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Global Threshold Dynamics of an Infection Age-Space Structured HIV Infection Model with Neumann Boundary Condition

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Abstract

This paper aims to the investigation of the global threshold dynamics of an infection age-space structured HIV infection model. The model is formulated in a bounded domain involving two infection routes (virus-to-cell and cell-to-cell) and Neumann boundary conditions. We first transform the original model to a hybrid system containing two partial differential equations and a Volterra integral equation. By appealing to the theory of fixed point problem together with Picard sequences, the well-posedness of the model is shown by verifying that the solution exists globally and the solution is ultimately bounded. Under the Neumann boundary condition, we establish the explicit expression of the basic reproduction number. By analyzing the distribution of characteristic roots of the associated characteristic equation in terms of the basic reproduction number, we achieve the local asymptotic stability of the steady states. The global asymptotic stability of the steady states is established by the technique of Lyapunov functionals, respectively. Numerical simulations are performed to validate our theoretical results.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments to the previous version of our manuscript. J. Wang was supported by National Natural Science Foundation of China (Nos. 12071115, 11871179), and Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems. R. Zhang was supported by the National Natural Science Foundation of China (No. 12101309), the China Postdoctoral Science Foundation (No. 2021M691577) and the Postdoctoral Fundation of Jiangsu Province.

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Authors and Affiliations

  1. School of Mathematical Science, Heilongjiang University, Harbin, 150080, People’s Republic of China

    Jinliang Wang & Yue Gao

  2. Department of Mathematics, College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, People’s Republic of China

    Ran Zhang

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  1. Jinliang Wang
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Wang, J., Zhang, R. & Gao, Y. Global Threshold Dynamics of an Infection Age-Space Structured HIV Infection Model with Neumann Boundary Condition. J Dyn Diff Equat 35, 2279–2311 (2023). https://doi.org/10.1007/s10884-021-10086-2

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