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Dynamic Behavior of a General Stochastic HIV Model with Virus-to-Cell Infection, Cell-to-Cell Transmission, Immune Response and Distributed Delays

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Abstract

In this paper, we construct a general four-dimensional delayed HIV infection model with virus-to-cell infection, cell-to-cell transmission, CTL immune response and parameter perturbations. By substitution, the four-dimensional delayed stochastic differential equations can be transformed into a degenerate eight-dimensional stochastic differential equations. The existence of the global positive solution of the system is obtained rigorously. By constructing appropriate Lyapunov functions, the existence of a stationary Markov process is derived when the stochastic reproduction number \({\mathcal {R}}_0^s\) is greater than one. Finally, we investigate the effects of noise level and the cell-to-cell transmission on the dynamic behavior of the model. Our model is a general model of the existing stochastic virus infection model, and the theoretical results improve and generalize the existing conclusion.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

The authors would like to thank the referees for their constructive criticisms and valuable comments, which helped us to improve our study. This work is supported by Shandong Provincial Natural Science Foundation (No. ZR2020MA039, ZR2021MA020), National Natural Science Foundation of China (No. 11871473), and the Fundamental Research Funds for the Central Universities (No. 22CX03030A).

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  1. College of Science, China University of Petroleum (East China), Qingdao, 266580, Shandong, China

    Yan Wang, Minmin Lu & Daqing Jiang

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  1. Yan Wang
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  2. Minmin Lu
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Correspondence to Yan Wang.

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Communicated by Changpin Li.

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Wang, Y., Lu, M. & Jiang, D. Dynamic Behavior of a General Stochastic HIV Model with Virus-to-Cell Infection, Cell-to-Cell Transmission, Immune Response and Distributed Delays. J Nonlinear Sci 33, 97 (2023). https://doi.org/10.1007/s00332-023-09955-5

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