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Open AccessFeature PaperArticle

Nonlinear Spatiotemporal Viral Infection Model with CTL Immunity: Mathematical Analysis

Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O.Box 146, Mohammedia, Morocco
CNRS UMR 5208 Institut Camille Jordan, University Claude Bernard Lyon 1, University de Lyon, 69622 Villeurbanne CEDEX, France
INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia
Author to whom correspondence should be addressed.
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Mathematics 2020, 8(1), 52;
Received: 27 November 2019 / Revised: 12 December 2019 / Accepted: 13 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue The Application of Mathematics to Physics and Nonlinear Science)
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. View Full-Text
Keywords: viral infection; diffusion; Lyapunov functional; convergence viral infection; diffusion; Lyapunov functional; convergence
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Danane, J.; Allali, K.; Tine, L.M.; Volpert, V. Nonlinear Spatiotemporal Viral Infection Model with CTL Immunity: Mathematical Analysis. Mathematics 2020, 8, 52.

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