Dynamics Of Two Types Vector-borne Diseases Model

Vector-borne diseases are those transmitted diseases through infected vampire arthropods(insect),which threaten to human health over a long time.To gain the insight into the effect of the various factors in the spread of infectious disease,we establish suitable mathematical model and theoretically analyze the model according to the transmission mechanism and outbreaks of vector-borne diseases.Based on relevant knowledge of vector-borne diseases and the theory of ordinary differential equations,in this dissertation,we formulate two mathematical models and mainly study the dynamical behaviors of these models.The primarily contents of this dissertation are listed as follows:1.A vector-borne disease mathematical model with two types of time delay are investigated.These delays are used to depict the maturation period of vector and incubation period of infectious diseases.By analyzing the corresponding characteristic equation,we discuss the local stabilities of the equilibria under different threshold con-ditions.By constructing suitable Lyapunov function and using the LaSalle's invariance principle,we obtain that the disease-free equilibrium is globally asymptotically stable when R0<1 and the unique endemic equilibrium is globally asymptotically stable when R0>1.The results illustrate that these two delay affect the persistence of the disease.2.A vector-borne disease mathematical model with prey-predator structure is studied.In this chapter,the existence of the endemic equilibrium is discussed and the sufficient condition for backward bifurcation and Hopf bifurcation is obtained.We prove the local asymptotic stability of the positive equilibrium by using the Gersgorin disk theory.Applying the Lyapunov stability method and geometric method,the global asymptotic stability of the disease-free equilibrium and endemic equilibrium are discussed.The results show that the diversity of predators will change the stability of the model.