Improvement of an interspecies brucellosis transmission model and its fractional optimal control

Brucellosis is a zoonotic disease caused by bacteria of the genus Brucella that is transmitted directly or indirectly from animals such as cattle, goats, cats, dogs, and pigs to animals and from animals to humans. The World Health Organization states that there are thousands of cases of brucellosis worldwide each year and considers it a zoonotic infection that causes great devastation on a global scale. In addition, this disease causes abortion and decreased milk production in animals, and causes serious organ failures in humans, creating a health and economic burden. In this thesis, optimal control strategies are proposed to control the brucellosis transmission between sheep and humans in Inner Mongolia, China. For this purpose, the shortcomings of the existing brucellosis model are eliminated and the model is discussed with the Atangana–Baleanu derivative, considering unit consistency. The existence and uniqueness of the solutions of the developed fractional brucellosis model are proven. The positivity and boundedness of the solutions are shown to verify that the model is biologically meaningful. Then, the basic reproduction number of the model is calculated and sensitivity analysis is performed. The local stability of the model at the equilibrium points is examined. The developed fractional brucellosis model is normalized in order to obtain more realistic results from the optimal control strategies proposed to prevent the brucellosis transmission between interspecies in the Inner Mongolia region of China. Then, culling, environmental hygiene and sanitation, educational campaigns, and treatment measures are adapted to the normalized fractional brucellosis model as time–dependent optimal control functions. The fractional-order optimality system is revealed by demonstrating the existence of optimal controls, with the help of Pontryagin's Maximum Principle. The parameters of the developed and normalized models are estimated by the least squares method. The optimality system is solved by the Adams–type predictor–corrector algorithm combined with the forward–backward sweep method, using these parameters. Numerical simulations are obtained with the help of MATLAB and the proposed strategies are compared to determine the most effective strategy.