Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function

A. Lamrani Alaoui; M. Tilioua; M. R. Sidi Ammi; P. Agarwal

doi:10.1007/978-981-16-2450-6_2

Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function

A. Lamrani Alaoui
, M. Tilioua
, M. R. Sidi Ammi
, P. Agarwal

Nonlinear Dynamic Research Centre (NDRC)

University of Moulay Ismail
International College of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

4 Scopus citations

Abstract

In this work, a fractional order SIR epidemic model is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of solutions to the considered model. We also study the existence of equilibrium points. Some sufficient conditions are derived to ensure, in terms of the basic reproduction number, the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, numerical simulations are illustrated to verify the validity of our theoretical results.

Original language	English
Title of host publication	Infosys Science Foundation Series in Mathematical Sciences
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	17-33
Number of pages	17
DOIs	https://doi.org/10.1007/978-981-16-2450-6_2
State	Published - 2021

Publication series

Name	Infosys Science Foundation Series in Mathematical Sciences
ISSN (Print)	2364-4036
ISSN (Electronic)	2364-4044

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Fractional derivative
Global stability
Lyapunov functionals
Nonlinear incidence function

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10.1007/978-981-16-2450-6_2

Cite this

Alaoui, A. L., Tilioua, M., Sidi Ammi, M. R., & Agarwal, P. (2021). Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function. In Infosys Science Foundation Series in Mathematical Sciences (pp. 17-33). (Infosys Science Foundation Series in Mathematical Sciences). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-981-16-2450-6_2

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title = "Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function",

abstract = "In this work, a fractional order SIR epidemic model is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of solutions to the considered model. We also study the existence of equilibrium points. Some sufficient conditions are derived to ensure, in terms of the basic reproduction number, the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, numerical simulations are illustrated to verify the validity of our theoretical results.",

keywords = "Fractional derivative, Global stability, Lyapunov functionals, Nonlinear incidence function",

author = "Alaoui, \{A. Lamrani\} and M. Tilioua and \{Sidi Ammi\}, \{M. R.\} and P. Agarwal",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.",

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language = "English",

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Alaoui, AL, Tilioua, M, Sidi Ammi, MR & Agarwal, P 2021, Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function. in Infosys Science Foundation Series in Mathematical Sciences. Infosys Science Foundation Series in Mathematical Sciences, Springer Science and Business Media Deutschland GmbH, pp. 17-33. https://doi.org/10.1007/978-981-16-2450-6_2

Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function. / Alaoui, A. Lamrani; Tilioua, M.; Sidi Ammi, M. R. et al.
Infosys Science Foundation Series in Mathematical Sciences. Springer Science and Business Media Deutschland GmbH, 2021. p. 17-33 (Infosys Science Foundation Series in Mathematical Sciences).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function

AU - Alaoui, A. Lamrani

AU - Tilioua, M.

AU - Sidi Ammi, M. R.

AU - Agarwal, P.

PY - 2021

Y1 - 2021

N2 - In this work, a fractional order SIR epidemic model is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of solutions to the considered model. We also study the existence of equilibrium points. Some sufficient conditions are derived to ensure, in terms of the basic reproduction number, the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, numerical simulations are illustrated to verify the validity of our theoretical results.

AB - In this work, a fractional order SIR epidemic model is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of solutions to the considered model. We also study the existence of equilibrium points. Some sufficient conditions are derived to ensure, in terms of the basic reproduction number, the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, numerical simulations are illustrated to verify the validity of our theoretical results.

KW - Fractional derivative

KW - Global stability

KW - Lyapunov functionals

KW - Nonlinear incidence function

UR - https://www.scopus.com/pages/publications/85117614499

U2 - 10.1007/978-981-16-2450-6_2

DO - 10.1007/978-981-16-2450-6_2

M3 - Chapter

AN - SCOPUS:85117614499

T3 - Infosys Science Foundation Series in Mathematical Sciences

SP - 17

EP - 33

BT - Infosys Science Foundation Series in Mathematical Sciences

PB - Springer Science and Business Media Deutschland GmbH

ER -

Alaoui AL, Tilioua M, Sidi Ammi MR, Agarwal P. Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function. In Infosys Science Foundation Series in Mathematical Sciences. Springer Science and Business Media Deutschland GmbH. 2021. p. 17-33. (Infosys Science Foundation Series in Mathematical Sciences). doi: 10.1007/978-981-16-2450-6_2

Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function

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