investigate the problem of designing event-triggered controllers for containing epidemic processes in complex networks. We focus on a deterministic susceptible–infected–susceptible (SIS) model, which is one of the well-known, fundamental models that capture the epidemic spreading. The event-triggered control is particularly formulated in the context of viral spreading, in which control inputs (e.g., the amount of medical treatments, a level of traffic regulations) for each subpopulation are updated only when the fraction of the infected people in the subpopulation exceeds a prescribed threshold. We analyze the stability of the proposed event-triggered controller and derive a sufficient condition for a prescribed control objective to be achieved. Moreover, we propose a novel emulation-based approach towards the design of the event-triggered controller, and show that the problem of designing the event-triggered controller can be solved in polynomial time using a geometric programming. We illustrate the effectiveness of the proposed approach through numerical simulations using an air transportation network.