Boundary Value Problems
Volume 2009 (2009), Article ID 958016, 19 pages
doi:10.1155/2009/958016
Research Article
A Viral Infection Model with a Nonlinear Infection Rate
1School of Science, Dalian Jiaotong University, Dalian 116028, China
2Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santioga de compostela, Spain
3Departamento de Psiquiatría, Radiología y Salud Pública, Facultad de Medicina, Universidad de Santiago de Compostela, 15782 Santioga de compostela, Spain
4Department of Computers Science, Third Military Medical University, Chongqing 400038, China
Received 28 February 2009; Revised 23 April 2009; Accepted 27 May 2009
Academic Editor: Donal O'Regan
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.
Abstract
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 (i.e., 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.