Analysis Of Wolbachia Spread Dynamics In Mosquitoes Population

In this thesis,we develop two models to study Wolbachia infection dynamics.We study the existence and stability of the equilibrium,and find the model undergoes saddle-node bifurcation when the probability of cytoplasmic incompatibility changed.When the delay is considered in the model,the positive equilibrium disappears if the maturation delay is large than critical value ?0.This thesis is composed of four chapters as follows:In Chapter 1,we systematically introduce the scientific background,relation the-ories knowledge and some previous works.Then we give some preliminaries and the main results of the paper.In Chapter 2,a Wolbachia-infected mosquitoes transmission model with incom-plete cytoplasmic incompatibility(CI)and nearly perfect maternal transmission is con-sidered.By using the Poincare-Bendixson theorem and constructing Lyapunov func-tion,we show that the global stability of the equilibriums is completely determined by the probability of cytoplasmic incompatibility(CI).A saddle-node bifurcation ap-pears when the value about the probability of cytoplasmic incompatibility(CI)Sh is changed.In Chapter 3,we consider the Wolbachia-infected mosquitoes transmission model with maturation delays and incomplete cytoplasmic incompatibility(CI).The local asymptotic stability of disease-free equilibrium and the positive equilibrium point for?= 0 is given by us.Moreover,we find the positive equilibrium will disappear when the maturation delay is large than the critical value ?0.At last,the main contents of this thesis are briefly summarized and some worth-while future works related to our results are put forward.