Research On The Dynamic Behavior And Control Strategy Of Disease Transmission Vector Mosquitoes

With the expansion of the world trade field and the rising global temperature,the outbreak of mosquito-borne diseases is becoming more and more widespread.The situation is becoming more and more serious,which causes a serious threat to people's life and property,especially in underdeveloped areas.According to statistics,there are hundreds of millions of people infected with mosquito-borne diseases every year and the diseases cause millions of deaths.Therefore,the control of mosquito-borne diseases is very important.At present,the main control methods include medical intervention,vector control,self protection and community education,etc.Vector control is the most direct and effective way,such as spraying insecticides,using bed nets,releasing natural enemies and sterilized mosquitoes.Especially the use of intercellular symbiotic bacteria Wolbachia is more and more popular in the control of mosquito-borne diseases for its characteristics of maternal transmission and cytoplasmic incompatibility.In order to study the effectiveness of control strategy from the quantitative point of view,mathematical models will be established to study the control strategy of mosquito vector for disease transmission in this thesis.There are five chapters in the thesis.In the first chapter,firstly,the research background of mosquito-borne diseases including the introduction of mosquito-borne diseases,the outbreak of the world,the control measures and the research status at home and abroad is introduced.Secondly,the basic knowledge used in this thesis are given.Finally,the main research contents and innovation points of this thesis are given.In the second chapter,an impulsive model with general birth and death rate functions is established to study the spread of Wolbachia in mosquito population.Two characteristics of Wolbachia are considered: maternal transmission and cytoplasmic incompatibility.If a female mosquito is infected with Wolbachia,its offspring will also be infected.Cytoplasmic incompatibility will cause the death of host zygote when Wolbachia-infected males mate with uninfected females.Firstly,the strategies of mosquito extinction or replacing Wolbachiauninfected mosquitoes with Wolbachia-infected mosquitoes partly or totally are analyzed.And the threshold for the successful spread of Wolbachia is obtained.Secondly,the results are applied to models with specific birth and death rate functions.It is shown that strategies may be different due to different birth and death rate functions,the type of Wolbachia strains and the initial occupancy of Wolbachia-infected mosquitoes.Furthermore,numerical simulations are conducted to illustrate our conclusions.In the third chapter,firstly,a sex-structured model with birth pulse is established to study the spread of Wolbachia in mosquito population.The results show that if the maternal transmission is perfect,Wolbachia will spread successfully.Moreover,all the mosquitoes will be infected with Wolbachia.If the maternal transmission is imperfect,a threshold of the initial occupancy of Wolbachia-infected mosquitoes is obtained.Only when the initial occupancy exceeds the threshold can Wolbachia spread successfully and the part replacement strategy come true.Furthermore,in consideration of the fact that the initial occupancy can not always exceed the threshold in the wild nature,to release Wolbachia-infected mosquitoes artificially into the wild nature becomes necessary.Therefore,we add a release strategy into the sex-structured model with birth pulse for further analysis.The conditions to ensure the existence and stability of the Wolbachia total replacement periodic solution are obtained.Finally,the effects of the release quantity are simulated numerically.In the forth chapter,an integrated mosquito control strategy is mainly explored by an impulsive state feedback control model.Firstly,an ordinary differential system with general birth and death rate functions is established to describe the effects of maternal transmission and cytoplasmic incompatibility.It is shown that whether Wolbachia can spread successfully in the mosquito population is determined by the initial infected frequency.And Wolbachia spreads more easily for greater maternal transmission and CI rate.Moreover,all the wild mosquitoes will be infected with Wolbachia eventually if the maternal transmission is complete.Secondly,in order to study the integrated mosquito control by the using of Wolbachia and the spraying of insecticides,the strategy of spraying insecticides is described by impulsive state feedback control.Insecticides are sprayed only when the quantity of mosquitoes reaches the Economic Threshold.The existence and stability of Wolbachia replacement periodic solution are discussed for the model.Furthermore,numerical simulations are conducted to illustrate our conclusions.In the fifth chapter,the research contents are summarized and discussed,and the future researches are directed.