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TW 321

T. Luzyanina, K. Engelborghs, S. Ehl, P. Klenerman and G. Bocharov
Low level viral persistence after infection with LCMV: a quantitative insight through numerical bifurcation analysis

Abstract

Many important viruses persist at very low levels in the body in the face of host immunity, and may influence the maintenance of this state of immunity. To analyse low level viral persistence or state of "infection immunity" in quantitative terms, we use a mathematical model of antiviral cytotoxic T lymphocyte (CTL) response to lymphocytic choriomeningitis virus (LCMV). This model is described by a nonlinear system of delay differential equations (DDEs). The model predictions related to coexistence of virus and CTL populations are obtained using recently developed numerical bifurcation analysis techniques for DDEs. Domains where low level LCMV coexistence with CTL memory is possible, either as an equilibrium state or an oscillatory pattern, are identified in spaces of the model parameters characterising the interaction between virus and CTL populations. In the "memory" phase, i.e.~after acute infection has been controlled, these include the rate constants of virus growth, precursor and effector CTL death, activation and differentiation of precursor CTL and CTL-mediated virus elimination. Our analysis suggests that the coexistence of replication competent virus below the conventional detection limit (of about 100 pfu per spleen) in the immune host as an equilibrium state requires the per day relative growth rate of the virus population to decrease at least 5 fold compared to the acute phase of infection. Oscillatory patterns in the dynamics of persisting LCMV and CTL memory, with virus population varying between 1 to 100 pfu per spleen, are possible within quite narrow intervals of the rates of virus growth and precursor CTL population death. This is due to a high sensitivity of the amplitude of oscillations to changes in the parameters. These observations may be relevant to low level viral persistence and CTL memory in human infections such as HBV, HCV and, probably, HIV.