Global Dynamics and Traveling Waves of a Delayed Diffusive Epidemic Model with Specific Nonlinear Incidence Rate
El Mehdi Lotfi, Khalid Hattaf, Noura Yousfi
Journal of Advances in Mathematics and Computer Science · pp. 1–17 · Published 24 Dec 2016
10.9734/BJMCS/2017/30573Abstract
In this paper, we investigate the global stability and the existence of traveling waves for a delayed diffusive epidemic model. The disease transmission process is modeled by a specific nonlinear function that covers many common types of incidence rates. In addition, the global stability of the disease-free equilibrium and the endemic equilibrium is established by using the direct Lyapunov method. By constructing a pair of upper and lower solutions and applying the Schauder fixed point theorem, the existence of traveling wave solution which connects the two steady states is obtained and characterized by two parameters that are the basic reproduction number and the minimal wave speed. Furthermore, the models and main results studied the existence of traveling waves presented in the literature are extended and generalized.
Cited by 2
Adnane Boukhouima, Houssine Zine, El Mehdi Lotfi · Mathematical Analysis of Infectious Diseases · 2022
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