Dynamic Behavior and Numerical Results for an SIR Epidemic Model with Distributed Delay, Vaccination and Treatment

Abdelhai Elazzouzi; Abdesslem Lamrani Alaoui; Mouhcine Tilioua; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 126

Dynamic Behavior and Numerical Results for an SIR Epidemic Model with Distributed Delay, Vaccination and Treatment

Abdelhai Elazzouzi, Abdesslem Lamrani Alaoui, Mouhcine Tilioua, Abdessamad Tridane

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 28, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: In this work, we study the global dynamics of an SIR epidemic model with a wide class of generalized nonlinear incidence rate, distributed delay, vaccination and treatment. By constructing a Lyapunov functionals, we show that the disease free equilibrium state is globally asymptotically stable when the basic reproduction number R0 is less than or equal to one, and that the disease endemic equilibrium is globally asymptotically stable when R0 is greater than one. we provide a numerical results to illustrate the eect of vaccination and treatment on our model.