Fig. 2

Functional forms for \(f_{1}(t)\) and \(f_{2}(t)\). (a) The assumed decline of available macro and micronutrients with increasing age, \(f_{1}(t)=1/(1+10^{-5.9+0.06\text {age}})+0.008\), and (b) the decline of pathogenic elimination by reduced autophagy, bacteria clearance, secretory IgA and SCFAs, \(f_{2}(t)=1(1+10^{-5.9+0.1\text {age}})+0.02\) where age=(t+7300)/365 years and \(0\le t\le 21900\) days.