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Stochastic effects on an HIV/AIDS infection model with incomplete diagnosis

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  • Rao, Feng
  • Luo, Junling

Abstract

In this paper, we establish a stochastic differential equation model of the HIV/AIDS infection including four classes: susceptible individuals, undiagnosed HIV infected, diagnosed HIV infected and AIDS infected individuals. For the deterministic model, we obtain that the basic reproduction number R0 can determine whether there is a unique disease-free equilibrium or an endemic equilibrium, and show the solution of the model is positive and global. The mathematical analysis of the stochastic model (SDE) corresponding to the deterministic model (ODE) is investigated to determine the conditions for the stability of the random equilibria. The reproduction number R0s of the SDE model is derived, and by applying the Markov semigroups, it shows that the threshold parameter R0s can be used to control the stochastic dynamics of the model. What’s more, by solving the Fokker-Planck equation, we derive an expression of the probability density function of the SDE model around the quasi-endemic equilibrium of the ODE model under a certain condition. A series of numerical simulations are performed to illustrate the analytical results. Our study demonstrates that (i) reducing the recruitment rate of susceptible population and increasing diagnosis rate are the effective methods for controlling the HIV/AIDS disease; and (ii) large environmental noise intensity and small valid disease contact rate can suppress the outbreak of disease.

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  • Rao, Feng & Luo, Junling, 2021. "Stochastic effects on an HIV/AIDS infection model with incomplete diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006986
    DOI: 10.1016/j.chaos.2021.111344
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    References listed on IDEAS

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    Cited by:

    1. Rao, Feng & Kang, Yun, 2023. "Dynamics of a stochastic prey–predator system with prey refuge, predation fear and its carry-over effects," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Tan, Yiping & Cai, Yongli & Sun, Xiaodan & Wang, Kai & Yao, Ruoxia & Wang, Weiming & Peng, Zhihang, 2022. "A stochastic SICA model for HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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