Mathematical analysis of a fractional-order epidemic model with nonlinear incidence function

Salih Djillali; Abdon Atangana; Anwar Zeb; Choonkil Park; Salih Djillali; Abdon Atangana; Anwar Zeb; Choonkil Park

doi:10.3934/math.2022123

AIMS Mathematics

2022, Volume 7, Issue 2: 2160-2175. doi: 10.3934/math.2022123

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Research article

Mathematical analysis of a fractional-order epidemic model with nonlinear incidence function

1.
Faculty of Exact and Computer Sciences, Mathematics Department, Hassiba Benbouali university, Chlef, Algeria
2.
Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, University of Tlemcen, Tlemcen, Algeria
3.
Institute for Groundwater Studies, faculty of natural and agricultural science, University of the Free State, Bloemfontein, 9300, South Africa
4.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, 22060, Khyber Pakhtunkhwa, Pakistan
5.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received: 16 September 2021 Accepted: 28 October 2021 Published: 08 November 2021
MSC : 49J15, 92D25, 93D20

In this paper, we are interested in studying the spread of infectious disease using a fractional-order model with Caputo's fractional derivative operator. The considered model includes an infectious disease that includes two types of infected class, the first shows the presence of symptoms (symptomatic infected persons), and the second class does not show any symptoms (asymptomatic infected persons). Further, we considered a nonlinear incidence function, where it is obtained that the investigated fractional system shows some important results. In fact, different types of bifurcation are obtained, as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation, where it is discussed in detail through the research. For the numerical part, a proper numerical scheme is used for the graphical representation of the solutions. The mathematical findings are checked numerically.
- nonlinear incidence,
- bifurcation analysis,
- fractional order derivative,
- symptomatic,
- asymptomatic
Citation: Salih Djillali, Abdon Atangana, Anwar Zeb, Choonkil Park. Mathematical analysis of a fractional-order epidemic model with nonlinear incidence function[J]. AIMS Mathematics, 2022, 7(2): 2160-2175. doi: 10.3934/math.2022123

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Abstract

In this paper, we are interested in studying the spread of infectious disease using a fractional-order model with Caputo's fractional derivative operator. The considered model includes an infectious disease that includes two types of infected class, the first shows the presence of symptoms (symptomatic infected persons), and the second class does not show any symptoms (asymptomatic infected persons). Further, we considered a nonlinear incidence function, where it is obtained that the investigated fractional system shows some important results. In fact, different types of bifurcation are obtained, as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation, where it is discussed in detail through the research. For the numerical part, a proper numerical scheme is used for the graphical representation of the solutions. The mathematical findings are checked numerically.

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