  This work focuses on optimal controls of a class of stochastic SIS epidemic
models under regime switching. By assuming that a decision maker can either
influence the infectivity period or isolate infected individuals, 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.
