Control of Generalized Discrete-time SIS Epidemics via Submodular Function Minimization

In this paper, we study a novel control method for a generalized SIS epidemic process. In particular, we use predictive control to design optimal protective resource distribution strategies which balance the need to eliminate the epidemic quickly against the need to limit the rate at which protective resources are used. We expect that such a controller may be useful in mitigating the spread of biological diseases which do not confer immunity to those who have been infected previously, with sexually transmitted infections being a prominent example of such. Technically, this paper provides a novel contribution in demonstrating that the particular combinatorial optimal control problem used to design resource allocations has an objective function which is submodular, and so can be solved in polynomial time despite its combinatorial nature. We test the performance of the proposed controller with numerical simulations, and provide some comments on directions for future work.