The awareness effect of the dynamical behavior of SIS epidemic model with Crowley-Martin incidence rate and holling type III treatment function

Document Type : Research Paper


1 Ministry of Education, Rusafa/1, Baghdad, Iraq

2 Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq

3 Centre Regional desMetiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco, & LAMS, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco


This article deals with the dynamical behaviors for a biological model of epidemic diseases with
holling type III treatment function. A Crowley-Martin formula to transmission of disease with
coverage media programs effect on the population are introduced and investigated. Through some
basic analyses, an explicit formula for the basic reproduction number of the model is calculated, and
some results such as the stability analysis and instability of all equilibrium points for the model are
established. The local bifurcation occurs near all equilibrium points for the model under some special
cases that are studied. The numerical simulations are executed to confirm the theoretical results