  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.
