Low viral persistence of an immunological model

Hepatitis B virus can persist at very low levels in the body in the face of host immunity, and reactive during immunosuppression and sustain the immunological memory to lead to the possible state of 'infection immunity'. To analyze this phenomena quantitatively, a mathematical model which is described by DDEs with relative to cytotoxic T lymphocyte (CTL) response to Hepatitis B virus is used. Using the knowledge of DDEs and the numerical bifurcation analysis techniques, the dynamical behavior of Hopf bifurcation which may lead to the periodic oscillation of populations is analyzed. Domains of low level viral persistence which is possible, either as a stable equilibrium or a stable oscillatory pattern, are identified in parameter space. The virus replication rate appears to have influence to the amplitude of the persisting oscillatory population densities.