This study presents a mathematical model of the transmission and spread of the Echinococcus granulosus parasite. The model incorporates host mobility, laws governing the dynamics of Echinococcosis transmission between hosts, and control and prevention measures. The basic reproductive number of the proposed model is calculated, and a sensitivity analysis is performed to identify the parameters that most influence the dynamics of transmission and spread of the disease among its hosts. The study evaluates two control strategies-dog deworming and sheep vaccination-based on their respective target reproductive numbers. The impact of these control and prevention measures is investigated through numerical simulations, which reveal that the dog deworming strategy consistently reduces infections in humans. In contrast, the sheep vaccination strategy demonstrates a more favorable scenario for disease eradication in both hosts. In addition, simulations show a close relationship between the early detection of the disease and the recovery of the patient.