Optimal policy design to mitigate epidemics on networks using an SIS model

TL;DR

This paper develops an optimal control strategy using model predictive control to mitigate epidemic spread on networks modeled by SIS, balancing health safety and societal normalcy without pharmaceutical interventions.

Contribution

It introduces a formal nonlinear control framework for the SIS epidemic model on networks, providing a novel approach to epidemic policy design.

Findings

Effective control policies can be derived using the proposed model predictive control approach.

The control scheme balances epidemic mitigation with minimal societal disruption.

Numerical simulations demonstrate the flexibility and performance of the control strategy.

Abstract

Understanding how to effectively control an epidemic spreading on a network is a problem of paramount importance for the scientific community. The ongoing COVID-19 pandemic has highlighted the need for policies that mitigate the spread, without relying on pharmaceutical interventions, that is, without the medical assurance of the recovery process. These policies typically entail lockdowns and mobility restrictions, having thus nonnegligible socio-economic consequences for the population. In this paper, we focus on the problem of finding the optimum policies that "flatten the epidemic curve" while limiting the negative consequences for the society, and formulate it as a nonlinear control problem over a finite prediction horizon. We utilize the model predictive control theory to design a strategy to effectively control the disease, balancing safety and normalcy. An explicit formalization of the control scheme is provided for the susceptible--infected--susceptible epidemic model over a network. Its performance and flexibility are demonstrated by means of numerical simulations.