Fig. 5
Functional forms for \(f_{10}(t)\), \(f_{11}(t)\), \(f_{12}(t)\), \(f_{13}(t)\), \(f_{14}(t)\) and \(f_{15}(t)\). (a) The assumed age-related decline of macrophage activation by pro-inflammatory cytokines (\(f_{10}(t)\)) and activation and production of anti-inflammatory cytokines by macrophages (\(f_{13}(t)\)) where \(f_{10}=f_{13}=1/(1+10^{-5.9+0.1\text {age}}+0.02\). (b) The age-related decline in T-cell (\(f_{11}(t)\)) and B-cell (\(f_{12}(t)\)) proliferation where \(f_{11}=f_{12}=-1.2\times 10^{-9}\text {age}^{5}+\) \(2.6\times 10^{-7}\text {age}^{4}-2.2\times 10^{-4}\text {age}^{3}+1.2\times 10^{-3}\text {age}^{2}-5.8\times 10^{-2}\text {age}+1.8\). (c) The increase with age of production of pro-inflammatory cytokines by macrophages (\(f_{14}(t)\)) and T-cells (\(f_{15}(t)\)) where \(f_{14}=f_{15}=3.4\times 10^{-9}\text {age}^{5}-9.6\times 10^{-7}\text {age}^{4}+ 1\times 10^{-4}\text {age}^{3}\) \(-4.6\times 10^{-3}\text {age}^{2}+9.1\times 10^{-2}\text {age}+0.33\). As in previous figures, age=(t+7300)/365 years and \(0\le t\le 21900\) days.
