Analysis Of A Pair Approximation Epidemic Model Of Host-parasite And A Type Of Delayed Models

In this paper, we mainly investigate a delayed SIS epidemic model that based on the classical mean-field theory and a pair approximation model of host-parasite that incorporate spatial structure.The whole thesis consists of three chapter.In chapter 1,we introduce the background and the relational works of epidemic dynam-ics.At the same time,the main work of this paper are given.In chapter 2,we analyze the Hopf bifurcation of a delayed SIS epidemic model with stage structure and nonlinear incidence rate.We investigate the stability of the equilibrium, the conditions that the Hopf bifurcation occurs. Applying the normal form theory and the center manifold argument,we derive the explicit formulas determining the properties of the bifurcating periodic solutions. In addition,we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are included.In chapter 3,we establish a pair approximation model of host-parasite. Through calcu-lating, we obtain critical value that the infection will be established and the whole population goes to extinction,respectively. Then,we investigate the local stability of the disease-free equilibrium and the extinction equilibrium. In addition,we study the effect of susceptible hosts movements on parasites invasion and host persistence and extinction. Also we use numerical simulations to examine our theoretical analysis.