mathematical modeling of echinococcosis in humans, dogs and livestock with optimal control strategies

In this paper, we present a deterministic model of cystic echinococcosis disease of eleven differential equations, describing complex interactions between three types of hosts, specifically humans, livestock and dogs. the model is analyzed; disease-free and endemic equilibrium exist and are globally asymptotically stable if the basic reproduction number is less than or greater than one, respectively. the optimal control represents the efficiency of health education and eg95 sheep vaccination. the existence of optimal controls is proven, the characterization is formulated using pontriyagin’s maximum principle, and the optimal system is derived. for the numerical simulation, the data used are from some studies done in morocco.