Effects Of Maternal Transmission Leakage On Wolbachia Spread In Mosquitoes

According to the qualified estimation of WHO, there are more than 700,000 people died of mosquito-borne diseases every year. Take dengue as an example,more than three billion six hundred million people worldwide suffer from dengue,among which one hundred million people are infected with dengue annually. Since Guangzhou has been hit by the unprecedented dengue virus, the city has become an epidemic area. How to control or kill mosquitoes is now still the spotlight for the people in this areas. The traditional way to control mosquitoes is spraying pesticides, which not only pollutes environment seriously, but also induces the mosquito resistance to pesticides. Since the pioneering work of Zhiyong Xi on establishing the stable Wolbachia strains in Aedes mosquitoes, a novel, safe and effective biological method is to release mosquitoes carrying bacterium Wolbachia into nature to suppress or replace the wild population with the Wolbachia infected mosquitoes who could block the disease transmission.As a highly maternally transmitted bacterium, Wolbachia can be inherited successfully by the offspring. The higher the maternal transmission rate, the easier the Wolbachia spread in mosquitoes. However, imperfect maternal transmission is frequently documented in Drosophila simulans. The lastest research indicated that maternal transmission leakage exist in Aedes aegypti and Anopheles stephensi,which are vectors for dengue and malaria, respectively. In particular, the leakage in these vectors is much larger than the leakage in Drosophila simulans. Motivated by these facts, we develop a mathematical model to analyze the effect of maternal leakage on the dynamics of Wolbachia spread in mosquitoes. The results offer some explanations on the 2013 wMelPop failure to establish in the natural populations in Vietnam.The thesis is divided into three chapters. Some background of mosquito-borne diseases,the current work on the dynamics of Wolbachia spread in mosquitoes and the main work of the thesis are included in Chapter 1. After proving the invariance and boundedness of solutions to our system and presenting two useful identities, we study the global dynamics in Chapter 2 and prove that our system can exhibit monomorphic, bistable, and polymorphic dynamics, and give sufficient and necessary conditions for each case. Some numerical simulation results are presented in Chapter 3. These results highlight some challenges associated with the release of Wolbachid infected mosquitoes into the wild to suppress or replace the wild ones. Compared to perfect maternal transmission, imperfect maternal transmission brings richer dynamics. As the increase of maternal leakage, the monomorphic, polymorphic and bistable behavior occurs consecutively. Take three different leakage patterns as examples, we plot three curves of threshold values,which manifests the effect of maternal leakage on designing the release strategies.