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\begin{document}

\title{Stability Analysis of a Fractional-Order SEIR Epidemic Model with
General Incidence Rate and Time Delay}



\author[1]{mahiéddine kouche}%
\author[2]{Ilhem Gacem}%
\author[3]{Bedr' Eddine Ainseba}%
\affil[1]{University of Badji Mokhtar Annaba}%
\affil[2]{Universite Badji Mokhtar Annaba}%
\affil[3]{Universite Victor Segalen}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\begin{abstract}
In the present paper we investigate the qualitative behaviour of a
fractional SEIR model with general incidence rate function and time
delay where the fractional derivative is defined in the Caputo sense.
The basic reproduction number \$\textbackslash{}mathcal\{R\}\_\{0\}\$ is
derived using the method of next generation matrix and we give a
complete study of local stability of both free and endemic equilibrium.
Using Liapunov method we prove the global stability of free and endemic
equilibrium under some hypotheses on the parameters of the system.
Finally to illustrate our results, we use the model to predict the first
peak of the COVID-19 epidemic in Algeria.%
\end{abstract}%



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