The design of an efficient curing policy, able to stem an epidemic process atan affordable cost, has to account for the structure of the population contactnetwork supporting the contagious process. Thus, we tackle the problem ofallocating recovery resources among the population, at the lowest cost possibleto prevent the epidemic from persisting indefinitely in the network.Specifically, we analyze a susceptible-infected-susceptible epidemic processspreading over a weighted graph, by means of a first-order mean-fieldapproximation. First, we describe the influence of the contact network on thedynamics of the epidemics among a heterogeneous population, that is possiblydivided into communities. For the case of a community network, ourinvestigation relies on the graph-theoretical notion of equitable partition; weshow that the epidemic threshold, a key measure of the network robustnessagainst epidemic spreading, can be determined using a lower-dimensionaldynamical system. Exploiting the computation of the epidemic threshold, wedetermine a cost-optimal curing policy by solving a convex minimizationproblem, which possesses a reduced dimension in the case of a communitynetwork. Lastly, we consider a two-level optimal curing problem, for which analgorithm is designed with a polynomial time complexity in the network size.
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