| Species do not exist alone in nature.They are always competing with others for food and outside environment or preying on other species. The infectious diseases that are spread among the species will affect the birth rate or the death rate of the species.So we should merge these two areas of research in order to make the model more realistic. In this paper,we study a density-dependent predator-prey model of prey with vertical epidemic and applications.We obtain the following results:1.When disease that is infected vertically is spread among the prey population,an au-tonomous predator-prey model of prey with epidemic is established.The boundedness of solutions of the proposed system and the existence of equilibrium are studied, and the suf-ficient conditions for locally asymptotical stability of the equilibrium are obtained. Fur-thermore, the sufficient conditions of the extinction of infective prey population, disease disappearance and epidemic persistence are obtained from analyzing the global stability of the equilibrium.2.When disease that is infected vertically is spread among the prey population,a nonautonomous predator-prey model of prey with epidemic is established.The perma-nence of the prey and the predator is discussed,and the sufficient conditions of the perma-nence of the prey and the extinction of the predator are obtained.The different functional responses are analyzed in the permanence of the systems.3.The applications of the above system in the pest control are considered.The eco-epidemiological models of the continuous biological control and the impulsive biological control are established respectively. When the inputting rate of the predator is constant,the global stability of the pest's extinctive equilibrium is obtained by mathematical analysis .When the inputting rate of the predator is impulsive, the boundedness of solutions and the sufficient conditions of the permanence are studied. The results provide some methods in the pest management.
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