Figure 7.

Validation of approximate solutions. (A) Evolution of the approximate perturbation ${\displaystyle \hat{u}}$ compared to the original model perturbation ${\displaystyle u=R-R_L}$. (B) Evolution of the energy function of the approximate linearized model defined in Eq. (14) against the energy estimated by using the original model (1)–(2). (C) The zero-rate energy function in Eq. (21) estimated by using the approximate solution of the system (13). (D) The immuno-modulatory function ${\displaystyle {\hat{z}}_{ext}\left(t\right)}$ for ${\displaystyle \alpha =-0.6}$ and ${\displaystyle \gamma =100}$ compared with the zero-rate energy function ${\displaystyle \hat{z}\left(t\right)}$.