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Table 1 Symbols and definitions

From: Mathematical modeling of solid cancer growth with angiogenesis

Symbols

Definitions

C

Concentration of normal cells at time t

E

Concentration of epithelial cells at time t

T

Concentration of cancer cells at time t

P

Concentration of pre-angiogenesis cells at time t

A

Concentration of angiogenesis cells at time t

α 1

Intrinsic growth rate of normal cells

α 2

Intrinsic growth rate of epithelial cells

α 3

Intrinsic growth rate of cancer cells

ε

Intrinsic growth rate of angiogenesis cells

μ 1

Mortality rate of normal cells

μ 2

Mortality rate of epithelial cells

μ 3

Mortality rate of cancer cells

μ 4

Mortality rate of pre-angiogenesis cells

μ 5

Mortality rate of angiogenesis cells

k 1

Carrying capacity of normal cells

k 2

Carrying capacity of epithelial cells

k 3

Carrying capacity of cancer cells

k 4

Carrying capacity of angiogenesis cells

δ

Transfer rate from pre-angiogenesis to angiogenesis cells

γ

Epithelial sprouting rate

β 1

Rate of inhibition of normal cells by cancer cells

β 2

Rate of inhibition of cancer cells by normal cells

  1. The summary of the variables and parameters of the model.