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.

这项工作的重点是在体制转换下对一类随机SIS流行病模型的最优控制。通过假设决策者可以影响传染期，我们的目标是使由于疾病，医疗以及对社会的不利影响而导致的预期折现成本降至最低。另外，提出了一种结合了疫苗接种的模型。通过使用马尔可夫链逼近方法逼近连续时间动力学来开发数值方案。结果表明，随着网格尺寸趋近于零，逼近方案收敛于最优策略。提供了数值示例来说明我们的结果。