A Viral Infection Model with a Nonlinear Infection Rate
1 School of Science, Dalian Jiaotong University, Dalian 116028, China
2 Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santioga de compostela, Spain
3 Departamento de Psiquiatría, Radiología y Salud Pública, 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
Boundary Value Problems 2009, 2009:958016 doi:10.1155/2009/958016Published: 29 June 2009
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.