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Spatiotemporal Dynamics of a Generalized HBV Infection Model with Capsids and Adaptive Immunity

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Abstract

In this study, we propose and analyze a new mathematical model formulated by partial differential equations in order to better understand the mechanisms and dynamics of hepatitis B virus (HBV) infection in vivo. The proposed model incorporates the intracellular HBV DNA-containing capsids, spatial diffusion in both capsids and viruses, and adaptive immune response exerted by cytotoxic T lymphocytes and antibodies. Further, the infection process is modeled by a general incidence function that includes many cases existing in the literature. We first show the global existence, uniqueness, positivity and boundedness of solutions. The global stability and instability of equilibria are established by means of Lyapunov’s direct and indirect methods. Finally, numerical simulations are presented to illustrate the dynamical behaviors of the model and to support the theoretical results.

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Acknowledgements

The authors convey their gratitude to the learned reviewer for his/her valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, 208016, India

    Kalyan Manna

  2. Centre Régional des Métiers de l’Education et de la Formation (CRMEF), 20340, Derb Ghalef, Casablanca, Morocco

    Khalid Hattaf

  3. Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955, Sidi Othman, Casablanca, Morocco

    Khalid Hattaf

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  1. Kalyan Manna
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  2. Khalid Hattaf
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Correspondence to Khalid Hattaf.

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Manna, K., Hattaf, K. Spatiotemporal Dynamics of a Generalized HBV Infection Model with Capsids and Adaptive Immunity. Int. J. Appl. Comput. Math 5, 65 (2019). https://doi.org/10.1007/s40819-019-0651-x

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