Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep

Abstract

In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number $R_0$ and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if $R_0>1$ . We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if $R_0<1$ . Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep ( ${\beta }_{\text{es}}$ ). Thus, the effective controlling strategies are associated with this parameter.