Figure 1.

Schematic of the model. The quantities being tracked are virus V, uninfected and infected cells with n virions bound to the surface, U_n and I_n, and an immune response X, all expressed in particles per millilitre. Free virions (black) attach to uninfected cells at rate or infected cells at rate The attachment is reversible, and detachment can occur at rates and (the extra factors of n or n+1 in the flow rates account for multiple bound virions). Bound virions (white) are internalized into uninfected or infected cells at rates g_u and g_i. If an internalized virion (grey) enters an already infected cell, it does not alter the state of the infected cell. A fraction f of virions internalized into uninfected cells turn those cells into productively infected cells. Infected cells produce progeny virions at rate p, which are initially bound to the infected cell membrane (not drawn in the figure). The virions bound to infected cells can detach from the infected cells at rate to become free virions. Infected cells die and virions are cleared at fixed rates d and c, respectively. Also modelled is an adaptive immune response, which we consider a simplified representation of either a B cell/antibody or CD8⁺ CTL response. The immune response is described by a simple exponential growth term at rate r, corresponding to clonal expansion of T cells/B cells. The immune response is assumed to either clear free virions at a rate w₁ (antibody/B-cell response) or kill infected cells at rate w₂ (CTL response).