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Stationary distribution and extinction of a multi-stage HIV model with nonlinear stochastic perturbation

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Abstract

In this paper, we investigate a stochastic multi-stage model to evaluate the influence of treatment intensification with the integrase inhibitor raltegravir on viral load and 2-LTR dynamics in HIV patients under suppressive therapy. Firstly, it is proven that the model has a unique global positive solution. Secondly, by constructing a Lyapunov function, we establish sufficient conditions for the existence of a unique ergodic stationary distribution if \(R_{0}^{S}>1\). Thirdly, we obtain sufficient criterions \(R_{0}^{s}<1\) for disease extinction. Finally, the analytical results are demonstrated via two simulation examples. Our contribution also concentrates on proposing a method constructing Lyapunov function, which can be successfully used for the research about stationary distribution of epidemic model with nonlinear stochastic perturbation.

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Acknowledgements

The authors thank the editor and reviewers for their valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Qingdao University of Technology, Qingdao, 266520, People’s Republic of China

    Chun Lu

  2. Department of Environmental Science, School of Environment and Municipal Engineering, Qingdao University of Technology, Qingdao, 266520, People’s Republic of China

    Guanzhen Sun

  3. Qindao College, Qingdao University of Technology, Qingdao, 266520, People’s Republic of China

    Yanmin Zhang

Authors
  1. Chun Lu
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  2. Guanzhen Sun
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  3. Yanmin Zhang
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All authors contributed equally and significantly in writing this paper.

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Correspondence to Chun Lu.

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Funding

This work is supported by grants from the Natural Science Foundation of Shandong Province of China (Nos. ZR2018MA023, ZR2020QA008, ZR2019BA022), the National Natural Science Foundation of China under grants no. 11901329, a Project of Shandong Province Higher Educational Science and Technology Program of China (Nos. J16LI09).

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Lu, C., Sun, G. & Zhang, Y. Stationary distribution and extinction of a multi-stage HIV model with nonlinear stochastic perturbation. J. Appl. Math. Comput. 68, 885–907 (2022). https://doi.org/10.1007/s12190-021-01530-z

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