Behavior of solutions of Eq (1).

A) Numerical simulations of Eq (1) reproduce the qualitative dynamics of T cell clonal expansion and contraction [32, 49]. 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 [37, 52]. C) According to Eq (1), 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 λ_AP, 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): k = 150, c = 40, λ_P = 50, α = 50, β = 0.01, y₀ = 10³, μ = 1, φ = 10⁶, λ_H = 10, and T_P(0) = 10. Each dot in C corresponds to a single numerical simulation of the model using the same parameters as in B, except for α and β, 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 λ_AP taking the values 25, 55, 85 and 115.