New numerical dynamics of the fractional monkeypox virus model transmission pertaining to nonsingular kernels

Maysaa Al Qurashi; Saima Rashid; Ahmed M. Alshehri; Fahd Jarad; Farhat Safdar; Maysaa Al Qurashi; Saima Rashid; Ahmed M. Alshehri; Fahd Jarad; Farhat Safdar

doi:10.3934/mbe.2023019

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 402-436. doi: 10.3934/mbe.2023019

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New numerical dynamics of the fractional monkeypox virus model transmission pertaining to nonsingular kernels

1.
Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia
2.
Department of Mathematics, Saudi Electronic University, Riyadh, Saudi Arabia
3.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
4.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
5.
Department of Mathematics, Cankaya University, Ankara, Turkey
6.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
7.
Department of Mathematics, SBK for Women University, Quetta, Pakistan

Academic Editor: Wandi Ding

Received: 03 July 2022 Revised: 22 September 2022 Accepted: 25 September 2022 Published: 09 October 2022

Monkeypox ($ \mathbb{MPX} $) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system's equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system's disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus's transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.
- Monkeypox virus model,
- Atangana-Baleanu differential operators,
- existence-uniqueness,
- qualitative analysis,
- Lagrangre interpolating polynomial
Citation: Maysaa Al Qurashi, Saima Rashid, Ahmed M. Alshehri, Fahd Jarad, Farhat Safdar. New numerical dynamics of the fractional monkeypox virus model transmission pertaining to nonsingular kernels[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 402-436. doi: 10.3934/mbe.2023019

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Abstract

Monkeypox ($ \mathbb{MPX} $) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system's equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system's disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus's transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.

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