Fig. 4

Functional forms for \(f_{8}(t)\) and \(f_{9}(t)\). (a) The assumed age-related decline of epithelial cell proliferation, reparation and macrophage clearance of damaged epithelial cells (\(f_{8}(t)=1/(1+10^{-5.4+0.07\text {age}})+0.02\)) and (b) the increase in damage to healthy epithelial cells due to the mucosal layer becoming less effective at protecting them (\(f_{9}(t)=3.4\times 10^{-9}\text {age}^{5}-9.6\times 10^{-7}\text {age}^{4}+1\times 10^{-4}\text {age}^{3}-4.6\times 10^{-3}\text {age}^{2}+9.1\times 10^{-2}\text {age}\) \(+0.33\)) where age=(t+7300)/365 years and \(0\le t\le 21900\) days.