关键词: 随机传染病模型, HPV, 白噪声, Markov切换, 持久性

Abstract: In order to study the influence of stochastic disturbance and environment switching on the HPV infection and provide a theoretical basis for the development of effective HPV disease prevention measures, in this paper we establish a kind of two-sex stochastic HPV epidemic model with white noise and Markov switching. We show that the model has a unique local positive solution and a unique global positive solution. Then we identify the threshold conditions for the persistence of the HPV epidemic, and verify the persistence of the disease using the Lyapunov method and the It$\hat{\rm o}$ formula. At last, the numerical simulation is carried out to illustrate the rationality of the theoretical results.

Key words: Stochastic epidemic model , HPV, White noise, Markov switching, Persistence