Monkeypox dynamical system with stability and computational analysis of the transmission

Volume 39, Issue 3, pp 300--324 https://dx.doi.org/10.22436/jmcs.039.03.01

Publication Date: April 08, 2025 Submission Date: December 17, 2024 Revision Date: January 04, 2025 Accteptance Date: February 19, 2025

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Authors

U. Khan - Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan. N. Ali - Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan. I. Ahmad - Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan. H. Khan - Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia. - Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan. D. K. Almutairi - Department of Mathematics, College of Science Al-Zulf, Majmaah University, 11952 Al‑Majmaah, Saudi Arabia. J. Alzabut - Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia. - Department of Industrial Engineering, OSTIM Technical University, 06374 Ankara, Türkiye. M. A. Azim - Preparatory Year Programme, College of Humanities and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia.

Abstract

This work offers a deterministic approach for the movement of monkeypox (Mpox) virus environmental transmission in the context of immunization and quarantine. It emphasizes the critical role of awareness and treatments in potentially slowing the spread of the disease. It highlights how global awareness and the use of medications, supported by a mathematical model (MM), can effectively reduce the incidence of newly acquired diseases and help control pandemic disease. This work improves our understanding of the structure and behavior of mpox, which affects control and prevention strategies. For this, population are {classified} into two parts, namely, human and rodent population. In this study, a novel mathematical model (MM) of the Mpox is developed and examined. For this, boundedness and positivity, both equilibrium states (DFE, EE), stability analysis (local and global) of the model are studied and analyzed {with the DFE and EE points, respectively}. Furthermore, bifurcation and sensitivity analysis of the model are investigated {using} the central manifold theory and {the} forward index method, respectively. Furthermore, numerical simulations of the model are performed by the \(RK\)-4 method, to validate the analytical findings.

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Keywords

• Monkeypox model
• equilibrium states
• the basic reproductive number
• stability analysis
• sensitivity and bifurcation analysis
• numerical simulations

MSC

•  34A08
•  34A09
•  34A34

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