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Stability of a diffusive-delayed HCV infection model with general cell-to-cell incidence function incorporating immune response and cell proliferation

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Abstract

In this work, we analyse the dynamics of a five-dimensional hepatitis C virus infection mathematical model including the spatial mobility of hepatitis C virus particles, the transmission of hepatitis C virus infection by mitosis process of infected hepatocytes with logistic growth, time delays, antibody response and cytotoxic T lymphocyte (CTL) immune response with general incidence functions for both modes of infection transmission, namely virus-to-cell as well as cell-to-cell. Firstly, we prove rigorously the existence, the uniqueness, the positivity and the boundedness of the solution of the initial value and boundary problem associated with the new constructed model. Secondly, we found that the basic reproductive number is the sum of the basic reproduction number determined by cell-free virus infection, determined by cell-to-cell infection and determined by proliferation of infected cells. It is proved the existence of five spatially homogeneous equilibria known as infection-free, immune-free, antibody response, CTL response and antibody and CTL responses. By using the linearization methods, the local stability of the latter is established under some rigorous conditions. Finally, we proved the existence of periodic solutions by highlighting the occurrence of a Hopf bifurcation for a certain threshold value of one delay.

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Authors and Affiliations

  1. Department of Mathematics, University of Maroua, Higher Teachers’ Training College, P.O. Box 55, Maroua, Cameroon

    Alexis Nangue

  2. Department of Mathematics and Computer Science, University of Maroua, Faculty of Science, P.O. Box 814, Maroua, Cameroon

    Yanick Junior Tchuimeni

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  1. Alexis Nangue
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  2. Yanick Junior Tchuimeni
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Contributions

AN provided the subject, wrote the introduction and the conclusion, checked the proofs and verified the calculation. He also managed the well-posedness of the initial and boundary value problem. YJT conceived the study, computed equilibria and studied their local stabilities. All the authors read and approved the final manuscript.

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Correspondence to Alexis Nangue.

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Nangue, A., Tchuimeni, Y.J. Stability of a diffusive-delayed HCV infection model with general cell-to-cell incidence function incorporating immune response and cell proliferation. Theory Biosci. 142, 235–258 (2023). https://doi.org/10.1007/s12064-023-00395-z

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