THE EFFECT OF STOCHASTIC VARIABILITY ON TRANSMISSION DYNAMICS OF ECHINOCOCCOSIS

Echinococcosis, one of the most serious zoonotic diseases, has a severe impact on the human health and economic development. This paper mainly focuses on the effect of stochastic variability on transmission dynamics of echinococcosis. A stochastic model describing the transmission of echinococcus granulosus in dog-livestock-human is proposed. By using the Itô formula, strong law of large numbers for martingale and the inequality analysis, the criteria on the extinction with probability one for the disease are obtained. In addition, by constructing an appropriate stochastic Lyapunov function, the existence of a unique ergodic stationary distribution is established. Furthermore, numerical simulations have been performed to not only support our analytical results but also display that noise intensities would have significant impact on the speed of the extinction for the echinococcosis disease, and as well as the shape for the probability density curve of the stationary distribution of the solution for this model.