Nonlinear Spatiotemporal Viral Infection Model with CTL Immunity: Mathematical Analysis

Jaouad Danane, Karam Allali, Léon Matar Tine and Vitaly Volpert
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Jaouad Danane: Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O.Box 146, Mohammedia, Morocco
Karam Allali: Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O.Box 146, Mohammedia, Morocco
Léon Matar Tine: CNRS UMR 5208 Institut Camille Jordan, University Claude Bernard Lyon 1, University de Lyon, 69622 Villeurbanne CEDEX, France
Vitaly Volpert: CNRS UMR 5208 Institut Camille Jordan, University Claude Bernard Lyon 1, University de Lyon, 69622 Villeurbanne CEDEX, France

Mathematics, 2020, vol. 8, issue 1, 1-13

Abstract: A mathematical model describing viral dynamics in the presence of the latently infected cells and the cytotoxic T-lymphocytes cells (CTL), taking into consideration the spatial mobility of free viruses, is presented and studied. The model includes five nonlinear differential equations describing the interaction among the uninfected cells, the latently infected cells, the actively infected cells, the free viruses, and the cellular immune response. First, we establish the existence, positivity, and boundedness for the suggested diffusion model. Moreover, we prove the global stability of each steady state by constructing some suitable Lyapunov functionals. Finally, we validated our theoretical results by numerical simulations for each case.

Keywords: viral infection; diffusion; Lyapunov functional; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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