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Echinococcosis has been recognized as one of the most important helminth zoonosis in China. Available models always consider dogs as the mainly definitive hosts. However, such models ignore the distinctions between domestic dogs and stray dogs. In this study, we propose a 10-dimensional dynamic model distinguishing stray dogs from domestic dogs to explore the special role of stray dogs and potential effects of disposing stray dogs on the transmission of Echinococcosis. The basic reproduction number R0, which measures the impact of bothdomestic dogs and stray dogs on the transmission, is determined to characterize the transmission dynamics. Global dynamic analysis of the model reveals that, without disposing the stray dogs, the Echinococcosis becomes endemic even the domestic dogs are controlled. Moreover, due to the difficulties in estimating the parameters involved in R0 with real data and the limitation of R0 in real-world applications, a new risk assessment tool called relative risk index Iriskis defined for the control of zoonotic diseases, and the studies of the risk assessment for Echinococcosis infection show that it is essential to distinguish stray dogs from domestic dogs in applications.
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