Qualitative Analysis Of Two Malaria Transmission Models With Sterile Mosquitoes

Malaria is one of the most common and serious tropical infectious diseases in the world,it brings great harm to humans' life.To control the spread of malaria,scientists have made a large number of studies.The World Health Organization and many countries also attach great importance to malaria,and have taken correspond-ing measures to combat malaria.This paper established two malaria transmission models containing sterile mosquitoes,then made qualitative analysis to the two models and draw the relevant conclusions.Finally,according to the conclusions drawn,this paper put forward the corresponding strategies to control malaria.This article is divided into four chapters,the introduction part of the first chapter introduced the pathogenesis and dissemination mechanism of malaria and related measures scientists have taken to fight against malaria.The prepared part of the knowledge introduced the related concepts and theorems involved in this paper.Finally,this paper introduced the development process of malaria dynamics model and put forward the basic model of this paper.In the second chapter,we studied the malaria epidemic model in which the releasing amount of sterile mosquitoes per unit of time was constant.Firstly,we studied the two-dimensional dynamics model that only contained sterile mosquitoes and wild mosquitoes in the first section.To find the releasing threshold b0,we need to do qualitative analysis to the malaria model.When the releasing number b is greater than or equal to b0,all wild mosquitoes are wiped out;When the releasing number b is less than b0,the sterile mosquitoes and wild mosquitoes coexist.Next we studied a eight-dimensional dynamics model in which contains both humans and mosquitoes.We could get the reproductive number R0 by investigating the local stability of the infection-free equilibrium.When R0 is less than one,the infection-free equilibrium is locally asymptotically stable;when R0 is more than one,there exists at least one endemic equilibrium.Let R0 is equal to one,we could find a more practical releasing threshold b*,which is less than b0.The numerical simulation shows that the conclusion is consistent with the actual.In the process of numerical simulation,we find that when R0 is less than one,the endemic equilibrium point still exists,so the system may have a backward bifurcation at R0 =1.We give the theoretical proof of the existence of backward bifurcation in the fourth part.This chapter shows that releasing sterile mosquitoes has a significant effect on malaria transmission.Considering that the number of wild mosquitoes in some areas is relatively small,from an economic point of view,the cost will be greater,if sterile mosquitoes are still releasing constantly.Thus we have studied the malaria transmission model in which sterile mosquitoes are releasing proportionally in the third chapter,and the Allee effect is added to the input item of wild mosquitoes corresponding.The specific analysis and calculation process aer similar to the case of constant,and the numerical simulation shows that the conclusion is consistent with the actual.It shows that the effect of the sterile mosquitoes on malaria is significant.According to the number of wild mosquitoes in different areas,it is also necessary to take different releasing measures.The cost of sterile mosquitoes is relatively large,so we have to reduce the cost as much as possible while controlling malaria.In the fourth chapter,we summarize the main conclusions of this paper and put forward the research targets that need us to do further research.