Nonlinear and dynamic programming for epidemic intervention

This paper studies an optimal control problem for a discrete-time, deterministic Susceptible/Infective/Susceptible (SIS) epidemic with a finite time horizon. The problem involves finding the minimum of an objective function of a controlled process subject to the constraints of limited resources. Control sequences are obtained through two alternative methods: nonlinear programming (NLP) and dynamic programming (DP). The NLP approach is restricted to problems of low dimension and, therefore, by this algorithm, one must be satisfied with an optimization over a restrictive subspace of the possible control sequences, whereas DP has the capability of finding an optimal control sequence over a richer domain. The advantage of NLP is that it requires less processing resources and is therefore capable of providing approximate solutions to larger problems than the DP method. However, our results show that the DP solutions, because they are exact over a relatively long time horizon, can result in considerable reduction in cost. It is also found that for our SIS epidemic, the character of the NLP and DP solutions are considerably different.