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Article http://dx.doi.org/10.26855/jamc.2021.12.010

Partial Differential Equations of A Virus Dynamical Model

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Urbain Traoré

Laboratory of Mathematics and Informatique (LAMI), Joseph KI-ZERBO University, Ouagadougou, Burkina Faso.

*Corresponding author: Urbain Traoré

Published: December 13,2021

Abstract

In this work, we investiguate a reaction-diffusion model with homogeneous Neumann boundary conditions of virus transmission. The model that we study in work is a generalization of the model developed by Zhang, et al.; in other words, we are trying to understand the influence of diffusion on virus dynamics. We prove global existence, uniqueness, positivity and boundness of the solution using a variational theory and some other useful tools from functional analysis. From the characteristic equation, we derive the local stability of the equilibriums. Moreover, the global asymptotical properties of the free-virus equilibrium and the endemic equilibruims of the model are studied by constructsing of a suitable Lyapunov functions. Finally, numerical simulations are performed to support the theoretical results obtained. Our numerical results indicate that the introduction of the diffusion in the model does not suppressthe dynamics of the virus, one obtains globally the configurations that in the absence of thediffusion. However, the mathematical analysis becomes more complicated.

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How to cite this paper

Partial Differential Equations of A Virus Dynamical Model

How to cite this paper: Urbain Traoré. (2021) Partial Differential Equations of A Virus Dynamical ModelJournal of Applied Mathematics and Computation5(4), 321-330.

DOI: http://dx.doi.org/10.26855/jamc.2021.12.010