Extinction Dynamics and Control in Adaptive Networks

Disease control is of paramount importance in public health. Moreover, models of disease spread are an important component in implementing effective vaccination and treatment campaigns. However, human behavior in response to an outbreak has only recently been included in epidemic models on networks. Here we develop the mathematical machinery to describe the dynamics of extinction in finite populations that include human adaptive behavior. The formalism enables us to compute the optimal, fluctuation-induced path to extinction, and predict the average extinction time in adaptive networks as a function of the adaptation rate. We find that both observables have several unique scalings depending on the relative speed of infection and adaptivity. Finally, we discuss how the theory can be used to design optimal control programs in general networks, by coupling the effective force of noise with treatment and human behavior.