Network-Based Epidemic Control Through Optimal Travel and Quarantine Management

TL;DR

This paper develops a network-based framework for epidemic control by optimizing travel restrictions and quarantine strategies, linking network structure to disease dynamics and ensuring convergence of the proposed methods.

Contribution

It introduces an optimization approach for travel reduction and an expanded SIR model with quarantined states, connecting network structure to epidemic control.

Findings

Optimized travel reduction strategies depend on network structure.

Incorporating quarantined states improves epidemic containment.

Simulation validates effectiveness using Massachusetts county data.

Abstract

Motivated by the swift global transmission of infectious diseases, we present a comprehensive framework for network-based epidemic control. Our aim is to curb epidemics using two different approaches. In the first approach, we introduce an optimization strategy that optimally reduces travel rates. We analyze the convergence of this strategy and show that it hinges on the network structure to minimize infection spread. In the second approach, we expand the classic SIR model by incorporating and optimizing quarantined states to strategically contain the epidemic. We show that this problem reduces to the problem of matrix balancing. We establish a link between optimization constraints and the epidemic's reproduction number, highlighting the relationship between network structure and disease dynamics. We demonstrate that applying augmented primal-dual gradient dynamics to the optimal quarantine problem ensures exponential convergence to the KKT point. We conclude by validating our approaches using simulation studies that leverage public data from counties in the state of Massachusetts.