Analysis of a mathematical model for the spreading of the monkeypox virus with constant proportional-Caputo derivative operator

Jutarat Kongson; Chatthai Thaiprayoon; Weerawat Sudsutad; Jutarat Kongson; Chatthai Thaiprayoon; Weerawat Sudsutad

doi:10.3934/math.2025187

AIMS Mathematics

2025, Volume 10, Issue 2: 4000-4039. doi: 10.3934/math.2025187

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Research article

Analysis of a mathematical model for the spreading of the monkeypox virus with constant proportional-Caputo derivative operator

1.
Research Group of Theoretical and Computational Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
2.
Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand

Received: 22 November 2024 Revised: 08 February 2025 Accepted: 18 February 2025 Published: 27 February 2025
MSC : 26A33, 34A08, 65L09, 92D25, 92D30

This work comprehensively analyzed the monkeypox virus utilizing a deterministic mathematical model within a constant proportional-Caputo derivative framework. The suggested model considered the interplay of human and rodent populations by incorporating certain realistic vaccination parameters. Our study was a testament to the thoroughness of this work. We explored the uniqueness result using Banach's contraction principle. The solution's positivity and boundedness were studied in detail, as were the basic reproduction number and the stability analysis of the system's equilibrium conditions. We performed a variety of Ulam's stability analyses to guarantee the solution existed. Additionally, we implemented a decomposition formula to obtain the numerical scheme. This numerical approach allowed for numerical simulation as a graphical representation for certain real data sets and different parameter values in order to understand the model's dynamic behavior.
- monkeypox disease,
- constant proportional-Caputo,
- Ulam stability,
- numerical algorithm,
- basic reproduction number
Citation: Jutarat Kongson, Chatthai Thaiprayoon, Weerawat Sudsutad. Analysis of a mathematical model for the spreading of the monkeypox virus with constant proportional-Caputo derivative operator[J]. AIMS Mathematics, 2025, 10(2): 4000-4039. doi: 10.3934/math.2025187

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Abstract

This work comprehensively analyzed the monkeypox virus utilizing a deterministic mathematical model within a constant proportional-Caputo derivative framework. The suggested model considered the interplay of human and rodent populations by incorporating certain realistic vaccination parameters. Our study was a testament to the thoroughness of this work. We explored the uniqueness result using Banach's contraction principle. The solution's positivity and boundedness were studied in detail, as were the basic reproduction number and the stability analysis of the system's equilibrium conditions. We performed a variety of Ulam's stability analyses to guarantee the solution existed. Additionally, we implemented a decomposition formula to obtain the numerical scheme. This numerical approach allowed for numerical simulation as a graphical representation for certain real data sets and different parameter values in order to understand the model's dynamic behavior.

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