Dynamics Analysis Of Several Avian Influenza Models

In recent years,human infection with avian influenza has occurred.It is reported by WHO that the disease may be potential threat to human disease.In the near future avian flu may bring greater harm to human beings and serious threat to human life and safety.It has the practical significance to study the spread and prevention strategies of avian flu virus.In this paper,we use several kinds of methods for infectious disease dynamics to establish mathematical models related with avian influenza according to the characteristics of the spread of avian flu.First of all,we formulate the mutual infection of SI-SIR avian influenza model with media,and discuss the global dynamics of the model.We obtain the basic reproduction number Ra and R0.If Ra＜1 and R0＜1,the disease free equilibrium is globally asymptotically stable and the disease extinction;if Ra＜1 and R0＞1,the boundary equilibrium is globally asymptotically stable and the disease just spread in the crowd;if Ra＞1,the positive equilibrium point E2* is globally asymptotically stable,and the disease is eventually persistent.Secondly,we establish and study the avian influenza model with media reports and saturated treatment.We obtain the basic reproduction number r0 and R0 corresponding to bird system and human system.We study the dynamics analysis by using V function,Dulac function and limit equation theory.When the number of patients is in the treatment range,the disease-free equilibrium E0 is globally asymptotically stable and the disease will be extinct if r0≤1;the endemic equilibrium E0* is globally asymptotically stable and the disease will continue if r0＞1;when the number of patients is over the treatment ability,the endemic equilibrium E1* is globally asymptotically stable and the disease will eventually continue if r0＞1 and R0＞1.Further numerical simulations support our theoretical results,and show the influence of media coverage on the scale of infectious diseases.Finally,we establish the avian influenza transmission model with virus variation.We analyze the stability of the equilibrium of the model and obtain the threshold value of the disease.The research results is to provide theoretical basis for prevention and control of avian influenza.