| Neglected tropical diseases annoy more than one billion people. Recently, the outbreak of Zika put spotlight on mosquito-borne diseases. No vaccine for most NTDs lead the current control method to eliminating vector mosquitoes through spraying insecticides during outbreak which could cause severe environmental issues.As Zhiyong Xi in Michigan State University established stable Wolbachia strain in Aedes aegypti, and proved that Wolbachia almost completely blocked the duplication of dengue virus, a novel strategy is then to release Wolbachia mosquito to wild populations.The strategy is feasible due to perfect maternal transmission and complete cytoplasmic incompatibility(CI). Thus, if enough Wolbachia infected females are released, they would outcompete the wild populations. And if enough Wolbachia infected males are released,then wild female mosquitoes would be suppressed once they mate with the infected males.However, the data in experiments showed that imperfect maternal transmission and incomplete CI occur frequently. Either of them could increase the threshold of population replacement or lower the speed of population suppression.In this paper, we study the dynamics of Wolbachia under these two cases separately.After introducing backgrounds of NTDs, mosquitoes and recent research on dynamics of Wolbachia in Chapter 1, Chapter 2 studies the dynamics of Wolbachia under imperfect maternal transmission. Existence and(in)stability are analyzed systematically. A sharp estimation on the threshold to ensure the success of population replacement is obtained.Chapter 3 focuses on the effect of incomplete CI. Similarly, sharp estimation on the attraction basin for Wolbachia replacement is obtained by analyzing the dynamics of Wolbachia in a population mixed with infected and uninfected individuals. The decrease of the CI intensity would lower the speed of population replacement or population suppression. Finally, we make a short summary and vision for our future work in Chapter 4. |
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