Table 1 Explanations of symbols

M

the total amount of cells in the media, it consists of RBCs and iRBCs

S(t)

the number of schizonts which infect RBCs at time t

R(t)

the number of fresh RBCs infected by schizont at time t

a _in

the average number of RBCs infected by one schizont during the infection period

a _af

the average number of RBCs infected by one schizont after the infection period

$\tilde{L}$

the normalized life span of individual iRBCs

$p_{\tilde{L}}\left(l\right)$

the probability density function of normalized life span $\tilde{L}$

L

the average life span of iRBCs

L'

the individual life span of iRBCs

ℓ

the cell age of iRBC in hours

{f _i (ℓ), ℓ ∈ [0, L]}

the intrinsic gene expression pattern of protein i

ℓ_re

the rescaled cell age according to its normalized life span $\tilde{L}$

{f _i (ℓ_re), ${\ell }_{\mathsf{\text{re}}}=\tilde{L}\ell$, ℓ ∈ [0, L']}

the gene expression profile of individual iRBC on protein i

S _f (t)

the number of fast-growing iRBCs which infect RBCs at time t

R _f (t)

the number of RBCs infected by fast-growing iRBCs at time t

N(t)

the total number of iRBCs that have been infected at time t

N(t, ℓ_re)

the number of iRBCs which reach rescaled cell age ℓ_re at time t

e _i (t)

the observed expression level of protein i at time t

${\tilde{f}}_i\left(\ell \right)$

the normalized gene expression pattern on protein i

s

the transitions between three stages of iRBC: ring, trophozoite, and schizont

L _i ( s )

the likelihood that protein kinases i is involved in regulating the stage transition s

T _s

the time point when stage transition s occur

n

the average number of merozoites released by one schizont

p

the probability that one merozoites does not infect any RBC

V

the volume of merozoites can travel after it is released from schizont

V _total

the volume of whole media

m

the total number of RBCs in the media