Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis ‎Incidence Rate and a Constant Infectious Period

PDF
  • Abdelali Raji_allah*1,
  • Hamad Talibi Alaoui2,
  1. Department of Mathematics , Faculty of Sciences, Chouaib Doukkali University B. P. 20, 24000, El Jadida, Morocco
  2. Department of Mathematics , Faculty of Sciences, Chouaib Doukkali University B. P. 20, 24000, El Jadida, Morocco

Revised: 08-01-2019

Accepted: 23-05-2019

Published in Issue 01-06-2019

How to Cite

Raji_allah, A., & Talibi Alaoui, H. (2019). Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis ‎Incidence Rate and a Constant Infectious Period. International Journal of Mathematical Modelling & Computations, 9(2), 83-100. http://oiccpress.com/ijm2c/article/view/11315

Abstract

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using comparison arguments. In contrast, if R0 > 1, we see that the disease-free equilibrium is unstable and the endemic equilibrium is permanent and locally asymptotically stable and we give sufficient conditions for the global asymptotic stability of the endemic equilibrium.
PDF