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Optimal strategy of vaccination and treatment in an SIRS model with Markovian switching
Author(s) -
Mu Xiaojie,
Zhang Qimin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5378
Subject(s) - pontryagin's minimum principle , mathematics , mathematical optimization , a priori and a posteriori , markov decision process , vaccination , maximum principle , white noise , markov process , markov chain , epidemic model , stochastic modelling , stochastic process , optimal control , medicine , statistics , virology , population , philosophy , environmental health , epistemology
Medical treatment and vaccination decisions are often sequential and uncertain. Markov decision process is an appropriate means to model and handle such stochastic dynamic decisions. This paper studies the near‐optimality of a stochastic SIRS epidemic model that incorporates vaccination and saturated treatment with regime switching. The stochastic model takes white noises and color noise into account. We first prove some priori estimates of the susceptible, infected, and recovered populations. Moreover, we establish some sufficient and necessary conditions of the near‐optimality by Pontryagin stochastic maximum principle. Our results show that the two kinds of environmental noises have great impacts on the infectious diseases. Finally, we illustrate our conclusions through numerical simulations.