Abstract: Tungiasis is a zoonotic disease in poverty-stricken areas, and its pathogenesis is easily affected by random fluctuation environmental factors. Therefore, a class of stochastic tungiasis model with correct hygiene habits as a control strategy is established and discussed. Firstly, the existence and uniqueness of global positive solutions of stochastic systems are proved by proper Lyapunov functions and It$\hat{\rm o}$ formula. Secondly, under certain conditions, the oscillation behavior of the positive solution of the stochastic system around the equilibrium point of the deterministic system is proved. Finally, the correctness of the theoretical analysis is verified by the numerical simulation. The results indicate that the disease will become extinct when the intensity of random interference is high enough.

Key words: stochastic tungiasis model, equilibrium point, asymptotic behavior, Lyapunov function, It$\hat{\rm o}$ formula