AIMS Mathematics, 2020, 5(4): 2843-2857. doi: 10.3934/math.2020182.

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Fractional order SEIR model with generalized incidence rate

1 Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
2 Department of mathematics City university of Science and Information Technology, Peshawar, KP, Pakistan
3 Department of mathematics university of Peshawar, KP, Pakistan
4 Department of mathematics Abdul Wali Khan university, Mardan, KP, Pakistan

The incidence rate function describes the mechanism of a disease transmission and has a key role in mathematical epidemiology. In the present paper, we develop a fractional SEIR epidemic model in the Caputo sense with generalized incidence function. Initially, we present the existence and positivity of the Caputo SEIR epidemic model and calculate the basic reproduction number. Further, we investigate the model equilibria and prove the detail stability analysis of the model. Finally, the numerical simulations are provided for various values of fractional order α and different incidence rates. From the numerical simulations we conclude that the order of the fractional derivative plays a significant role to provides more insights about the disease dynamics.
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Keywords Incidence rate function; SEIR model; Caputo fractional derivative; stability analysis

Citation: Muhammad Altaf Khan, Sajjad Ullah, Saif Ullah, Muhammad Farhan. Fractional order SEIR model with generalized incidence rate. AIMS Mathematics, 2020, 5(4): 2843-2857. doi: 10.3934/math.2020182

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