Analysis of dengue transmission using fractional order scheme

Kottakkaran Sooppy Nisar; Aqeel Ahmad; Mustafa Inc; Muhammad Farman; Hadi Rezazadeh; Lanre Akinyemi; Muhammad Mannan Akram; Kottakkaran Sooppy Nisar; Aqeel Ahmad; Mustafa Inc; Muhammad Farman; Hadi Rezazadeh; Lanre Akinyemi; Muhammad Mannan Akram

doi:10.3934/math.2022469

AIMS Mathematics

2022, Volume 7, Issue 5: 8408-8429. doi: 10.3934/math.2022469

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Analysis of dengue transmission using fractional order scheme

1.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam Bin Abdulaziz University, Saudi Arabia
2.
Department of Mathematics, Ghazi University D. G. Khan, Pakistan
3.
Biruni University, Department of Computer Engineering, Istanbul, Turkey
4.
Firat University, Science Faculty, Department of Mathematics, 23119 Elazig, Turkey
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
6.
Department of Mathematics and Statistics, University of Lahore, Lahore-54590, Pakistan
7.
Faculty of Engineering Technology Amol University of Special Modern Technologies Amol, Iran
8.
Department of Mathematics, Lafayette College, Easton, Pennsylvania, USA

Received: 02 November 2021 Revised: 22 January 2022 Accepted: 25 January 2022 Published: 28 February 2022
MSC : 37C75, 93B05, 65L07

In this paper, we will check the existence and stability of the dengue internal transmission model with fraction order derivative as well as analyze it qualitatively. The solution has been determined using Atangana-Baleanu in Caputo sense (ABC) with the help of Sumudu transform (ST). Atangana-Toufik (AT) and fractal fractional operator are used to analyze the dengue transmission which is an advanced approach for such types of biological models. Existence theory and uniqueness for the equilibrium solution are provided via nonlinear functional analysis and fixed point theory. Global stability of the system was also proved by using the Lyapunov function. Such kind of study helps us to analyze dengue transmission which shows the actual effect of dengue transmission in society, also will be helpful in future analysis and control strategies.
- dengue model,
- Sumudu transform,
- Atangana-Toufik scheme,
- uniqueness,
- fractal fractional operator
Citation: Kottakkaran Sooppy Nisar, Aqeel Ahmad, Mustafa Inc, Muhammad Farman, Hadi Rezazadeh, Lanre Akinyemi, Muhammad Mannan Akram. Analysis of dengue transmission using fractional order scheme[J]. AIMS Mathematics, 2022, 7(5): 8408-8429. doi: 10.3934/math.2022469

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Abstract

In this paper, we will check the existence and stability of the dengue internal transmission model with fraction order derivative as well as analyze it qualitatively. The solution has been determined using Atangana-Baleanu in Caputo sense (ABC) with the help of Sumudu transform (ST). Atangana-Toufik (AT) and fractal fractional operator are used to analyze the dengue transmission which is an advanced approach for such types of biological models. Existence theory and uniqueness for the equilibrium solution are provided via nonlinear functional analysis and fixed point theory. Global stability of the system was also proved by using the Lyapunov function. Such kind of study helps us to analyze dengue transmission which shows the actual effect of dengue transmission in society, also will be helpful in future analysis and control strategies.

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