Optimal resource allocation for containing epidemics on time-varying networks

This paper studies the Susceptible-Infected- Susceptible (SIS) epidemic model on time-varying interaction graphs in contrast to the majority of other works which only consider static graphs. After presenting the mean-field model and characterizing its stability properties, we formulate and solve an optimal resource allocation problem. More specifically, we first assume that a cost can be paid to reduce the amount of interactions certain nodes can have with others (e.g., by imposing travel restrictions between certain cities). Then, given a budget, we are interested in optimally allocating the budget to best combat the undesired epidemic. We show how this problem can be equivalently formulated as a geometric program and solved in polynomial time. Simulations illustrate our results.