Parameters description.

Lumpy skin disease (LSD) is a viral infection that affects cattle, resulting from the lumpy skin disease virus. This study investigates the impact of vaccination and quarantine strategies on LSD outbreaks. This study analyzes a nonlinear model for LSD using the Caputo fractional operator. The positivity and boundedness of the model’s solutions are confirmed. Equilibrium points for both disease-free and endemic states are derived, and the basic reproduction number is determined using the next-generation matrix method. An equilibrium point stability analysis is performed. The bifurcation graphs for steady states are presented. Sensitivity indices are calculated to identify the parameters that most significantly influence the dynamics of the disease. The dynamical behavior is analyzed using a Lagrange polynomial interpolation-based numerical scheme. The results demonstrate that increasing the vaccination rate can lead to the elimination of the disease. Increasing movement restrictions for the exposed cattle population reduces infection rates, but does not eliminate the disease. In addition, the spread of LSD is more sensitive to the recruitment of susceptible individuals.