Boundary Value Problems
Volume 2009 (2009), Article ID 958016, 19 pages
doi:10.1155/2009/958016
A viral infection model with a nonlinear infection rate
Yumei Yu1
, Juan J. Nieto2
, Angela Torres3
and Kaifa Wang4
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
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.