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Low level viral persistence after infection with LCMV: A quantitative insight through numerical bifurcation analysis. (English) Zbl 0988.92014

Summary: 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 ‘infection immunity’. To analyse low level viral persistence in quantitative terms, we use a mathematical model of antiviral cytotoxic T lymphocyte (CTL) response to lymphocytic choriomeningitis virus (LCMV). This model, described by a nonlinear system of delay differential equations (DDEs), is studied using 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.
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 and 100 pfu per spleen, are possible within quite narrow intervals of the rates of virus growth and precursor CTL population death. Whereas the virus replication rate appears to determine the stability of the low level virus persistence, it does not affect the steady-state level of the viral population, except for very low values.

MSC:

92C50 Medical applications (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K18 Bifurcation theory of functional-differential equations

Software:

DDE-BIFTOOL
PDFBibTeX XMLCite
Full Text: DOI

References:

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