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<p>Lumpy skin disease (LSD) is a potentially deadly viral disease of cattle that causes nodules on the skin, fever, and swollen lymph nodes. If left untreated, LSD can result in severe economic losses owing to reduced milk production, weight loss, and even death. To monitor the increasing prevalence of LSD and develop cost-effective prevention strategies, disease modeling is a crucial tool. We propose a fractional-order mathematical model for LSD that captures the interval between an individual contracting the infection and the onset of symptoms using the Mittag-Leffler kernel. The proposed system undergoes a qualitative study, including a quantitative investigation and a well-posedness assessment. We create endemic and disease-free equilibrium points and analyze the proposed system’s stability. The major reproductive number condition is derived for a newly developed system to verify the rate of spread of the lumpy virus. The first derivative tests are utilized using the Lyapunov function for the analysis of global stability. In addition, fixed-point theory and the Lipschitz condition are employed to verify that the precise solution is bounded and unique, which are the key properties to verify the newly developed model. To analyze the impact of the fractional operator using numerical simulations and highlight the influence of the disease through various parameters, a two-step Lagrange polynomial is utilized based on the generalized Mittag-Leffler kernel for approximate solutions. The model’s robustness in predicting an infectious disease like LSD, which can assist managers in taking preventive measures, such as gathering adequate human, pharmacological, and logistical resources.</p>

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Dynamics of lumpy skin disease with treatment and viral factor monitoring through fractional operator

  • 期刊论文

  • 发表日期：

    2025年7月19日

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  • Parvaiz Ahmad Naik,
  • Aqeel Ahmad,
  • Qazi Muhammad Farooq,
  • Muhammad Farman,
  • Abdul Ghaffar,
  • Kottakkaran Sooppy Nisar,
  • Aceng Sambas,
  • Zhengxin Huang

摘要

Lumpy skin disease (LSD) is a potentially deadly viral disease of cattle that causes nodules on the skin, fever, and swollen lymph nodes. If left untreated, LSD can result in severe economic losses owing to reduced milk production, weight loss, and even death. To monitor the increasing prevalence of LSD and develop cost-effective prevention strategies, disease modeling is a crucial tool. We propose a fractional-order mathematical model for LSD that captures the interval between an individual contracting the infection and the onset of symptoms using the Mittag-Leffler kernel. The proposed system undergoes a qualitative study, including a quantitative investigation and a well-posedness assessment. We create endemic and disease-free equilibrium points and analyze the proposed system’s stability. The major reproductive number condition is derived for a newly developed system to verify the rate of spread of the lumpy virus. The first derivative tests are utilized using the Lyapunov function for the analysis of global stability. In addition, fixed-point theory and the Lipschitz condition are employed to verify that the precise solution is bounded and unique, which are the key properties to verify the newly developed model. To analyze the impact of the fractional operator using numerical simulations and highlight the influence of the disease through various parameters, a two-step Lagrange polynomial is utilized based on the generalized Mittag-Leffler kernel for approximate solutions. The model’s robustness in predicting an infectious disease like LSD, which can assist managers in taking preventive measures, such as gathering adequate human, pharmacological, and logistical resources.