Analysis For Two Kinds Of Corruption Dynamic Models

Corruption is a common problem in all countries of the world,which seriously affects social sta-bility and the long-term development of the country,which has aroused great concern of all countries.Therefore,it is of great practical significance to study the spread and control of corruption.Through research,we have found that there are many similarities between the types of people and the ways of transmission within the scope of government officials' corruption and epidemics.So,in this paper,two kinds of corruption models with time delay are established to study the propagation of corruption.In the first part,we establish a model of lag effect with the duration ?1 from perishable to corrupt.The expression of the basic reproduction number of the model and the existence conditions of the equilibrium point are given.The corruption-free equilibrium point Eo is locally and globally asymptotically stable,and the sufficient condition of the local asymptotic stability of the corruption equilibrium point E*and the existence of the Hopf branch are obtained.In the second part,we established a class of lag model with time intervals of r2 ranging from self-disciplined to perishable.The expression of the basic reproduction number of the model and the existence conditions of the equilibrium point are given.The corruption-free equilibrium point E0 is locally and globally asymptotically stable.Then the sufficient condition of the local asymptotic stability of the corruption equilibrium point E*and the existence of the Hopf branch are obtained.The results of our research show that by strengthening the anti-corruption propaganda,the legal awareness can be deeply rooted among people,and can effectively control the spread of corruption;by increasing the punishment,the corrupter will feel afraid psychologically,thus the corruption phe-nomenon can be decreased in society.