Mathematical modelling of echinococcosis in human, dogs and sheep with intervention

In this study, a model for the spread of cyst echinococcosis with interventions is formulated. The disease-free and endemic equilibrium points of the model are calculated. The control reproduction number Rc for the model is derived, and the global dynamics are established by the values of Rc. The disease-free equilibrium is globally asymptotically stable if and only if Rc<1. For Rc>1, using Volterra-Lyapunov stable matrices, it is proven that the endemic equilibrium is globally asymptotically stable. Sensitivity analysis to identify the most influential parameters in the dynamics of CE is carried out. To establish the long-term behaviour of the disease, numerical simulations are performed. The impact of control strategies is investigated. It is shown that, whenever vaccination of sheep is carried out solely or in combination with cleaning or disinfecting of the environment, cyst echinococcosis can be wiped out.