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Journal of Applied Nonlinear Dynamics 13(1) (2024) 97--128 | DOI:10.5890/JAND.2024.03.008

Fatiha Najm, Radouane Yafia

Department of Mathematics Faculty of Sciences, Ibn Tofail University, Campus Universitaire B.P. 133, Kénitra, Morocco

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Abstract

In this paper, we study a delayed spatio-temporal mathematical model which modeling the spreading of viral infection in the tissues and the activation of virus-specific T lymphocytes with a new explicit virus load function ``bi-phasic and tri-phasic". The model is given in reaction diffusion systems with two delays which represent the local interaction and the propagation of the virus in tissues. The reduced and layer subsystems are studied and we establish that the slow manifold is an attracting one. We prove that the diffusion has no effect on the dynamics of the system, but time delays can modify the dynamics of the system with/without diffusion. Numerical simulations are carried out to illustrate such situations.

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