| In recent years, the population dynamics and epidemic dynamics have beenextensively researched with many excellent research results produced, however,people pay little attention to their mergence, namely the eco-epidemiological model. Itis widespread that diseases transmit in different populations in the nature, therefore,researches on eco-epidemiological model about how to control and prevention ofinfectious diseases spread disease in populations is very important.In this paper, we mostly study a class of predator-prey system with disease in theprey and the new model with Holling type â…¡functional response function which ison the basis of the fist system. Then we get the local stability of the equilibrium pointsand use a new method to get the global stability. Hopf bifurcation of the new model isdiscussed. The text is divided into five chapters:The first chapter mainly introduces the background of the research questions andresearch status in this field.The second chapter is prepared knowledge, the stability theory knowledge,Hurwitz judging rules, the Hopf bifurcation theory as well as the geometry method ofthe global stability.The third chapter mainly discusses a three-dimensional eco-epidemiologicalmodel with disease in the prey, it is proved that this model is only suitable for thelower animals, such as algae, fungi, ect.. We analyze the dynamics of the system suchas, boundedness of the solutions, existence of non-negative equilibria and the localstability of the equilibrium points in this chapter and use the geometric method toinvestigate global stability.The fourth chapter mainly studies the stability and Hopf bifurcation of athree-dimensional eco-epidemiological model with Holling type â…¡functional responsefunction, the model is on the basis of the model of the third chapter, it is suitable forvertebrates invertebrates. This chapter mainly discusses the boundedness of thesolutions, existence of non-negative equilibria and the local stability of theequilibrium points, then we use the geometric method to investigate global stability. Using the qualitative of ordinary differential equations and stability theory, we choosetransmission rate as bifurcation parameters and discuss the existence of Hopfbifurcation of the interior equilibrium. Finally, a numerical simulation is given. |
