Open Access

ARTICLE

Mathematical Model of the Monkeypox Virus Disease via Fractional Order Derivative

Rajagopalan Ramaswamy^1,*, Gunaseelan Mani², Deepak Kumar³, Ozgur Ege^4,*

1 Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, 11942, Saudi Arabia
2 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, India
3 Department of Mathematics, Lovely Professional University, Phagwara, 144411, India
4 Department of Mathematics, Faculty of Science, Ege University, Bornova, 35100, Turkey

* Corresponding Authors: Rajagopalan Ramaswamy. Email: ; Ozgur Ege. Email:

(This article belongs to the Special Issue: Analytical and Numerical Solution of the Fractional Differential Equation)

Computer Modeling in Engineering & Sciences 2025, 143(2), 1843-1894. https://doi.org/10.32604/cmes.2025.063672

Received 21 January 2025; Accepted 24 April 2025; Issue published 30 May 2025

Abstract

The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No. 3 is “Good Health and Well-being”, which mainly emphasizes the strategies to be adopted for maintaining a healthy life. The Monkeypox Virus disease was first reported in 1970. Since then, various health initiatives have been taken, including by the WHO. In the present work, we attempt a fractional model of Monkeypox virus disease, which we feel is crucial for a better understanding of this disease. We use the recently introduced fractional derivative to closely examine the Monkeypox virus disease model. The evaluation of this model determines the existence of two equilibrium states. These two stable points exist within the model and include a disease-free equilibrium and endemic equilibrium. The disease-free equilibrium has undergone proof to demonstrate its stability properties. The system remains stable locally and globally whenever the effective reproduction number remains below one. The effective reproduction number becoming greater than unity makes the endemic equilibrium more stable both globally and locally than unity. To comprehensively study the model’s solutions, we employ the Picard-Lindelof approach to investigate their existence and uniqueness. We investigate the Ulam-Hyers and UlamHyers Rassias stability of the fractional order nonlinear framework for the Monkeypox virus disease model. Furthermore, the approximate solutions of the fractional order Monkeypox virus disease model are obtained with the help of a numerical technique combining the Lagrange polynomial interpolation and fundamental theorem of fractional calculus with the fractional derivative.

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