Differential Equations and Dynamical Systems

, Volume 23, Issue 4, pp 403–413 | Cite as

Effect of Discretization on Dynamical Behavior in an Epidemiological Model

  • Khalid HattafEmail author
  • Abid Ali Lashari
  • Brahim El Boukari
  • Noura Yousfi
Original Research


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.


Discrete epidemic model Forward and backward Euler methods Stability Lyapunov functional 


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2014

Authors and Affiliations

  • Khalid Hattaf
    • 1
    • 3
    Email author
  • Abid Ali Lashari
    • 2
  • Brahim El Boukari
    • 1
  • Noura Yousfi
    • 1
  1. 1.Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sikHassan II UniversityCasablancaMorocco
  2. 2.School of Natural SciencesNational University of Sciences and TechnologyIslamabadPakistan
  3. 3.Centre Régional des Métiers de l’Education et de la Formation (CRMEF)CasablancaMorocco

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