On the optimal control of virus spread in networks

We study the design of optimal controllers for virus spread dynamics over undirected networks. The network designer is capable of controlling the curing rates of the nodes, and his objective is to reduce infection across the network at minimum cost. We employ Pontryagin's maximum principle to study the switching behavior of optimal controllers. Further, we propose two static control laws and identify graph classes over which the static control laws exhibit performance similar to that of the optimal dynamic controller. Finally, we propose a linear transformation for the virus spread dynamics and demonstrate that the optimal controllers for these dynamics exhibit at most a single switch.