The Near-Optimal Control Of Stochastic SIV Epidemic Model

Infectious diseases have always been a major enemy that endangers human physical and mental health and affects human normal life.The new outbreak of pneumonia in 2020 will not only cause a large number of deaths,but also cause huge losses to the society and economy.Studying the spread and control of epidemics through mathematical modeling has become a hot topic.We often assume that the parameters of the epidemic models are constants,however,due to changes in ambient temperature and humidity.Markov process can reveal how to affect the spread of infectious diseases.The paper reveals how noise affects infectious disease system.The following two aspects will be studied:1.We have take markov chains,vaccination and saturated treatment control into a random SIV infectious disease model,and the near-optimal control problem of SIV system was analyzed.The sufficient and necessary conditions for the near-optimal control problem is proved based on the Pontryagin stochastic maximum principle.Numerical simulations demonstrate the effectiveness of the theoretical results and verify the effectiveness of saturation treatment and vaccination for the SIV model.2.Impulse vaccination strategy and markov switching were introduced into the random SIV infectious disease model.Based on the Pontryagin stochastic maximum principle,we give the sufficient condition for the near optimal control of a stochastic SIV model.Further,we give the necessary conditions for the near optimal control of the SIV model with impulse control.Theoretical results show that impulse vaccination ways can effectively inhibit the spread of infectious disease.Finally,several numerical examples are given to verify the impulse vaccination valid.