The Effects Of Disease On The Relationship Between The Predators And The Preys

In this paper,a predator-prey model with two genotypes both in the predators and the preys,a Lotka-Volterra predator-prey model with disease spreading in the preys and a power law predator-prey model with disease spreading in the preys are discussed mainly.In chapter one,the researches and development are introduced for the epidemic models,the population models and the eco-epidemic models,and the main results of the paper are given.In chapter two,some definitions and theories of differential equations used in the paper are introduced.Considering two genotypes both in the predators and the preys,a predator-prey model with two genotypes is proposed in chapter three.First,the sufficient condition is given for existence of positive equilibrium.Then,the sufficient conditions for the stability of equilibria and the function expression of local center manifold are obtained by the eigenvalue method and the center manifold theory and Routh-Hurwitz stability criterion,respectively.Finally,the main results are verified by numerical simulations.Considering the disease spreading in the preys,a Lotka-Volterra predator-prey model with disease in the preys is proposed in chapter four.The sufficient condition for existence of positive equilibrium is discussed,and the sufficient conditions for the stability of equilibria and the function expression of periodic solutions on local center manifold are obtained by the eigenvalue method and the center manifold theory,respectively.Then,the periodic solutions around zero-Hopf equilibria are shown by numerical simulations,and the threshold for prevalence of disease is given.Considering the disease spreading in the preys,a power law predator-prey model with disease in the preys is proposed in chapter five.The sufficient condition for existence of positive equilibrium is discussed,and the sufficient conditions for stability of equilibria are obtained by the eigenvalue method,Routh-Hurwitz stability criterion.Furthermore,the threshold for the prevalence of disease is given,and the main results are verified by numerical simulations.In chapter six,summaries and further studies of the paper are given.