A robust numerical study on modified Lumpy skin disease model

Parveen Kumar; Sunil Kumar; Badr Saad T. Alkahtani; Sara S. Alzaid; Parveen Kumar; Sunil Kumar; Badr Saad T. Alkahtani; Sara S. Alzaid

doi:10.3934/math.20241116

AIMS Mathematics

2024, Volume 9, Issue 8: 22941-22985. doi: 10.3934/math.20241116

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A robust numerical study on modified Lumpy skin disease model

1.
Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 15 March 2024 Revised: 08 July 2024 Accepted: 09 July 2024 Published: 25 July 2024
MSC : 26A33, 34A08, 78A70, 93C10, 93C15

This paper was to present a mathematical model of non-integer order and demonstrated the detrimental consequences of lumpy skin disease (LSD). The LSD model included primarily affected cattle and other animals, particularly buffalo and cows. Given the significant drop in the number of livestock and dairy products, it was essential to use mathematical models to raise awareness of this issue. We examined the suggested LSD model to understand as well as every possible avenue that could result in the illness spreading throughout the community. Ulam-Hyers stability made it easier to analyze the stability of the LSD model, and fixed-point theory was a valuable tool for finding the existence and uniqueness of the solution to the suggested model. We have used new versions of power law and exponential decay fractional numerical methods. Numerical calculations were showing the influence of various fractional orders on the spread of disease and provided more informations than integer orders for the sensitive parameters of the proposed model. The graphical depiction is showed an understanding of the proposed LSD model.
Citation: Parveen Kumar, Sunil Kumar, Badr Saad T. Alkahtani, Sara S. Alzaid. A robust numerical study on modified Lumpy skin disease model[J]. AIMS Mathematics, 2024, 9(8): 22941-22985. doi: 10.3934/math.20241116

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Abstract

This paper was to present a mathematical model of non-integer order and demonstrated the detrimental consequences of lumpy skin disease (LSD). The LSD model included primarily affected cattle and other animals, particularly buffalo and cows. Given the significant drop in the number of livestock and dairy products, it was essential to use mathematical models to raise awareness of this issue. We examined the suggested LSD model to understand as well as every possible avenue that could result in the illness spreading throughout the community. Ulam-Hyers stability made it easier to analyze the stability of the LSD model, and fixed-point theory was a valuable tool for finding the existence and uniqueness of the solution to the suggested model. We have used new versions of power law and exponential decay fractional numerical methods. Numerical calculations were showing the influence of various fractional orders on the spread of disease and provided more informations than integer orders for the sensitive parameters of the proposed model. The graphical depiction is showed an understanding of the proposed LSD model.

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