Near-optimal control for a stochastic multi-strain epidemic model with age structure and Markovian switching

Stochastic noise can affect the dynamics of infectious diseases. In this paper, a new stochastic multi-strain epidemic model with white noise, Markovian switching, vaccination control and age structure is established. Some priori estimates of the susceptible, infected and recovered are obtained. Under the condition of the objective function is minimised, we formulate sufficient and necessary conditions for the near-optimal control problems of the system, which is using a nearly maximum condition of the Hamiltonian function. The great influence of age structure, white noise, Markovian switching and vaccination control on the dynamical behaviour of infectious diseases and the existence of near-optimal control are demonstrated by numerical simulations.