A State Feedback Controller for Mitigation of Continuous-Time Networked SIS Epidemics

TL;DR

This paper develops a state feedback control strategy for continuous-time networked SIS epidemic models, enabling real-time infection mitigation and ensuring system stability to disease-free or endemic states.

Contribution

It introduces a novel feedback controller that accounts for agent behavior changes, maintaining infection levels below thresholds and guaranteeing convergence to equilibrium states.

Findings

Controller effectively keeps infection levels below thresholds

Ensures convergence to disease-free or endemic equilibrium

Demonstrated via numerical simulations

Abstract

The paper considers continuous-time networked susceptible-infected-susceptible (SIS) diseases spreading over a population. Each agent represents a sub-population and has its own healing rate and infection rate; the state of the agent at a time instant denotes what fraction of the said sub-population is infected with the disease at the said time instant. By taking account of the changes in behaviors of the agents in response to the infection rates in real-time, our goal is to devise a feedback strategy such that the infection level for each agent strictly stays below a pre-specified value. Furthermore, we are also interested in ensuring that the closed-loop system converges either to the disease-free equilibrium or, when it exists, to the endemic equilibrium. The upshot of devising such a strategy is that it allows health administration officials to ensure that there is sufficient capacity in the healthcare system to treat the most severe cases. We demonstrate the effectiveness of our controller via numerical examples.