Table 3 Parameters’ description and value

\(d_{A_{\beta }^{i}}\)

Degradation rate of \(A_{\beta }^{i}\)

9.51/day [82]

\(d_{A_{\beta }^{o}}\)

Degradation rate of \(A_{\beta }^{o}\)

9.51/day [82]

\(d_{A_{\beta }^{o}{M}}\)

Clearance rate of \(A_{\beta }^{o}\) by microglia

2×10⁻³/day estimated

\(d_{A_{\beta }^{o}\hat {M}}\)

Clearance rate of \(A_{\beta }^{o}\) by macrophages

10⁻²/day estimated

d _τ

Degradation rate of tau proteins

0.277/day [88]

\(d_{F_{i}}\)

Degradation rate of intracellular NFT

2.77×10⁻³/day estimated

\(d_{F_{o}}\)

Degradation rate of extracellular NFT

2.77×10⁻⁴/day estimated

d _N

Death rate of neurons

1.9×10⁻⁴/day estimated

d _NF

Death rate of neurons by NFTs

3.4×10⁻⁴/day estimated

d _NT

Death rate of neurons by TNF- α

1.7×10⁻⁴/day estimated

\(d_{N_{d}M}\phantom {\dot {i}\!}\)

Clearance rate of dead neurons by M

0.06/day estimated

\(d_{N_{d}\hat {M}}\)

Clearance rate of dead neurons by \(\hat {M}\)

0.02/day estimated

d _A

Death rate of astrocytes

1.2×10⁻³ day ⁻¹ estimated

\(d_{{M}_{1}}\phantom {\dot {i}\!}\)

Death rate of M ₁ microglias

0.015 day ⁻¹ [47, 74]

\(d_{{M}_{2}}\phantom {\dot {i}\!}\)

Death rate of M ₂ microglias

0.015 day ⁻¹ [47, 74]

\(d_{\hat {M}_{1}}\phantom {\dot {i}\!}\)

Death rate of M ₁ macrophages

0.015 day ⁻¹ [47, 74]

\(d_{\hat {M}_{2}}\phantom {\dot {i}\!}\)

Death rate of M ₂ macrophages

0.015 day ⁻¹ [47, 74]

\(D_{A_{O}}\)

Degradation rate of A βO

0.951/day estimated

d _H

Degradation rate of HMGB-1

58.71/day [95]

\(D_{T_{\alpha }}\)

Degradation rate of TNF- α

55.45 day ⁻¹ [47, 74]

\(d_{T_{\beta }}\)

Degradation rate of TGF- β

3.33×10² day ⁻¹ [56, 99]

\(d_{I_{10}}\phantom {\dot {i}\!}\)

Degradation rate of IL-10

16.64 day ⁻¹ [47]

d _P

Degradation rate of MCP-1

1.73 day ⁻¹[47, 74]

R ₀

Initial inflammation by ROS

6 estimated

M ₀

Monocytes concentration in blood

5×10⁻² estimated

N ₀

Reference density of neuron

0.14 g/c m ³ estimated

\({M_{G}^{0}}\phantom {\dot {i}\!}\)

Source of microglia

0.047 g/c m ³ estimated

A ₀

Reference density of astrocytes

0.14 g/c m ³ estimated

\(\bar {K}_{A_{\beta }^{o}}\)

Michaelis-Mention coefficient for \(A_{\beta }^{o}\)

7×10⁻³ g/ c m ³ estimated

\(\bar {K}_{N_{d}}\)

Michaelis-Mention coefficient for N _d

10⁻³ g/ml estimated

\(K_{I_{10}}\phantom {\dot {i}\!}\)

Half-saturation of IL-10

2.5×10⁻⁶ g/ c m ³ estimated

\(K_{T_{\beta }}\phantom {\dot {i}\!}\)

Half-saturation of TGF- β

2.5×10⁻⁷ g/ml [90]

K _M

Half-saturation of microglias

0.047 g/ml estimated

\(K_{\hat {M}}\)

Half-saturation of macrophages

0.047 g/ml estimated

\(K_{M_{1}}\phantom {\dot {i}\!}\)

Half-saturation of M ₁ microglias

0.03 g/ml estimated

\(K_{M_{2}}\phantom {\dot {i}\!}\)

Half-saturation of M ₂ microglias

0.017 g/ml estimated

\(K_{\hat {M}_{1}}\)

Half-saturation of \(\hat {M}_{1}\) macrophages

0.04 g/ml estimated

\(K_{\hat {M}_{2}}\)

Half-saturation of \(\hat {M}_{2}\) macrophages

0.007 g/ml estimated

\(K_{F_{i}}\phantom {\dot {i}\!}\)

Half-saturation of intracellular NFTs

3.36×10⁻¹⁰ g/ml [89]

\(K_{F_{o}}\phantom {\dot {i}\!}\)

Average of extracellular NFTs

2.58×10⁻¹¹ g/ml estimated

\(K_{A_{O}}\phantom {\dot {i}\!}\)

Average of of A βO

1×10⁻⁷ g/ml estimated

K _P

Half-saturation of MCP-1

6×10⁻⁹ g/ml estimated

\(K_{T_{\alpha }}\)

Half-saturation of TNF- α

4×10⁻⁵ g/ml estimated