Abstract
This paper considels ani optimal-cointrol problem for the dyniamics of ati epidemic spread, the optimal cointrol beiing the level of medical program effort to achieve a terminal nuimber of infectives withini specified limits in a way that minimizes the present value of the social and medical costs over a finiite horizoni. Filst, the special polar cases of fixed alid free-end-points are solved for large as well as small capability of the health delivery system in delivering the medical care. The complete soltutioin to the general problem is then construicted from these polal cases. The fixed-end-poinit case with stfficiently large capability of the health delivery system is solved by utsing Green's theorem, while the other cases requiire additiolnal uise of switchilug point ainalysis based on the maximum priniciple. The optimal control is characterized by a combiniationl of bang-bang, impulse, anid singular cointrol, with the singular arc forming a turnpike. It is showin that the ttulrnpike behavior of the optimal control genieralizes to short horizon aiid botunded control sittiationis.
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