Research On Hybrid Population Model Under Seasonal Alternation And A Class Of Multi-group Alcoholism Model

Differential equations play a very important role in describing the growth rate of populations and infectious diseases models,many scholars at home and abroad have drown many important conclusions about various models.This paper mainly takes pop-ulation and infectious diseases models for the research background,a class of predator-prey model based on alternation of fishing season and fishing ban season,and two kinds of functional responses,a class of population competitive model with the season-al alternation and harvesting and analysis of an age-structure multi-group alcoholism model with public health education are discussed,and discuss these models dynamic behaviors.The main research contents can be arranged as follows:1.In the first part,firstly,the biological background and current situation of the research contents in this paper are given.Secondly,some achievements in popula-tion and infectious disease are introduced.Finally,the main research of this paper is introduced.2.In the second part,we study the fishing season,fishing ban season alternat-ing with Holling?functional response and Beddington-Deangelis functional response of two species predator-prey model with harvesting.We mainly study the dynamic behaviors such as boundedness,persistence,and extinction of the system.By con-structing appropriate Lyapunov function,we study the global asymptotic stability of the equilibrium,and establish corresponding criteria.Finally,the theoretical results are illustrated by numerical simulation.3.In the third part,a species competition model with harvesting and seasonal alternation have been established.We analyse the dynamic behavior of the model in a single population,then by using the theory of discrete dynamic system and the theory of spectral radius,the dynamic behavior of the whole system is obtained.Finally,the correctness of the theoretical analysis is verified by numerical simulation.4.In the fourth part,an age-structure multi-group alcoholism model with public health education is considered.Furthermore,we prove that the existence and unique-ness of the solution,and the basic reproduction number R₀plays an important role in the long-time behavior of the model.We establish the right Lyapunov function to get the global stability:If R₀?1,the alcohol-free equilibrium P₀is global asymptot-ical stability,and the alcohol-present equilibrium P^*is global asymptotic stability if R₀>1.