Global Dynamics and Traveling Waves of a Delayed Diffusive Epidemic Model with Speci c Nonlinear Incidence Rate
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 20, Issue 2
Abstract
In this paper, we investigate the global stability and the existence of traveling waves for a delayed di usive epidemic model. The disease transmission process is modeled by a speci c 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 xed 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.
Authors and Affiliations
El Mehdi Lot fi, Khalid Hattaf, Noura Yous fi
Keywords
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- EP ID EP321989
- DOI 10.9734/BJMCS/2017/30573
- Views 91
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