Mathematical Models Of Proportional Release Strategy On Killing Mosquitoes With More Mosquitoes

Dengue fever is a mosquito-borne diseases transmitted by dengue virus through mosquito bites.At present,over 2.5 billion people in more than 100 countries and regions are at risk and it has a tendency to increase,which makes mosquito control become one of the most common public health issues in the world.The traditional method to eliminate mosquitoes is spraying insecticide,but this method can only achieve short-term effect due to the development of insecticide resistance.Some countries are working on vaccines and effective drugs for dengue fever.With some progress though,there is still a lack of commercially available and safe dengue vaccines.A novel approach is to use a bacterium called Wolbachia,which exists up to 60%of insects,including mites,spider and some mosquito species.Wolbachia can induce cytoplasmic incompatibility(CI)which results in embryo death from matings of Wolbachia-infected males and uninfected females or females harboring different Wolbachia strains.This makes Wolbachia-infected males as killers of wild female mosquitoes and a new weapon to suppress and control mosquitoes.Our Chinese "mosquito factory" located in High-tech Industrial Development Zone in Luogang District of Guangzhou City breeding 5 million male mosquitoes a week,and releasing them on the Shazai island to mate with wild female mosquitoes since March 2015 which has suppressed more than 95%mosquito population on the island.As a biological safe and sustainable method,using lab-grown mosquitoes to kill mosquito pests has been tested extensively in many countries in recent years.Brazil has allowed large-scale releases of such mosquitoes in response to an epidemic of the Zika virus that began in 2015.In this thesis,we developed mathematical models with ordinary differen-tial equations for a proportional release policy of "Killing mosquitoes with more mosquitoes".The thesis is divided into three chapters.In Chapter 1,the history background of dengue,Wolbachia,current research and development prospects of Wolbachia spread in mosquitoes were introduced.In addition,we gave a short description of the innovations of this thesis.Under the assumption of complete CI and equal mating competitiveness of Wolbachia-infected males as that of wild males,we modeled the proportional release policy in Chapter 2 where the num-ber of releases males is maintained as a fixed ratio to the number of wild males,and dynamics of the model was analyzed.On the release ratio,we obtained the threshold value over which wild females will eventually be wiped out by Wolbachia-infected males.The model in Chapter 3 is a generalizaton of the one in Chapter 2 in that we included incomplete CI and a reduction of mating competitiveness of Wolbachia-infected male mosquitoes.The complex dynamics due to these two parameters was presented.The proportional release policy has been proved to be more effective than constant release policy in some field trials.And our result may be helpful in designing optimal release policies for large-scale releases.