Analysis of Monkeypox viral infection with human to animal transmission via a fractional and Fractal-fractional operators with power law kernel

Alia M. Alzubaidi; Hakeem A. Othman; Saif Ullah; Nisar Ahmad; Mohammad Mahtab Alam; Alia M. Alzubaidi; Hakeem A. Othman; Saif Ullah; Nisar Ahmad; Mohammad Mahtab Alam

doi:10.3934/mbe.2023287

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 6666-6690. doi: 10.3934/mbe.2023287

Previous Article Next Article

Research article Special Issues

Analysis of Monkeypox viral infection with human to animal transmission via a fractional and Fractal-fractional operators with power law kernel

1.
Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University, Saudi Arabia
2.
Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan
3.
Institute of Numerical Sciences Kohat University of Science and Technology (KUST) Kohat, Pakistan
4.
Department of Basic Medical Sciences, College of Applied Medical Science, King Khalid University, Abha 61421, Saudi Arabia

Academic Editor: Alexander Pisarchik

Received: 25 November 2022 Revised: 05 January 2023 Accepted: 17 January 2023 Published: 03 February 2023

Monkeypox (MPX) is a global public health concern. This infectious disease affects people all over the world, not just those in West and Central Africa. Various approaches have been used to study epidemiology, the source of infection, and patterns of transmission of MPX. In this article, we analyze the dynamics of MPX using a fractional mathematical model with a power law kernel. The human-to-animal transmission is considered in the model formulation. The fractional model is further reformulated via a generalized fractal-fractional differential operator in the Caputo sense. The basic mathematical including the existence and uniqueness of both fractional and fractal-fractional problems are provided using fixed points theorems. A numerical scheme for the proposed model is obtained using an efficient iterative method. Moreover, detailed simulation results are shown for different fractional orders in the first stage. Finally, a number of graphical results of fractal-fractional MPX transmission models are presented showing the combined effect of fractal and fractional orders on model dynamics. The resulting simulations conclude that the new fractal-fractional operator added more biological insight into the dynamics of illness.
- Monkeypox mathematical model,
- fractal-fractional Caputo operator,
- existence and uniqueness,
- numerical results
Citation: Alia M. Alzubaidi, Hakeem A. Othman, Saif Ullah, Nisar Ahmad, Mohammad Mahtab Alam. Analysis of Monkeypox viral infection with human to animal transmission via a fractional and Fractal-fractional operators with power law kernel[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6666-6690. doi: 10.3934/mbe.2023287

Related Papers:

Abstract

Monkeypox (MPX) is a global public health concern. This infectious disease affects people all over the world, not just those in West and Central Africa. Various approaches have been used to study epidemiology, the source of infection, and patterns of transmission of MPX. In this article, we analyze the dynamics of MPX using a fractional mathematical model with a power law kernel. The human-to-animal transmission is considered in the model formulation. The fractional model is further reformulated via a generalized fractal-fractional differential operator in the Caputo sense. The basic mathematical including the existence and uniqueness of both fractional and fractal-fractional problems are provided using fixed points theorems. A numerical scheme for the proposed model is obtained using an efficient iterative method. Moreover, detailed simulation results are shown for different fractional orders in the first stage. Finally, a number of graphical results of fractal-fractional MPX transmission models are presented showing the combined effect of fractal and fractional orders on model dynamics. The resulting simulations conclude that the new fractal-fractional operator added more biological insight into the dynamics of illness.

References

[1]	World Health Organization, Monkeypox, 2022. Available from: https://www.who.int/news-room/fact-sheets/detail/monkeypox.
[2]	World Health Organization, Monkeypox, 2022. Available from: https://www.who.int/news-room/questions-and-answers/item/monkeypox.
[3]	Centers for Disease Control and Prevention. Available from: https://www.cdc.gov/poxvirus/monkeypox/.
[4]	S. Ullah, M. A. Khan, M. Farooq, T. Gul, Modeling and analysis of tuberculosis (tb) in khyber pakhtunkhwa, pakistan, Math. Comput. Simul., 165 (2019), 181–199. https://doi.org/10.1016/j.matcom.2019.03.012 doi: 10.1016/j.matcom.2019.03.012
[5]	A. Khan, R. Ikram, A. Din, U. W. Humphries, A. Akgul, Stochastic covid-19 seiq epidemic model with time-delay, Results Phys., 30 (2021), 104775. https://doi.org/10.1016/j.rinp.2021.104775 doi: 10.1016/j.rinp.2021.104775
[6]	X. Liu, S. Ullah, A. Alshehri, M. Altanji, Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study, Chaos, Solitons Fractals, 153 (2021), 111534. https://doi.org/10.1016/j.chaos.2021.111534 doi: 10.1016/j.chaos.2021.111534
[7]	S. Usman, I. I. Adamu, Modeling the transmission dynamics of the monkeypox virus infection with treatment and vaccination interventions, J. Appl. Math. Phys., 5 (2017), 81078. https://doi.org/10.4236/jamp.2017.512191 doi: 10.4236/jamp.2017.512191
[8]	O. J. Peter, S. Kumar, N. Kumari, F. A. Oguntolu, K. Oshinubi, R. Musa, Transmission dynamics of monkeypox virus: a mathematical modelling approach, Model. Earth Syst. Environ., 8 (2022), 3423–3434. https://doi.org/10.1007/s40808-021-01313-2 doi: 10.1007/s40808-021-01313-2
[9]	C. P. Bhunu, S. Mushayabasa, J. Hyman, Modelling hiv/aids and monkeypox co-infection, Appl. Math. Comput., 218 (2012) 9504–9518. https://doi.org/10.1016/j.amc.2012.03.042 doi: 10.1016/j.amc.2012.03.042
[10]	A. Khan, Y. Sabbar, A. Din, Stochastic modeling of the monkeypox 2022 epidemic with cross-infection hypothesis in a highly disturbed environment, Math. Biosci. Eng., 19 (2022), 13560–13581. https://doi.org/10.3934/mbe.2022633 doi: 10.3934/mbe.2022633
[11]	I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier, 1998.
[12]	M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 1–13. http://dx.doi.org/10.12785/pfda/010201 doi: 10.12785/pfda/010201
[13]	A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 20 (2016), 763–769. https://doi.org/10.2298/TSCI160111018A doi: 10.2298/TSCI160111018A
[14]	O. J. Peter, F. A. Oguntolu, M. M. Ojo, A. O. Oyeniyi, R. Jan, I. Khan, Fractional order mathematical model of monkeypox transmission dynamics, Phys. Scr., 97 (2022), 084005. https://doi.org/10.1088/1402-4896/ac7ebc doi: 10.1088/1402-4896/ac7ebc
[15]	A. El-Mesady, A. Elsonbaty, W. Adel, On nonlinear dynamics of a fractional order monkeypox virus model, Chaos, Solitons Fractals, 164 (2022), 112716. https://doi.org/10.1016/j.chaos.2022.112716 doi: 10.1016/j.chaos.2022.112716
[16]	A. Atangana, Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system, Chaos, Solitons Fractals, 102 (2017), 396–406. https://doi.org/10.1016/j.chaos.2017.04.027 doi: 10.1016/j.chaos.2017.04.027
[17]	W. Wang, M. Khan, Analysis and numerical simulation of fractional model of bank data with fractal-fractional Atangana-Baleanu derivative, J. Comput. Appl. Math., 369 (2019), 112646. https://doi.org/10.1016/j.cam.2019.112646 doi: 10.1016/j.cam.2019.112646
[18]	X. P. Li, S. Ullah, H. Zahir, A. Alshehri, M. B. Riaz, B. A. Alwan, Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach, Results Phys., 34 (2022), 105179. https://doi.org/10.1016/j.rinp.2022.105179 doi: 10.1016/j.rinp.2022.105179
[19]	S. Qureshi, E. Bonyah, A. A. Shaikh, Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data, Phys. A, 535 (2019), 122496. https://doi.org/10.1016/j.physa.2019.122496 doi: 10.1016/j.physa.2019.122496
[20]	C. Li, F. Zeng, Numerical Methods for Fractional Calculus, Chapman and Hall/CRC, 2015.
[21]	A. Atangana, S. Qureshi, Modeling attractors of chaotic dynamical systems with fractal–fractional operators, Chaos, Solitons Fractals, 123 (2019), 320–337. https://doi.org/10.1016/j.chaos.2019.04.020 doi: 10.1016/j.chaos.2019.04.020

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)