Optimal control strategy analysis for an human-animal brucellosis infection model with multiple delays

Firstly, we consider an animal-human infection model of brucellosis with three distributed delays, representing the latent period of brucellosis in infected animal and human population and the survival time of brucella in the environment, respectively. The equilibrium points and basic reproduction number $$ are calculated. By building appropriate Lyapunov functionals and applying LaSalle's invariance principle, the sufficient conditions for global asymptotic stability of two equilibria are given. Secondly, by introducing four control variables, we set the corresponding optimal control model and drive the first order necessary conditions for the existence of optimal control solution. Finally, we perform several numerical simulations to validate our theoretical results and show effects of different control strategies.