A transmission dynamics model with the logistic growth of cystic echinococcus in sheep was formulated and analyzed. The basic reproduction number was derived and the results showed that the global dynamical behaviors were determined by its value. The disease-free equilibrium is globally asymptotically stable when the value of the basic reproduction number is less than one; otherwise, there exists a unique endemic equilibrium and it is globally asymptotically stable. Sensitivity analysis and uncertainty analysis of the basic reproduction number were also performed to screen the important factors that influence the spread of cystic echinococcosis. Contour plots of the basic reproduction number versus these important factors are presented, too. The results showed that the higher the deworming rate of dogs, the lower the prevalence of echinococcosis in sheep and dogs. Similarly, the higher the slaughter rate of sheep, the lower the prevalence of echinococcosis in sheep and dogs. It also showed that the spread of echinococcosis has a close relationship with the maximum environmental capacity of sheep, and that they have a remarkable negative correlation. This reminds us that the risk of cystic echinococcosis may be underestimated if we ignore the increasing number of sheep in reality.
Keywords: basic reproduction number; cystic echinococcosis; epidemic model; global asymptotic stability; sensitivity analysis.