Modeling And Analysis Of Continuous And Impulsive Releases Of Sterile Mosquitoes

To prevent the transmissions of mosquito-borne disease such as malaria and dengue fever,one of the effec-tive measures is the sterile mosquito technique in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population.To study the impact of the sterile mosquitoes on disease transmission,we pro-pose three novel mathematical models with impulsive releasing sterile mosquitoes to discuss their dynamical behaviors and present its findings' application in practice.The preface is in chapter one,we introduce the research background of the article.In chapter two,the first part that a mathematical model with continuous releasing is formulated.Besides,it gains the conditions of the equilbrium points being stability of the model,combining with continuous dy-namical system.In chapter three,to study the impact of the sterile mosquitoes on wild mosquitoes in the state of period.On model incorporates the periodic impulsive releasing sterile mosquitoes is established.In this model,we gain its positive and boundedness and globally stability of a wild mosquito-eradication period solution by using some theories of impulsive differential equations.Besides we also show that the system is uniformly permanent provided some conditions are satisfied.Then having taken account more rigorous and conform to the actual situation.A model with impulsive releasing sterile mosquitoes measures is presented by using impulsive state feedback system to investigate the existences of order one periodic solution and its orbital asymptotic stability.Finally,the article is summarized,laid the foundation for later study.