Fractional-Order Model for Evolution of Bovine Tuberculosis with Vaccination and Contaminated Environment

Bovine tuberculosis (bTB) is a zoonotic disease that is commonly transmitted via inhaling aerosols, drinking unpasteurized milk, and eating raw meat. We use a fractional-order model with the Caputo sense to examine the evolution of bovine tuberculosis transmission in human and animal populations, including a vaccine compartment for humans. We derived and obtained the threshold quantity R0 to ascertain the illness state. We established conditions guaranteeing the asymptotic stability of the equilibria (locally and globally). Sensitivity analysis was conducted to identify the factors that govern the dynamics of tuberculosis. The study demonstrates that the rate of human-to-animal transmission of tuberculosis and environmental pollution and the rate of bTB transmission between animals all affect tuberculosis transmission. However, as vaccination rates increase and fewer individuals consume contaminated environment products (such as meat, milk, and other dairy products), the disease becomes less common in humans. To manage bovine TB, it is advised that information programmes be implemented, the environment be monitored, infected persons be treated, contaminated animals be vaccinated, and contaminated animals be quarantined. The usefulness of the discovered theoretical results is demonstrated through numerical experiments.