Analyzing The Control Of Dengue By Releasing Wolbachia-infected Male Mosquitoes Through A Delay Differential Equation Model

In this thesis,we established a delay differential equation model to analyze how Wolbachia-infected male mosquitoes affect the dynamic behavior of mosquito vectors and mosquito-borne diseases.There are three delays,the intrinsic incubation period(?P)in humans between infection and the onset of infectiousness,the maturation delay between mating and emergence of adult mosquitoes,the extrinsic incubation period(EIP)for a female mosquito taking a viraemia blood meal to be infectious.Under the proportional release policy where Wolbachia-infected male mosquitoes are released at a fixed ratio to the total mosquito population size,the model is embedded with mosquito,virus and human.We determine two explicit expressions of the threshold value of the release ratio,which indicate the eradication of mosquitoes and the eradication of dengue virus,respectively.These results may provide guidance for the development of release strategies for the control of mosquito vectors and mosquito-borne diseases.In Chapter 1,some background and current control measures of dengue are introduced.To date,an innovative biological method to control dengue involves the endosymbiotic bacteria Wolbachia.The transmission mechanisms of Wolbachia is summarized,together with mathematical models for Wolbachia spread dynamics in mosquito population.Finally,we introduce our main results of this thesis.In Chapter 2,we build a delay differential equation model with three delays under the proportional release policy.We analyzed the existence and the stability of disease-free equilibria to obtain the sufficient and necessary condition on the existence of the disease-endemic equilibrium and two threshold values of the release ratio,?,denoted by ?1*and ?2*with ?1*>?2*.When ?>?1*,the mosquito population will be eradicated eventually.If it fails for mosquito eradication but ?2*<?<?1*,virus eradication is ensured together with the persistence of susceptible mosquitoes.When ?<?2*,the disease-endemic equilibrium emerges that allows dengue virus to circulate between humans and mosquitoes through mosquito bites.In Chapter 3,we carry out sensitivity analysis of the basic reproduction number in terms of the model parameters as well as the dynamics of the threshold values?1*and ?2*.Also we simulate several possible control strategies,which confirm the public awareness that reducing mosquito bites and killing adult mosquitoes are the most effective strategy to control the epidemic.We end the whole dissertation by offering a brief summary on the main results and possible future work.