| Mosquito-borne diseases have been a serious health hazard in terms of human health for many years.It is characterized by a wide variety and strong infectivity.Therefore,it is difficult to control by conventional medical means.Now the most effective control method is to reduce the number of mosquitoes.It is difficult to make long-term impact on mosquito population by hunting or using chemical insecticides in the wild environment.At present,the most reliable way to kill mosquitoes is to release a large number of sterile mosquitoes.Establishing and analyzing the dynamic model of interaction between wild and sterile mosquitoes based on mosquito control technology can help biologists explain many thorny problems in mosquito control,and it is also an important research direction for solving mosquito-borne diseases.In this paper,we established models based on sterile insect release technology and insect incompatibility technology,respectively.We use the pulse differential equation to describe the release process of sterile mosquitoes,and obtain a semi-discrete pulse model,then perform dynamic analysis around its periodic solution.The aim is to study the feasibility of controlling the population of wild mosquitoes by releasing sterile mosquitoes periodically.The chapters of this article are arranged as follows:In the Chapter 1,we introduced the research background,research significance,research status and the main work of this paper.In the Chapter 2,the basic knowledge and related theories of ordinary differential equation and impulsive differential equations are briefly described.In the Chapter 3,we study a stage-structured wild and sterile mosquito interaction impulsive model with SIT as the background.In this model,we assume that mosquitoes only have density-dependent mortality in the "aquatic" stage.The existence of trivial periodic solutions is obtained,and the corresponding local stability is proved by Floquet theory theorem.Then we prove the existence conditions of non-trivial periodic solutions and their local stability.We can find that the system has the bistable phenomenon in which the trivial periodic solution and the non-trivial periodic solution can coexist under certain threshold conditions.All the results show that the appropriate release period and release amount of sterile mosquitoes can control the wild mosquito population within a certain range,and even make them extinct.Finally,numerical simulation verifies our theoretical results.In the Chapter 4,we study an impulse release Wolbachia-infection male mosquito model with IIT as the background.The model adds a gender-structure on the basis of retaining the mosquito stage-structure.We assume in this model that Wolbachia-infected male mosquitoes have an incomplete sterilization rate.First,we prove the threshold conditions that determine the local stability and global stability of trivial periodic solutions respectively,and obtain the existence conditions of non-trivial periodic solutions.Then we illustrate the stability of nontrivial periodic solutions under specific parameter conditions.Finally,the periodic solution and pulse bifurcation phenomena are simulated by numerical methods.In the Chapter 5,We summarized the article and looked forward to the future research. |
