Optimal control and numerical methods for hybrid stochastic SIS models |
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Institution: | 1. Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA;2. Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA |
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Abstract: | This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can influence the infectivity period, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results. |
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Keywords: | Controlled regime-switching diffusion SIS epidemic model Markov chain approximation Vaccination Disease transmission coefficient |
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