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.

In this article, we study a fractional-order prey-predator model incorporating prey refuge and predator harvesting, employing a Holling type III functional response. The model’s dynamics are explored using the consumption number C 0 , providing a comprehensive understanding of its ecological implications. We establish the existence and uniqueness of the solution, ensuring the model’s mathematical robustness. Stability analysis is conducted to determine the conditions under which the system remains in equilibrium. Sensitivity analysis is performed to assess the importance of various parameters on the system’s behaviour with respect to the consumption number. Additionally, we investigate the occurrence of transcritical bifurcations, utilizing the prey refuge as a bifurcation parameter. Numerical simulations are carried out to illustrate the theoretical results and to provide deeper insights into the model’s dynamics. Our findings contribute to the understanding of fractional-order systems in ecological modelling and offer valuable perspectives on the management of predator-prey interactions in the presence of prey refuge and predator harvesting.