A Mathematical Model Of Constant Release Strategy On Killing Mosquitoes With More Mosquitoes

As a mosquito-borne disease,dengue virus has put more than one-third of the world' s population at risk for infection,and more than 50 million people are infected annually.Due to the lack of applicable vaccines and effective drugs,intervention methods still are arrested in controlling the mosquito vectors.The current method is killing mosquitoes by spraying insecticide,which not only con-taminate the environment,but also induce the resistance of mosquitoes,resulting in a short-term effect of insecticide application.Once the application is terminated,the mosquito population bounce back quickly.A novel method involves the bacterium,named as Wolbachia.The studies found that it produces cytoplasmic incompatibility after the mosquitoes carry the bacteria Wolbachia.It means that the male mosquitoes with Wolbachia and the females without Wolbachia do not produce offspring.However,it is regrettable that there is no Wolbachia in Aedes aegypti and Aedes albopictus,or the Wolbachia that is carried by itself cannot stop the replication of the virus in mosquitoes.In 2005,Prof Xi Zhiyong at Michigan State University and his team established a stable Wolbachia strains in Aedes aegypti and Aedes albopictus by micro-injection.Their further study showed that once infected with Wolbachia,the dengue virus could not be replicated in mosquitoes anymore,resulting in the block of the virus transmission from mosquitoes to human being.Cytoplasmic incompatibility occurs between Wolbachia infected males and wild females:eggs from the wild females mated with infected males will not hatch.This leads to a mosquito control strategy called "Kill Mosquitoes with More Mosquitoes",or population suppression.We focus on the constant release policy of population suppression,which is the first choice when the rearing output is enough for weekly release.This thesis is divided into three chapters.Chapter 1 introduces some backgrounds of dengue fever,together with an introduction on the current models on Wolbachia spread dynamics in mosquito populations.We develop the mathematical model with constant release policy in Chapter 2.The global stability analysis is offered with respect to the system parameters.Also,our numerical simulations show that there exist thresholds,dependent on the wild population size,to guarantee the success of population suppression.Finally,we make a conclusion of our work and state our future work.