学术报告（庾建设 1.9）

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 biocontrol of diseases transmitted by mosquitoes has been proposed that uses Wolbachia pipiens to stop the transmission of pathogens. In this paper, we establish a discrete periodic model, including all the works in the existing literature since 1959 as some special cases, to study the Wolbachia infection dynamics in mosquito populations by impulsively releasing infected mosquitoes in laboratory cage. Let µ ∗ be the maximal maternal leakage rate threshold 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 ∗ , to ensure that Wolbachia infection can persist, we must release Wolbachia-infected mosquitoes into the cage such that the infection frequency can achieve f ∗ after several consecutive releases with a fixed release rate. For the periodic release rate case, we put forward some interesting questions to be further investigated.