Nonlinear Oscillations in Models of Immune Responses to Persistent Viruses

This paper compares several population models for HIV dynamics. The effect of perfect or nonperfect drugs proposed by Ho, Perelson, and others are considered in the more complicated models of Nowak and Bangham for immune responses to persistent viruses. It is pointed out that two models proposed by Nowak and Bangham have different dynamical behaviors. One of them can have sustained oscillations via the Hopf bifurcation and the other does not. To overcome the difficulty in symbolic computations for complicated systems, we use parameter transforms and introduce a semisymbolic method. This method is very efficient in finding Hopf bifurcation parameters and can be used for other models.