Optimal Control of Interdependent Epidemics in Complex Networks

TL;DR

This paper develops a framework for optimally controlling two interdependent epidemics on complex networks, balancing control costs and epidemic severity through a gradient descent algorithm.

Contribution

It introduces a novel model capturing epidemic coupling, analyzes equilibrium stability, and proposes an optimal control strategy using a fixed point iterative scheme.

Findings

The control strategy effectively balances epidemic severity and control costs.

Optimal control induces switching between epidemic equilibria.

Theoretical results are validated through case studies.

Abstract

Optimal control of interdependent epidemics spreading over complex networks is a critical issue. We first establish a framework to capture the coupling between two epidemics, and then analyze the system's equilibrium states by categorizing them into three classes, and deriving their stability conditions. The designed control strategy globally optimizes the trade-off between the control cost and the severity of epidemics in the network. A gradient descent algorithm based on a fixed point iterative scheme is proposed to find the optimal control strategy. The optimal control will lead to switching between equilibria of the interdependent epidemics network. Case studies are used to corroborate the theoretical results finally.