The Study Of Dynamic Behaviors For Avian Influenza Model

In recent years, the avian influenza virus is gradually known by everyone. The main reason is that the virus gradually changes to a health-threatening subspecies of human infection. For this reason, the World Health Organization has identified the avian influenza as one of the diseases with potential threat to human. It is important for human to study and determine its development rules and the prevention and control measures using scientific methods. In this paper, several avian influenza mathematical models are established and analyzed with epidemic dynamic method and traditional compartment ideology.Firstly, consider an epidemic model of the avian influenza with no infection between people. Through the analysis of model, the basic reproduction number0 R, as a threshold parameter to disease transmission, is obtained. If 0R ?1, only disease- free equilibrium exists in the system and such equilibrium is globally asymptotically stable. If 0R ?1, the disease- free equilibrium is unstable while the endemic equilibrium is globally asymptotically stable. As the basic reproduction number is unrelated to people, it shows that the hunting and isolation are great help to the avian influenza control.Secondly, since the modern information technology is developed, the influence of media on people's life becomes greater and greater. Thus build an avian influenza epidemic model under media influence. Through the analysis of the global dynamic behaviors of the system, the basic reproductive number is got. The diseases-free equilibrium is globally asymptotically stable and the disease will extinct if R0 1?; the endemic equilibrium is globally asymptotically stable and the disease will continue to spread if 0R ?1. From the analysis above, the size of the infectious diseases could be controlled by media reports.Thirdly, due to the limitations of medical resources and so on, the treatment rate will be saturated along with the increasing number of patients. According to this situation, establish the avian influenza model with saturated treatment rate and investigate the influence on the avian influenza spread from media reports and saturated treatment. The basic reproduction number of the model is obtained and the dynamic behavior has been analyzed with V function, Dulac function and the limit equation theory. The diseases- free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to 1; the endemic equilibrium is globally asymptotically stable if the reproduction number is larger than 1. O ur theoretical results have already been supported by numerical simulation.Finally, consider an epidemic model with vaccination. After dynamic analysis, a basic reproductive number R0 is got. The system's diseases-free equilibrium0 E is global asymptotic stability in K if 0R ?1. The system has a unique endemic equilibrium, and the endemic equilibrium is global asymptotic stability in K if 0R ?1. This shows that the size of the disease could be controlled by improving the vaccination rate and reducing the contact rate, in other words- isolation and vaccination.