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Table 3 Model parameters

From: A qualitatively validated mathematical-computational model of the immune response to the yellow fever vaccine

Parameter

Equation

Description

Value

π V

1

Viral replication rate

4.0 (day−1)

c v1

1

Maximum viral clearance rate by the innate system

2 × 103 (virus titer×day−1)

c v2

1

Half saturation constant

3 × 101 (virus titer)

k v1

1

YFV neutralization rate per unit of neutralizing antibodies

4.875 × 10−4 (day−1×A−1)

k v2

1

YFV neutralization rate per unit of CD8 + T cells

1.5694 × 10−3\(\left (\text {day}^{-1} \times T_{E}^{-1}\right)\)

α A P

2

Homeostasis rate of immature APCs

2.5 × 10−3 (day−1)

\(\beta _{A_{P}}\)

2,3

APC maturation rate

3.0 × 10−1 (day−1)

\(k_{A_{P1}}\)

2,3

With \(\beta _{A_{P}}\), defines the minimum production rate of A PM

1.0 (dimensionless)

\(k_{A_{P2}}\)

2,3

Defines the saturation point of A PM

2 × 102 (virus titer)

\(\delta _{A_{PM}}\)

3

Death rate of mature APCs

5.38 × 10−1 (day−1)

\(\alpha _{T_{N}}\)

4

Homeostasis rate of CD8 + T cells

2.17 × 10−4 (day−1)

π T

4,5

Activation rate of naïve CD8 + T cells

1 × 10−2 (day−1)

\(k_{T_{E}}\)

5

Replication rate of effector CD8 + T cells

1 × 10−5 (day−1)

\(\delta _{T_{E}}\)

5

Death rate of effector CD8 + T cells

1 × 10−1 (day−1)

α B

6

Homeostasis rate of B cells

6.0 (day−1)

π B

6

Replication rate of active B cells

1.77 × 10−3 (day−1)

β S

6,7

Differentiation rate of active B cells in short-lived plasma cells

6.72 × 10−1 (day−1)

β L

6,8

Differentiation rate of active B cells in long-lived plasma cells

8.05 × 10−3 (day−1)

β BM

6,9

Differentiation rate of active B cells in memory B cells

1 × 10−3 (day−1)

δ S

7

Death rate of short-lived plasma cells

2.0 (day−1)

δ L

8

Death rate of long-lived plasma cells

2.22 × 10−4 (day−1)

γ M

8,9

Differentiation rate of memory B cells in long-lived plasma cells

1.95 × 10−6 (day−1)

\(k_{B_{M1}}\)

9

Proliferation rate of memory B cell

1 × 10−5 (day−1)

\(k_{B_{M2}}\)

9

Maximum growth constant

10.0 (B M )

π AS

10

Antibody secretion rate (short-lived plasma cell)

5 × 10−1 (day−1)

π AL

10

Antibody secretion rate (long-lived plasma cell)

1.7 × 10−1 (day−1)

δ A

10

Antibody death rate

4 × 10−2 (day−1)a

  1. The value marked with a was extracted from [66, 67] apud [68]