A Viral Infection Model with a Nonlinear Infection Rate

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. This work is supported by the National Natural Science Fund of China nos. 30770555 and 10571143, the Natural Science Foundation Project of CQ CSTC 2007BB5012, and the Science Fund of Third Military Medical University 06XG001 SI