Stability Analysis Of Several Population Dynamic Models With Stage-structure

In this paper,two kinds of population dynamics models with stage structure and three kinds of epidemic model with stage structure are studied.The main content is as follows.Firstly,the growth of individual is divided into two stages:the young stage and the adult stage.According to two situations,only the growth of adult individuals is density-dependent and only the growth of young individuals is density-dependent,two population dynamics models with stage structure are formulated.The basic reproduction numbers of all population were obtained respectively,and the global stability of each equilibrium is obtained by constructing proper Lyapunov function.The obtained results shown that the basic reproduction numbers completely determine the dynamic behavior of the model.Secondly,an epidemic model with bilinear incidence and stage structure is established.In the model,the disease transmits only among adult individuals,and the growth of adult individuals is density-dependent,the growth of juvenile and transfer from juvenile to adult is exponential.The basic reproduction numbers of population and infection transmission are determined.The global stability of the equilibrium is obtained by constructing appropriate Lyapunov functions,the obtained results are verified by numerical simulation,and some feasible control measures are proposed.The obtained results illustrate that the two basic reproduction numbers of the model completely determine the dynamic behaviors of the model.Thirdly,an epidemic model with stage-structure is established by assuming that the disease can transmit only among adult individuals and that the growth of the young individuals is density-dependent.The basic reproduction numbers of population and infection transmission are determined.The global stability of the equilibrium is obtained by constructing appropriate Lyapunov functions.The obtained results illustrate that the two basic reproduction numbers completely determine the dynamic behaviors of the model.Fourthly,an epidemic model with horizontal transmission is established in which diseases transmits only among adult individuals,and the infected adult produce normally.The locally asymptotically stability of equilibrium is obtained.The global stability of population extinction equilibrium and the population survival-disease extinction equilibrium are obtained by con-structing appropriate Lyapunov functions.Finally,the obtained results are verified by numerical simulation.