Analysis of a fractional order Bovine Brucellosis disease model with discrete generalized Mittag–Leffler kernels

Abstract

Bovine Brucellosis, a zoonotic disease, can infect cattle in tropical and subtropical areas. It remains a critical issue for both human and animal health in many parts of the world, especially those where livestock is an important source of food and income. An efficient method for monitoring the illness’s increasing prevalence and developing low-cost prevention strategies for both its effects and recurrence is brucellosis disease modeling. We create a fractional-order model of Bovine Brucellosis using a discrete modified Atangana–Baleanu fractional difference operator of the Liouville–Caputo type. An analysis of the suggested system’s well-posedness and a qualitative investigation are both conducted. The examination of the Volterra-type Lyapunov function for global stability is supported by the first and derivative tests. The Lipschitz condition is also used for the model in order to meet the criterion of the uniqueness of the exact solution. We created an endemic and disease-free equilibrium. Solutions are built in the discrete generalized form of the Mittag-Leffler kernel in order to analyze the effect of the fractional operator with numerical simulations and emphasize the effects of the sickness due to the many factors involved. The capacity of the suggested model to forecast an infectious disease like brucellosis can help researchers and decision-makers take preventive actions.