Greedy and speedy: optimal vaccination strategies in multi-region heterogeneous networks

Vaccinations mechanisms are common strategies for controlling the spread of viral spreading processes, such as epidemics and computer viruses. Their supply is often limited, and thus devising optimal strategies for their allocation and for their time of administration can be of high value to fight the epidemic spread. We account for arbitrary heterogeneous networks (populations) and consider the problem of multi-region systems. We prove a general property of the effective reproduction number: its reduction (under SIR models) is convex. Using this property, we analyze the effects of vaccination strategies on the acquirement of herd immunity and derive an efficient greedy algorithm that finds the optimal (HIT minimizing) allocation and administration timing of vaccines.