| The predator-prey relationship is a very important research object in population ecology,and it is also one of the most important relationships that regulate the interaction between species.Through the study of such models,the trend of the number of animal populations can be predicted.Since diseases can spread between species,while studying the predator-prey model,considering the factor of ecological epidemics will make the research results more realistic.In this paper,the stability of two predator-prey models will be studied separately.Firstly,we discuss a predator-prey model with stage structure.Beddington-De Angelis functional response function is used to describe the interference effect between predators.The juvenile of the prey jellyfish is the polyp,and predator only feeds on the adult jellyfish.By using the asymptotic system theory and the uniform persistence theory,the global asymptotic stability of the boundary equilibrium points in the model and the permanence of the predator are proved respectively.Numerical simulation is used to verify and supplement the results of qualitative theoretical analysis.Secondly,in this paper,a predator-prey model with infected disease for predator is established.Both infected predators and susceptible predators have the ability to catch prey,and it is assumed that the disease will not spread in the prey population.The global stability of boundary equilibrium points is proved by using the limit theory and the method of constructing the Lyapunov function.In addition,the sufficient conditions of uniform persistence for the infected predators are obtained by using the uniform persistence theory.Finally,the rationality of the results is further verified by numerical simulation. |
