About stability analysis in epidemic reaction-diffusion model
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Date
2022
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Larbi Tebessi University - Tebessa
Abstract
The purpose of this thesis is to study the local and global asymptotic stability of the nonnegative constant steady states of an epidemic reaction-diffusion system (susceptible-infectious) with a nonlinear incidence in the case of ordinary and partial differential equations depending on the basic reproduction number, with determining the linearity of the studied system in both cases . Where the local asymptotic stability is determined by the nature of the eigenvalues, but for the global asymptotic stability we use the Lyapunov method, in addition to illustrate the analytical results through numerical examples
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The reaction-diffusion system, nonlinear incidence, global and local asymptotic stability, equilibrium, basic reproduction number, Lyapunov function, linearization., نموذج التفاعل والانتشار، حدوث غير خطي، الاستقرار المقارب الكلي والمحلي، التوازن، رقم الاستنساخ، دالة ليابونوف، التوسيع الخطي, Système de réaction-diffusion, incidence non linéaire, stabilité asymptotique globale et locale, équilibre, nombre de reproduction de base, fonction de Lyapunov, linéarisation.