Behavior of solutions of Eq (1).

<p>A) Numerical simulations of <a href="" target="_blank">Eq (1)</a> reproduce the qualitative dynamics of T cell clonal expansion and contraction [<a href="" target="_blank">32</a>, <a href="" target="_blank">49</a>]. B) In agreement with empirical data, a transient increase in total memory is eventually damped out to a structural carrying capacity (dashed line), which entails the loss of some pre-existing memory T cells [<a href="" target="_blank">37</a>, <a href="" target="_blank">52</a>]. C) According to <a href="" target="_blank">Eq (1)</a>, infections by pathogens with higher growth rates or lower clearance rates result in the formation of more memory T cells. D) The number of memory T cells also increases with parameter <i>λ</i><sub><i>AP</i></sub>, i.e, clones showing higher affinities for antigens of the pathogen, or clones targeting more abundant antigens produce more memory T cells. The values of the parameters used in A and B are the following (in suitable units): <i>k</i> = 150, <i>c</i> = 40, <i>λ</i><sub><i>P</i></sub> = 50, <i>α</i> = 50, <i>β</i> = 0.01, <i>y</i><sub>0</sub> = 10<sup>3</sup>, <i>μ</i> = 1, <i>φ</i> = 10<sup>6</sup>, <i>λ</i><sub><i>H</i></sub> = 10, and <i>T</i><sub><i>P</i></sub>(0) = 10. Each dot in C corresponds to a single numerical simulation of the model using the same parameters as in B, except for <i>α</i> and <i>β</i>, which are randomly chosen within the ranges [20, 40] and [0.5, 1.2] respectively. Parameter values in D are the same as in C, with <i>λ</i><sub><i>AP</i></sub> taking the values 25, 55, 85 and 115.</p>