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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Bifurcation of Periodic Solutions of a Delayed SEIR Epidemic Model with Nonlinear Incidence Rate

Journal of Applied Nonlinear Dynamics 10(3) (2021) 351--367 | DOI:10.5890/JAND.2021.09.001

Amine Bernoussi

'{e}quations aux d'{e}riv'{e}es partielles, Alg`{e}bre et G'{e}om'{e}trie spectrales, Faculty of Science, Ibn Tofail University, BP 133, 14000 Kenitra, Morocco

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Abstract

In this paper, we propose the SEIR epidemic model with delay and nonlinear incidence rate. The resulting model has two possible equilibria: if $R_{0} \leq 1,$ then the SEIR epidemic model has a disease-free equilibrium and if $R_{0} > 1,$ then the SEIR epidemic model admits a unique endemic equilibrium. By using suitable Lyapunov functionals and LaSalle's invariance principle, the global stability of a disease-free equilibrium is established. Our main contribution affirms the existence of non constant periodic solutions which bifurcate from the endemic equilibrium when the delay crosses some critical values. Finally, some numerical simulations are presented to illustrate our theoretical results.

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