Asymptotic Stability of an Epidemic Reaction-Diffusion model

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Lamia Djebara
The purpose of this thesis is to study two types of problems, the question of global existence and global asymptotic stability of solutions of epidemic reaction-diffusion models. For the first, we establish a result on the global existence in time of the solutions of a class of disease epidemics systems, our techniques of proof are based on Lyapunov functional method. The asymptotic behavior of these solutions via a Lyapunov functional in particular case and under suitable conditions on the non-linearity we contribute to the study of the behaviour of the solutions. As for the second problem through, we calculate the basic reproduction number of reaction-diffusion epidemic phenomena and by analyzing the eigenvalues and an appropriately constructed Lyapunov functional we establish both locally and globally in the ODE and PDE cases, with giving numerical analysis examples of the two problems.