Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Viral Infection Model with a Nonlinear Infection Rate | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 958016 19 pages doi 2009 958016 Research Article A Viral Infection Model with a Nonlinear Infection Rate Yumei Yu 1 Juan J. Nieto 2 Angela Torres 3 and Kaifa Wang4 1 School of Science Dalian Jiaotong University Dalian 116028 China 2 Departamento de Analisis Matemứtico Facultad de Matemứticas Universidad de Santiago de Compostela 15782 Santioga de compostela Spain 3 Departamento de Psiquiatria Radiologia y Salud Publica Facultad de Medicina Universidad de Santiago de Compostela 15782 Santioga de compostela Spain 4 Department of Computers Science Third Military Medical University Chongqing 400038 China Correspondence should be addressed to Kaifa Wang kaifawang@ Received 28 February 2009 Revised 23 April 2009 Accepted 27 May 2009 Recommended by Donal O Regan A viral infection model with a nonlinear infection rate is constructed based on empirical evidences. Qualitative analysis shows that there is a degenerate singular infection equilibrium. Furthermore bifurcation of cusp-type with codimension two . Bogdanov-Takens bifurcation is confirmed under appropriate conditions. As a result the rich dynamical behaviors indicate that the model can display an Allee effect and fluctuation effect which are important for making strategies for controlling the invasion of virus. Copyright 2009 Yumei Yu et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Mathematical models can provide insights into the dynamics of viral load in vivo. A basic viral infection model 1 has been widely used for studying the dynamics of infectious agents such as hepatitis B virus HBV hepatitis C virus HCV and human immunodeficiency virus HIV which has the following forms dx _ 1 I - dx - pxv dt dyy pxv - ay a1 dv dt k - uv 2 .