Modelling the dynamics of avian influenza with nonlinear recovery rate and psychological effect |
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Authors: | Xiaoyu Jiang Yu Yang Fanwei Meng and Yancong Xu |
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Institution: | Hangzhou Normal University,School of Statistics and Mathematics, Shanghai Lixin University of Account-ing and Finance, Shanghai, 201209, China,School of Mathematical Sciences, Qufu Normal University, Qufu, 273165,China and Hangzhou Normal University |
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Abstract: | In this paper, a 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 Lyapunov 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. |
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Keywords: | Avian influenza epidemic model psychological effect nonlinear recovery rate nonlinear incidence rate globally asymptotically stable |
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