  Effects of immune delay on symmetric dynamics are investigated within a model
of antigenic variation in malaria. Using isotypic decomposition of the phase
space, stability problem is reduced to the analysis of a cubic transcendental
equation for the eigenvalues. This allows one to identify periodic solutions
with different symmetries arising at a Hopf bifurcation. In the case of small
immune delay, the boundary of the Hopf bifurcation is found in a closed form in
terms of system parameters. For arbitrary values of the time delay, general
expressions for the critical time delay are found, which indicate bifurcation
to an odd or even periodic solution. Numerical simulations of the full system
are performed to illustrate different types of dynamical behaviour. The results
of this analysis are quite generic and can be used to study within-host
dynamics of many infectious diseases.
