Abstract:
The development of a viral infection in the organism is a complex process which depends on the competition
race between virus replication in the host cells and the immune response. To study different regimes of infection
progression, we analyze the general mathematical model of immune response to viral infection. The model
consists of two ODEs for virus and immune cells non-dimensionalized concentrations. The proliferation rate of
immune cells in the model is represented by a bell-shaped function of the virus concentration. This function
increases for small virus concentrations describing the antigen-stimulated clonal expansion of immune cells, and
decreases for sufficiently high virus concentrations describing down-regulation of immune cells proliferation by
the infection. Depending on the virus virulence, strength of the immune response, and the initial viral load, the
model predicts several scenarios: (a) infection can be completely eliminated, (b) it can remain at a low level
while the concentration of immune cells is high; (c) immune cells can be essentially exhausted, or (d) completely
exhausted, which is accompanied (c, d) by high virus concentration. The analysis of the model shows that virus
concentration can oscillate as it gradually converges to its equilibrium value. We show that the considered model
can be obtained by the reduction of a more general model with an additional equation for the total viral load
provided that this equation is fast. In the case of slow kinetics of the total viral load, this more general model
should be used.
Keywords:dynamics of viral infection, immune response, bistability, damped oscillations,
mathematical modeling, qualitative analysis of ordinary differential equations.
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