Mathematical modelling and optimal control the spread of Capripoxvirus

Capripoxvirus is an infectious disease that affects cattle, presenting clinical symptoms such as fever, conjunctivitis, skin nodules, necrotic lesions in internal organs, dilation of lymph vessels, and potentially death. The disease is primarily transmitted through bites from cage flies infected with the Capripoxvirus. This paper develops and analyzes a mathematical model to study the disease dynamics and the impact of control strategies. The model incorporates key parameters such as transmission rates, recovery rates, and control measures. The analysis focuses on the stability of the equilibrium points within the model and the effectiveness of optimal control strategies, specifically vaccination and culling (annihilation) of infected cattle. Without control measures, the model reveals two equilibrium points: A non-endemic state and an endemic state. The stability of these equilibrium points is determined by the basic reproduction number, R0. The non-endemic equilibrium is asymptotically stable when R0 1, while the endemic equilibrium is asymptotically stable when R0 1. The application of Pontryagin's Maximum Principle allows for the determination of optimal control strategies. Numerical simulations demonstrate that the simultaneous application of both vaccination and culling is more effective in controlling the spread of the disease.