Dynamical modeling of Lumpy Skin Disease using Atangana–Baleanu derivative and optimal control analysis

Lumpy Skin Disease (LSD) poses a significant challenge to cattle health and causes substantial economic losses in affected regions. This study introduces a new fractional model of LSD dynamics incorporating the Atangana–Baleanu derivative to capture memory effects and complex transmission patterns of the disease. The use of this derivative provides a more accurate representation of disease dynamics compared to traditional integer order models. The model demonstrates a unique, positive, and bounded solution. The basic reproduction number, R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0$$\end{document}, is calculated to assess disease transmissibility. Sensitivity analysis is performed to identify key parameters influencing R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0$$\end{document}. Optimal control strategies involving vaccination and quarantine are formulated and numerically analyzed to assess their efficacy. A comparative analysis is carried out across three different scenarios: vaccination alone, quarantine alone, and the combination of both strategies. Our findings indicate that a combined approach of vaccination and quarantine is the most effective strategy for minimizing disease spread. This study not only provides valuable insights for practical disease management but also emphasizes the critical importance of implementing control measures to combat the spread of Lumpy Skin Disease.