Impulsive-Systems And Application Research Of Vector-borne Control Based On Wolbachia Bacteria

Dengue diseases(DDs),as one of mosquito-borne diseases,are mainly caused by the transmission of dengue virus(DENV)between human and mosquitoes through Aedes aegypti and Aedes albopictus.Recently,with the continuing outbreak of DDs and the rapid increase of dengue cases,DDs have caused extensive concern from each country’s the hygiene and epidemic prevention center.At present,although the recent vaccine which can reduce the risk of the diseases has been approved in a few countries,there is no specific antiviral therapy to fight against DDs,so vector population control remains the principal means for the prevention of DDs.The traditional use of insecticides with high frequency and dose inevitably leads to the development of insecticide resistance in mosquitoes,the destruction of ecolog-ical environment and harm to human health.Similarly,it is inadvisable to reduce mosquito populations by destroying mosquitoes’ oviposition sites over large areas.These factors stimulate researchers to search for novel technologies based on genetic manipulation of mosquito vectors to break the transmission cycle of DENV.The research has found that endosymbiotic Wolbachia bacteria can interfere with their hosts’ reproductive mechanisms through maternal inheritance,cytoplas-mic incompatibility(CI)and so on.They can effectively prevent the replication and transmission of DENV in mosquitoes.In the experiments,in order to inhib-it the transmission of DENV,a certain amount of Wolbachia-carrying mosquitoes are released to realize the strategies of mosquito suppression or Wolbachia-carrying mosquito replacement.However,experiment research indicates that not all of the releases of Wolbachia-carrying mosquitoes can realize the above two strategies,and there are significant influences of the release method of Wolbachia-carrying mosquitoes and the dynamic variation of mosquito populations on the implementa-tion of the above two strategies.Therefore,there are important theory significance and practical value when we develop some novel mathematical models to depict the natural dynamic variation of mosquito population with the consideration of the natural phenomena or human interventions which are caused by the fertility pattern of mosquitoes,the release quantities,the release time and the releases with different sex and so on,then we systematically and thoroughly investigate the model and discuss the effects of these factors on the two control strategies.Based on the fertility pattern and the difference of density-dependent death process,in the first part,birth-pulse models about the effect of Wolbachia on the growth pattern of mosquito populations are proposed to investigate whether different density-dependent death rates may lead to the choice of different control strategies,and how to better achieve corresponding control purposes.Firstly,we obtain stro-boscopic maps of impulsive systems and corresponding equivalent systems.Then we ensure the existence of multiple stable states for the systems which indicate the existence of Allee effect for mosquito populations.The research conclusions show that the strategy of Wolbachia-mosquito replacement(or mosquito eradication)can be realized under certain conditions,and perfect maternal inheritance rate can lead to the complete replacement.For a weak density-dependent death rate,it is difficult to achieve mosquito eradication due to the solutions of the system being sensitive to initial values,so only when parameters lie in particular regions and the initial density of natural mosquitoes is low enough,the strategy of mosquito eradication can be achieved.Considering some critical factors which affect the success or failure of the release trials of Wolbachia-carrying mosquitoes,in the second part,we aim to investigate:Why do release trials in some countries fail in the end?and how make them succeed?What affect the success of Wolbachia-carrying mosquito replacement?If there is no mosquito releases,considering the different reproduction effects for Wolbachia-carrying mosquitoes,we separate analyze the existence and stability of equilibria,backward bifurcations and the effects of different parameter space on the control strategies in three cases,including without fitness cost,perfect maternal inheritance and general situation.In addition,in order to study how to make the densities of mosquitoes lie in the objective basins of attraction,we systematically analyze the effects of the initial densities of mosquitoes,release timings,release quantities and the number of releases on the success of population replacement under finite and infinite mosquito releases.Further,considering in practice not all release trials of Wolbachia-carrying mosquitoes with the same release quantity for different sex,in the third part,an im-pulsive differential system with four state variables(natural females,natural males,Wolbachia-carrying females and Wolbachia-carrying males)is used to depict the releases of Wolbachia-carrying mosquitoes with different sex,and we aim to inves-tigate the effects of each parameter and mosquito releases with different sex on the success of two control strategies.With perfect transmission rate,we first prove the stability of periodic solution depicting the periodic variation of Wolbachia-carrying mosquitoes and the permanence of natural mosquitoes.Secondly,the conditions of the existence of forward and backward bifurcations are investigated by employing the bifurcation theory of impulsive different equation.The effects of each parameter on the degree of population replacement are investigated by the method of partial rank correlation coefficient(PRCC).Moveover,we systematically discuss how ini-tial densities of mosquitoes,release period and the mosquito releases with different sex make the success of the two control strategies being faster and the transition conditions for the two strategies.This thesis,based on the release field-trials of Wolbachia-carrying mosquitoes,the novel biological control objectives of the transmission of vectors for DDs,gradu-ally developed and improved mathematical models which can systematically depict different fertility patterns,death patterns and release patterns(including the re-leases with different sex and release quantity,release moment and period,release sequence and times).We systematically discussed the effects of different density-dependence death rates on the choice of the two control strategies,and analyze the critical factors which affect the success or failure of release trials?The main results obtained in this work provide an important decision-making basis and theoretical guidance.Moreover,the modelling ideals,analytical and numerical techniques in-volved in this thesis can be employed to study the control of other vector-borne diseases,including Zika,Chikungunya and West Nile diseases and so on.