Markovian switching for near-optimal control of a stochastic SIV epidemic model

Abstract

As it is known that environmental perturbation is a key component of epidemic models, and Markov process reveals how the noise affects epidemic systems. The paper introduces Markov chain into a stochastic susceptible-infected-vaccination(SIV) epidemic model composed of vaccination and saturated treatment to analyze the near-optimal control. Based on Pontryagin stochastic maximum principle, the paper gives adequate and all necessary conditions for near-optimal control. Numerical simulations are presented to display the theoretical results and verify the effect of treatment control on epidemic diseases.

Keywords

• siv epidemic model
• markov chain
• near-optimal control
• hamiltonian function
• sufficient and necessary conditions