摘要：How to prevent and control the outbreak of Mosquito-borne diseases, such as malaria, dengue fever and Zika, is a worldwide public health security problem. The most conventional method for the control of these diseases is to directly kill mosquitoes by relying on insecticides to stomp down their numbers, larval source reduction and community mosquito eradication, which has been one of the major intensive efforts in many years. However, this traditional method is not sustainable to keep the mosquito density below the epidemic risk threshold. More recently,a novel strategy for bio-control of diseases transmitted by mosquitoes has been proposed that uses Wolbachia pipiens to stop the transmission of pathogens. In this paper, our purpose is to formulate models to study the Wolbachia infection dynamics based on a discrete dynamical equation. Our analysis shows that there is a maximal maternal leakage rate threshold, denoted by μ∗, such that infected mosquitoes can persist provided the maternal leakage rate μ does not go up to μ∗.For the situation when μ ≤ μ∗, we find the minimal Wolbachia infection frequency threshold, denoted by f∗, such that the infected mosquitoes can persist provided the initial infrequency x0 is not less than f∗. For the case when x0 < f ∗, we find the release rate threshold, denoted by a∗, such that Wolbachia infection can also persist provided the release rate α is not less than α∗. When the first release is not successful, that is, the next generation infection frequency still fails to reach f∗, we find the least release times,denoted by n∗, such that the infection frequency can achieve f∗ after n∗ consecutive releases with a fixed release rate.