An Optimal Control Problem Over Infected Networks

We study an optimal control problem over a network whose nodes are infected by a virus. The infection levels in the network evolve according to a nonlinear dynamical system that belongs to the susceptible-infected-susceptible epidemiological models class. A network designer attempts to regulate the infection levels in the network via adapting the curing rates of the nodes. We show that the optimal controller of this problem exhibits multiple switches between the allowed actions. Further, we present a method for approximating the optimal controller while keeping the deviation from the optimal cost at a minimum. We support our findings by numerical studies.