Analysis Of Three Kinds Of Eco-Epidemiological Models With Holling Functional Response

In this paper, the three types of eco-epidemiological model with the saturation incidence rate and Holling ? functional response, Holling ? functional response and general function-al response are studied. They are arranged in the second chapter, the third chapter and the forth chapter in this article.First of all, the boundedness of solutions of the three types of eco-epidemiological model are analyzed. Then the existence of non-negative equilibrium points are discussed. The locally asymptotical stability of these non-negative equilibrium points is judged by using the characteristic root method and the Hurwitz criterion respectively. Finally using Lasalle invar-iable set, limit theory, Dulac rule and Liapunov function to prove the globally asymptotical stability of the non-negative equilibrium points. Through discussing the three types of eco-epidemiological models, the thresholds that can make the disease-free equlibrium points to be locally asymptotical stability are obtained. The sufficient conditions which make disea-se-free equlibrium points to be the globally asymptotical stability are also obtained in the article. Some conclusions are showed in the second chapter and the third chapter in this article:(1) If R0<1, R1<0, the susceptible predator exists. When R1>0, the predators tend to be extincted.(2) If R0<1,R1<0 and M<d2+?/?, the epidemic is eliminated, the susceptible predator and the prey are both existing in harmony.(3) If R3<0,R4>0, the epidemic is eliminated. The predators tend to be extincted, the number of prey population will be close to K(1-qE/r).One of the main aims to study the eco-epidemiological models is to eliminate the spread of the disease, thus the conclusions obtained by studying the eco-epidemiological models, can make a good supplement for the senior research and also have a great help in the practical life.