Analysis Of Several Kinds About Predator-Prey Models With Epidemic And Saturation Rates

Nowadays,the rapid development of science and technology have triggered the emergence of a series of ecological problems.Experts have deepened their researches on the mathematical model of ecological epidemic dynamics,whose results will provide guidance for relevant departments to predict and control diseases.Ecological epidemic dynamics is mainly used for quantitative studies of epidemics.It can be applied to analyze the existing questions in ecological environment,to establish a mathematics model with typical characteristics of ecological epidemic,and to summarize the spread rules and ranges of the diseases by researching relevant models.With the research findings,experts are able to infer the development trend of the epidemic,to explore the key factors that influence the spread of the diseases.By analyzing and controlling its influencing factors,experts could establish relevant control mechanisms and develop prevention and control measures.This paper mainly studies several types of ecological epidemic models with saturated incidence,recovery rate,and shelters.The specific arrangements are as follows:The first chapter is the introduction.In this part,the writer gives elaborate analysis about the research background and significance of this paper,and introduces the research status of ecological epidemic in details,and states the main research contents of this paper.Finally,the writer presents a series of basic definitions about ecological epidemic and lists the relevant lemmas and theorems that are needed in this paper.In the second chapter,the writer establishes and studies a model with shelter and prey infection.Firstly,the boundedness of the system solution is analyzed in detail.Secondly,all kinds of equilibrium points are calculated,and the local stability of these non-negative equilibrium points is demonstrated by characteristic root method and Hurwitz theorem,and the threshold of local asymptotic stability at the equilibrium point of extinction of infectious diseases is found.Subsequently,by using the principle of Lasalle invariant set,limit theory,Dulac criterion,Liapunov function and other related knowledge,the writer proves the global stability of the non-negative equilibrium points of the ecological epidemic model.Finally,through the research and analysis of the system,the writer presents the sufficient conditions for the global asymptotical stability of the epidemic extinction equilibrium point of the system.In the third chapter,the writer discusses the spread of epidemic in predator population.By establishing and studying an ecological epidemic model with saturation rate,recovery rate and shelter,the writer proves the boundedness of system solution,and calculates the corresponding equilibrium points,and deduces and analyze the stability of non-negative equilibrium points,and proves the permanence of the system.In the fourth chapter,the writer mainly considers the spread of epidemic in the prey and predator population.In this part,by establishing and studying a kind of ecological epidemic model with recovery rate and vertical spread in both prey and predator,the writer proves the boundedness of the solution,and calculates and analyzes the stability of the non-negative equilibrium points of the model.