grow_baranyi: The Baranyi and Roberts Growth Model

In growthrates: Estimate Growth Rates from Experimental Data

The Baranyi and Roberts Growth Model

Description

The growth model of Baranyi and Roberts (1995) written as analytical solution of the system of differential equations.

Usage

grow_baranyi(time, parms)

Arguments

time	vector of time steps (independent variable).
parms	named parameter vector of the Baranyi growth model with: y0 initial value of abundance, mumax maximum growth rate (1/time), K carrying capacity (max. abundance), h0 parameter specifying the initial physiological state of organisms (e.g. cells) and in consequence the lag phase (h0 = max growth rate * lag phase).

Details

The version of the equation used in this package has the following form:

A = time + 1/mumax * log(exp(-mumax * time) + exp(-h0) - exp(-mumax * time - h0))

log(y) = log(y0) + mumax * A - log(1 + (exp(mumax * A) - 1) / exp(log(K) - log(y0)))

Value

vector of dependent variable (y).

References

Baranyi, J. and Roberts, T. A. (1994). A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology, 23, 277-294.

Baranyi, J. and Roberts, T.A. (1995). Mathematics of predictive microbiology. International Journal of Food Microbiology, 26, 199-218.

See Also

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

Examples

time <- seq(0, 30, length=200)
y    <- grow_baranyi(time, c(y0=0.01, mumax=.5, K=0.1, h0=5))[,"y"]
plot(time, y, type="l")
plot(time, y, type="l", log="y")

growthrates documentation built on Oct. 4, 2022, 1:06 a.m.