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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Stability and Hopf Bifurcation of an Epidemic Model With Logistic Growth and Delay

Discontinuity, Nonlinearity, and Complexity 8(4) (2019) 379--389 | DOI:10.5890/DNC.2019.12.003

El Mehdi Lotfi$^{1}$, Khalid Hattaf$^{1}$,$^{2}$, Noura Yousfi$^{1}$

$^{1}$ Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco

$^{2}$ Centre Régional des Métiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco

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In this work, we propose and analyze a delayed epidemic model with logistic growth, in which the growth of susceptible individuals is governed by the logistic equation and the delay represents the latent period of the disease. Firstly, we prove that our model is mathematically and biologically well posed. In addition, the stability of equilibria and the existence of Hopf bifurcation are established. Moreover, several epidemic models existing in the previous studies are extended and generalized. Finally, some numerical simulations are given to illustrate our main results.


We would like to express our gratitude to the editor and the anonymous reviewers for their constructive comments and suggestions, which helped to enrich this paper. An earlier version of the paper has been presented as conference abstract in Fourth International Conference on Complex Dynamical Systems in Life Sciences: Modeling and Analysis 4thICCDS’2016, october 26, 2016, Ibn Zohr University, Agadir, Morocco.


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