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On an Age-Structured Hepatitis B Virus Infection Model with HBV DNA-Containing Capsids

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Abstract

In this paper, we study an age-structured hepatitis B virus model with DNA-containing capsids. We obtain the well-posedness of the model by reformulate the model as an abstract Cauchy problem, and we find a threshold number \(\mathfrak {R}_0\) for the existence of the steady states. The local stability of each steady states is established by linearizing the system and analyze the corresponding characteristic equation. Furthermore, we investigate the uniform persistence of the system and constructing Lyapunov functionals to show the global stability of each steady states. We observe that the virus-free steady state is globally asymptotically stable when \(\mathfrak {R}_0<1\), while the infection steady state is globally asymptotically stable when \(\mathfrak {R}_0>1\). Numerical simulations are also presented to support the analytical results.

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Acknowledgements

The authors are very grateful to the editors and two reviewers for their valuable comments and suggestions that have helped us improving the presentation of this paper. S. Liu was partially supported by the National Natural Science Foundation of China (Grant No.11871060). R. Zhang was partially supported by the National Natural Science Foundation of China (Grant No.11871179). The authors would like to thank Professor Shigui Ruan for his supervision and suggestions. The authors would also acknowledge the kind hospitality received from the Department of Mathematics at University of Miami, where part of the work was completed.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, 437100, China

    Sanhong Liu

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Ran Zhang

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  1. Sanhong Liu
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  2. Ran Zhang
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Correspondence to Ran Zhang.

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Communicated by Syakila Ahmad.

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Liu, S., Zhang, R. On an Age-Structured Hepatitis B Virus Infection Model with HBV DNA-Containing Capsids. Bull. Malays. Math. Sci. Soc. 44, 1345–1370 (2021). https://doi.org/10.1007/s40840-020-01014-6

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