growthrates (version 0.8.4)

grow_baranyi: 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)

Value

vector of dependent variable (y).

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:

$$A = time + 1/mumax * log(exp(-mumax * time) + exp(-h0) - exp(-mumax * time - h0))$$ $$log(y) = log(y0) + mumax * A - log(1 + (exp(mumax * A) - 1) / exp(log(K) - log(y0)))$$

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")