Optimal Resource Allocation to Control Epidemic Outbreaks in Networked Populations

We study the problem of controlling epidemic outbreaks in networked populations by distributing protection resources throughout the nodes of the network. We assume that two types of protection resources are available: (i) Preventive resources able to defend individuals in the population against the spreading of the disease (such as vaccines or disease-awareness campaigns), and (ii) corrective resources able to neutralize the spreading (such as antidotes). We assume that both preventive and corrective resources have an associated cost and study the problem of finding the cost-optimal distribution of resources throughout the networked population. We analyze these questions in the context of a viral outbreak and study the following two problems: (i) Given a fixed budget, find the optimal allocation of preventive and corrective resources in the network to achieve the highest level of disease containment, and (ii) when a budget is not specified, find the minimum budget required to eradicate the disease. We show that both resource allocation problems can be efficiently solved for a wide class of cost functions. We illustrate our approach by designing optimal protection strategies to contain an epidemic outbreak that propagates through the air transportation network.