Stability Analysis Of Several Avian Influenza Models

Human infect with avian infuenza is caused by avian infuenza viruses in human disease.Avian infuenza virus, which belongs to the infuenza A virus, according to the diferent ofthe pathogenic avian infuenza virus in chicken and Turkey,divided it into three level:high,medium, low/non pathogenic.In this paper, according to the actual situation:just like, the incidence of disease, birth,immune therapy and other factors which has an important infuence on the spread of avianfu, we used infectious disease dynamics, diferential equations and the stability theories,and other relevant theories and research methods to establish the corresponding model. weanalysis and discussed the stability of the system deeply, and numerical simulation of themodel.Firstly, we present a highly pathogenic Avian infuenza epidemic model with saturatedcontact rate. According to study the dynamics, we calculated the basic reproduction numberof the model. Through the analysis of this model,we have the following conclusion:if R01,There is only one disease-free equilibrium is globally stable, and the disease will die; if R0>1,There is only one endemic equilibrium, which is globally stable, disease will be popular. Atlast, numerical simulations are performed to illustrate and verify the conclusions.Secondly,the establishment and stability analysis for a class of models based on avianinfuenza is studied. Using the next-generation matrix to get the reproduction numbers of themodel, Using Hurwitz criterion, the local stability of the disease-free equilibrium and endemicequilibrium of system is proved. we get stability of the disease-free equilibrium and endemicequilibrium for the model by means of suitable Lyapunov functions and LaSalle’s invarianceprinciple. At last, the conclusions above are verifed by numerical simulations.And the visualdisplay of the efect of vaccination on avian infuenza control by numerical simulation.Finally, we establish a epidemic model with Logistic growth of highly pathogenic Avianinfuenza. The basic reproduction number R0is obtained. we have proved the local stabilityof the system’s disease-free equilibrium and endemic equilibrium and the global stability using certain Lyapunov function method. If R0≤1,there exist a unique disease-free equilib-rium, which means the disease would die out fnally. R0>1, there exist a unique endemicequilibrium, which means the disease would become epidemic. The correctness of the theo-retical analysis is verifed by numerical simulation. Numerical simulations are performed toillustrate and verify the conclusions. Meanwhile, we fnd out it is useful for controlling thespread of the infectious disease to quarantine infected individuals.