Insights into mathematical model with efficient control measures for lumpy skin disease of cattle considering the presence of contaminated environment

In this paper, we introduce a mathematical simulation that captures the dynamics of lumpy skin disease (LSD) by considering three key transmission paths: vector-borne, direct cattle-to-cattle contact and environmental contamination. Additionally, this model incorporates three control measures, including vector control, environmental management and isolation/treatment of infected cattle. We perform a comprehensive mathematical analysis to demonstrate the model well-posedness, like proving the existence, uniqueness, positivity and boundedness of the solution. The basic reproduction number (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>) is calculated. The local and global stability analysis is presented for the disease-free and endemic equilibrium points. Sensitivity analysis for the model parameters is shown, which reveals that isolation and treatment control measures are the most effective in eliminating disease transmission. We construct an objective function to formulate an optimal control problem (OCP) and derive the optimality necessary conditions. Numerical simulations confirm the theoretical findings, demonstrating that strategic implementation of combined control measures can efficiently suppress LSD.