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Modelling the dynamics of avian influenza with nonlinear recovery rate and psychological effect
Yancong Xu,Xiaoyu Jiang,Yu Yang,Fanwei Meng
Keywords:Avian influenza epidemic model, psychological effect, nonlinear recovery rate function, nonlinear incidence rate, globally asymptotically stable
      In this paper, an SI-SEIR type avian influenza epidemic model with psychological effect, nonlinear recovery rate and saturation inhibition effect is formulated to study the transmission and control of avian influenza virus. By setting the basic reproductive number as the threshold parameter and constructing Liapunov function, Dulac function and using the Li-Muldowney"s geometry approach, we prove the local and global stability of disease-free equilibria and endemic equilibrium. Theoretical analysis are carried out to show the role of the saturation inhibition effect, psychological effect and effective medical resources in this model, and numerical simulations are also given to verify the results.