A comprehensive study of monkeypox disease through fractional mathematical modeling

Year 2025, Volume: 5 Issue: 1, 65 - 96, 31.03.2025

M. Manivel , A. Venkatesh , Shyamsunder Kumawat

https://doi.org/10.53391/mmnsa.1571609

Abstract

This research investigates a fractional-order mathematical model for analyzing the dynamics of Monkeypox (Mpox) disease using the Caputo-Fabrizio derivative. The model incorporates both human and rodent populations, aiming to elucidate the disease's transmission mechanics, which is demonstrated to be more effective than integer-order models in capturing the complex nature of disease spread. The study determines the fundamental reproduction number ($R_{0}$) while assessing the existence and uniqueness of the solutions. Numerical simulations are conducted to validate the model using Adams-Bashforth technique and illustrate the influence of different factors on the progression of the disease. The findings shed light on Mpox control and prevention, emphasizing the importance of fractional calculus in epidemiological modeling.

Keywords

Adams-Bashforth technique, Caputo-Fabrizio derivative, existence and uniqueness, fixed point theorem, monkeypox virus

Ethical Statement

The authors state that this research complies with ethical standards. This research does not involve either human participants or animals.

References

• [1] Worldometer, United States Population, (2022). https://www.worldometers.info/ world-population/us-population/
• [2] Centers for Disease Control and Prevention (CDC), What You Should Know About Monkeypox, (2022). https://www.cdc.gov/poxvirus/monkeypox/
• [3] World Health Organization (WHO), Monkeypox, (2022). https://www.who.int/news-room/ factsheets/detail/Mpox
• [4] Bunge, E.M., Hoet, B., Chen, L., Lienert, F., Weidenthaler, H., Baer, L.R. and Steffen, R. The changing epidemiology of human monkeypox-A potential threat? A systematic review. PLoS Neglected Tropical Diseases, 16(2), e0010141, (2022).
• [5] Bhatter, S., Jangid, K., Abidemi, A., Owolabi, K.M. and Purohit, S.D. A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks. Decision Analytics Journal, 6, 100156, (2023).
• [6] Jose, S.A., Yaagoub, Z., Joseph, D., Ramachandran, R. and Jirawattanapanit, A. Computational dynamics of a fractional order model of chickenpox spread in Phuket province. Biomedical Signal Processing and Control, 91, 105994, (2024).
• [7] Okyere, S. and Ackora-Prah, J. Modeling and analysis of monkeypox disease using fractional derivatives. Results in Engineering, 17, 100786, (2023).
• [8] Peter, O.J., Kumar, S., Kumari, N., Oguntolu, F.A., Oshinubi, K. and Musa, R. Transmission dynamics of Monkeypox virus: a mathematical modelling approach. Modeling Earth Systems and Environment, 8, 3423–3434, (2022).
• [9] Venkatesh, A., Manivel, M. and Baranidharan, B. Numerical study of a new time-fractional Mpox model using Caputo fractional derivatives. Physica Scripta, 99(2), 025226, (2024).
• [10] Manivel, M., Venkatesh, A., Arunkumar, K., Prakash Raj, M. and Shyamsunder. A mathematical model of the dynamics of the transmission of monkeypox disease using fractional differential equations. Advanced Theory and Simulations, 7(9), 2400330, (2024).
• [11] Venkatesh, A., Manivel, M., Arunkumar, K., Prakash Raj, M., Shyamsunder and Purohit, S.D. A fractional mathematical model for vaccinated humans with the impairment of Monkeypox transmission. European Physical Journal Special Topics, (2024).
• [12] Bozkurt, F., Baleanu, D. and Bilgil, H. A mathematical model of mobility-related infection and vaccination in an epidemiological case. Computer Methods in Biomechanics and Biomedical Engineering, 1-21, (2024).
• [13] Öztürk, Z., Bilgil, H. and Sorgun, S. Application of fractional SIQRV model for SARS-CoV-2 and stability analysis. Symmetry, 15(5), 1048, (2023).
• [14] Öztürk, Z., Yousef, A., Bilgil, H. and Sorgun, S. A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs. An International Journal of Optimization and Control: Theories & Applications, 14(2), 134-146, (2024).
• [15] Jothika, S. and Radhakrishnan, M. Dynamics of an SIR pandemic model using constrained medical resources with time delay. Communications in Mathematical Biology and Neuroscience, 2023, 90, (2023).
• [16] Bankuru, S.V., Kossol, S., Hou, W., Mahmoudi, P., Rychtáˇr, J. and Taylor, D. A game-theoretic model of Monkeypox to assess vaccination strategies. PeerJ, 8, e9272, (2020).
• [17] Manivel, M., Venkatesh, A., Kumar, K.A., Raj, M.P., Fadugba, S.E. and Kekana, M. Quantitative modeling of monkeypox viral transmission using Caputo fractional variational iteration method. Partial Differential Equations in Applied Mathematics, 13, 101026, (2025).
• [18] Usman, S. and Adamu, I.I. Modeling the transmission dynamics of the monkeypox virus infection with treatment and vaccination interventions. Journal of Applied Mathematics and Physics, 5(12), 2335-2353, (2017).
• [19] Caputo, M. and Fabrizio, M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73-85, (2015).
• [20] Losada, J. and Nieto, J.J. Properties of a new fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 87-92, (2015).
• [21] Van den Driessche, P. and Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1- 2), 29-48, (2002).
• [22] Atangana, A. and Owolabi, K.M. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena, 13(1), 3, (2018).
• [23] Li, S., Ullah, S., AlQahtani, S.A., Tag, S.M. and Akgül, A. Mathematical assessment of Monkeypox with asymptomatic infection: Prediction and optimal control analysis with real data application. Results in Physics, 51, 106726, (2023).