Stochastic dynamics of HIV models with switching parameters and pulse control

Abstract This paper studies stochastic dynamics of epidemic HIV (Human Immunodeficiency Virus) models with switching parameters and pulse control. First, the switching is introduced by assuming that the models׳ parameters are time-varying (smoothly varying or abruptly varying) and the stochasticity is incorporated into the model of infected cells due to random effects. Stochastic switched HIV models are presented and investigated. Some new criteria ensuring stochastic stability for the above models are obtained by utilizing stochastic Ito lemma. Pulse control strategies are then applied to infected cells, and uninfected cells and infected cells, respectively. Each control strategy is analyzed to guarantee its success in eradicating the disease. Finally, the effectiveness of the proposed results is illustrated by some simulation examples, and future directions are also suggested.

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