Differ Equ Dyn Syst (October 2015) 23(4):403–413 DOI 10.1007/s12591-014-0221-y ORIGINAL RESEARCH Effect of Discretization on Dynamical Behavior in an Epidemiological Model Khalid Hattaf · Abid Ali Lashari · Brahim El Boukari · Noura Yousfi Published online: 27 August 2014 © Foundation for Scientific Research and Technological Innovation 2014 Abstract Dynamical behavior of two discrete epidemic models for disease with nonlinear incidence rate is studied. Both discrete models are derived from the continuous case by applying forward and backward Euler methods. The effect of the two different discretizations on the stability behavior of the disease-free equilibrium and endemic equilibrium is discussed. Finally, numerical simulations are presented to illustrate our theoretical results. Keywords Discrete epidemic model · Forward and backward Euler methods · Stability · Lyapunov functional Introduction The discrete-time models or difference equations are more accurate to describe epidemics than the continuous-time models or ordinary differential equations because statistical data on epidemics is collected in discrete time. In addition, the numerical simulations of continuous- time models are obtained by discretizing the models or by using other methods proposed by Khan et al. in [1–3]. In the literature, many discrete models have been developed in order to understand disease transmission dynamics. Zhou et al. [4] formulated a discrete mathematical model to inves- tigate the transmission of severe acute respiratory syndrome (SARS) and their simulation K. Hattaf (B ) · B. El Boukari · N. Yousfi Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, Sidi Othman, P.O Box 7955, Casablanca, Morocco e-mail: kh.hattaf@gmail.com; k.hattaf@yahoo.fr A. A. Lashari School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, Pakistan K. Hattaf Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Derb Ghalef, Casablanca, Morocco 123