ode_twostep {growthrates}

Twostep Growth Model

Description

System of two differential equations describing bacterial growth as two-step process of activation (or adaptation) and growth.

Usage

ode_twostep(time, y, parms, ...)

grow_twostep(time, parms, ...)

Arguments

time

actual time (for the ode) resp. vector of simulation time steps.

y

named vector with state of the system (yi, ya: abundance of inactive and active organisms, e.g. concentration of inactive resp. active cells).

parms

parameters of the two-step growth model:

• yi, ya initial abundance of active and inactive organisms,

• kw activation (“wakeup”) constant (1/time),

• mumax maximum growth rate (1/time),

• K carrying capacity (max. abundance).

...

placeholder for additional parameters (for user-extended versions of this function)

Details

The model is given as a system of two differential equations:

dy_i/dt = -kw * yi

dy_a/dt = kw * yi + mumax * (1 - (yi + ya)/K) * ya

that are then numerically integrated ('simulated') according to time (t). The model assumes that the population consists of active (y_a) and inactive (y_i) cells so that the observed abundance is (y = y_i + y_a). Adapting inactive cells change to the active state with a first order 'wakeup' rate (kw).

Function ode_twostep is the system of differential equations, whereas grow_twostep runs a numerical simulation over time.

A similar two-compartment model, but without the logistic term, was discussed by Baranyi (1998).

Value

For ode_twostep: matrix containing the simulation outputs. The return value of has also class deSolve.

For grow_twostep: vector of dependent variable (y):

• time time of the simulation

• yi concentration of inactive cells

• ya concentration of active cells

• y total cell concentration

References

Baranyi, J. (1998). Comparison of stochastic and deterministic concepts of bacterial lag. J. heor. Biol. 192, 403–408.

See Also

Other growth models: grow_baranyi(), grow_exponential(), grow_gompertz2(), grow_gompertz(), grow_huang(), grow_logistic(), grow_richards(), growthmodel, ode_genlogistic()

Other growth models: grow_baranyi(), grow_exponential(), grow_gompertz2(), grow_gompertz(), grow_huang(), grow_logistic(), grow_richards(), growthmodel, ode_genlogistic()

Examples

time <- seq(0, 30, length=200)
parms <- c(kw = 0.1,	mumax=0.2, K=0.1)
y0    <-  c(yi=0.01, ya=0.0)
out   <- ode(y0, time, ode_twostep, parms)

plot(out)

o <- grow_twostep(0:100, c(yi=0.01, ya=0.0, kw = 0.1,	mumax=0.2, K=0.1))
plot(o)