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

ZongWang; Qimin Zhang; Xining Li; ZongWang; Qimin Zhang; Xining Li

doi:10.3934/mbe.2019066

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 3: 1348-1375. doi: 10.3934/mbe.2019066

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Research article

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

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, P.R. China
2.
School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. China

Received: 23 November 2018 Accepted: 21 January 2019 Published: 20 February 2019

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.
- SIV epidemic model,
- Markov chain,
- near-optimal control,
- Hamiltonian function,
- sufficient and necessary conditions
Citation: ZongWang, Qimin Zhang, Xining Li. Markovian switching for near-optimal control of a stochastic SIV epidemic model[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1348-1375. doi: 10.3934/mbe.2019066

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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.

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