Optimal curing policy for epidemic spreading over a community network with heterogeneous population

TL;DR

This paper develops an optimal, cost-effective curing strategy for epidemic control over community networks, leveraging network structure and mean-field models to improve resource allocation.

Contribution

It introduces a novel approach to determine cost-optimal curing policies using graph theory and mean-field approximation for heterogeneous community networks.

Findings

Epidemic threshold can be computed via a reduced dynamical system.

Optimal curing policy is obtained by solving a convex minimization problem.

Algorithm for two-level curing problem has polynomial time complexity.

Abstract

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.