Open Access Research Article

A Viral Infection Model with a Nonlinear Infection Rate

Yumei Yu1, JuanJ Nieto2, Angela Torres3 and Kaifa Wang4*

Author Affiliations

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

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Boundary Value Problems 2009, 2009:958016  doi:10.1155/2009/958016

Published: 29 June 2009

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.