A mathematical model for fractal-fractional monkeypox disease and its application to real data

Weerawat Sudsutad; Chatthai Thaiprayoon; Jutarat Kongson; Weerapan Sae-dan; Weerawat Sudsutad; Chatthai Thaiprayoon; Jutarat Kongson; Weerapan Sae-dan

doi:10.3934/math.2024414

AIMS Mathematics

2024, Volume 9, Issue 4: 8516-8563. doi: 10.3934/math.2024414

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A mathematical model for fractal-fractional monkeypox disease and its application to real data

1.
Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand; Email:weerawat.s@rumail.ru.ac.th
2.
Research Group of Theoretical and Computational Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand; Email: chatthai@go.buu.ac.th
3.
Department of Computer Engineering, Faculty of Engineering, Ramkhamhaeng University, Bangkok 10240, Thailand; Email: weerapan.s@rumail.ru.ac.th

Received: 25 December 2023 Revised: 13 February 2024 Accepted: 19 February 2024 Published: 28 February 2024
MSC : 26A33, 34A08, 65L09, 92D25, 92D30

In this paper, we developed a nonlinear mathematical model for the transmission of the monkeypox virus among populations of humans and rodents under the fractal-fractional operators in the context of Atangana-Baleanu. For the theoretical analysis, the renowned theorems of fixed points, like Banach's and Krasnoselskii's types, were used to prove the existence and uniqueness of the solutions. Additionally, some results regarding the stability of the equilibrium points and the basic reproduction number were provided. In addition, the numerical schemes of the considered model were established using the Adams-Bashforth method. Our analytical findings were supported by the numerical simulations to explain the effects of changing a few sets of fractional orders and fractal dimensions. Some graphic simulations were displayed with some parameters calculated from real data to understand the behavior of the model.
- monkeypox model,
- fractal-fractional operators,
- stability,
- existence and uniqueness,
- numerical Scheme
Citation: Weerawat Sudsutad, Chatthai Thaiprayoon, Jutarat Kongson, Weerapan Sae-dan. A mathematical model for fractal-fractional monkeypox disease and its application to real data[J]. AIMS Mathematics, 2024, 9(4): 8516-8563. doi: 10.3934/math.2024414

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Abstract

In this paper, we developed a nonlinear mathematical model for the transmission of the monkeypox virus among populations of humans and rodents under the fractal-fractional operators in the context of Atangana-Baleanu. For the theoretical analysis, the renowned theorems of fixed points, like Banach's and Krasnoselskii's types, were used to prove the existence and uniqueness of the solutions. Additionally, some results regarding the stability of the equilibrium points and the basic reproduction number were provided. In addition, the numerical schemes of the considered model were established using the Adams-Bashforth method. Our analytical findings were supported by the numerical simulations to explain the effects of changing a few sets of fractional orders and fractal dimensions. Some graphic simulations were displayed with some parameters calculated from real data to understand the behavior of the model.

References

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