Estimating the Cost of a CTL Escape Mutation

<div><p>(A) Plots the hypothetical changes in the replication rate of the virus during the acute phase of infection. We assume that initially (until time <i>T_r</i>) the virus population expands exponentially at rate <i>r_max</i>, and after <i>t</i> = <i>T_r ,</i> the virus replication rate is reduced exponentially at rate λ to a smaller value <i>r_min</i>. Biologically this would correspond to the acute phase of SIV/HIV infection when the replication rate of the virus depends on the availability of target cells, which are depleted by the virus.</p><p>(B) Plots changes in the ratio <i>z</i>(<i>t</i>) calculated using Equation 8 with <i>k</i>(<i>t</i>) = 0 for the replication rate <i>r</i>(<i>t</i>) shown by a solid line in (A). For two measurements of the ratio <i>z</i> at <i>t_s</i> = 0 and <i>t_e</i> = 25 d, we obtain a minimal estimate of the cost of the escape mutation assuming exponential virus growth with <i>r_max</i> = 1.5 d⁻¹ (shown by dashed lines), i.e., <i>c_min</i> = 0.065 which is 65% of the actual fitness cost. Other parameters: <i>r_min</i> = 0.5 d⁻¹, <i>T_r</i> = 10 d, λ = 0.5 d⁻¹, <i>z</i>(0) = 0.1, <i>c</i> = 0.1.</p>