study of a mathematical model of an epidemic via dynamic programming approach

We use some recent developments in dynamics programming method to obtain a rigorous solution of the epidemic model formulated in [19] as an unsolved problem. in fact, this problem is proposed in the context of using pontryagin’s maximum principle. we use a certain refinement of cauchy’s method of characteristics for stratified hamilton-jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by a certain admissible control. the optimality is justified by using of one of the well-known verification theorems as an argument for sufficient optimality conditions.