Qualitative Research On Solutions Of Several Delay Stage-Structured Biological Models

This dissertation is mainly concerned with the qualitative behavior of the solutions for several classes of stage-structured biological models with time delays. This dissertation is divided into four chapters, and the main contents are as follows.First, the research background and status of the biological mathematical model are reviewed. Further more, the main results of this dissertation is summarized.In Chapter2, a delay predator-prey model with stage structure of the predators is investigated. By using the Lyapunov function and the technique of differential inequality, some sufficient conditions for permanence and extinction of the model are obtained.In the third chapter, the qualitative behavior of a delay predator-prey model with stage structure of prey is discussed. Based on the method of Lyapunov functions, some results are established, such as permanence and extinction for the model.Finally, a class of infection model with stage structure is considered. Similar to the previous chapters, by using the method of Lyapunov function, sufficient conditions for permanence and extinction for the model are obtained.