A stochastic epidemic model with nonmonotone incidence rate: Sufficient and necessary conditions for near-optimality

In this paper, we studied the near-optimal control of a stochastic susceptible-infected-recovered-susceptible (SIRS) model that includes a nonmonotone incidence rate. The near-optimal control problem was formulated by reducing the infected population while keeping the treatment cost to a minimum. We obtained the sufficient and necessary conditions for the near-optimality. We showed that any near-optimal control can be solved by using the Hamiltonian function to approximate the cost function. According to the adjoint equations, we derived the estimate for the error bound of the near-optimality. Numerical simulations were performed to illustrate the results and confirm the effect of treatment control on the disease dynamics.