Baranyi and Roberts reduced growth model

BaranyiRM function to fit the Baranyi and Roberts growth model to a reduced microbial growth curve. Returns the model parameters estimated according to data collected in microbial growth experiments.

Usage

BaranyiRM(t, Y0, MUmax, lag)

Arguments

t

is a numeric vector indicating the time of the experiment

Y0

is the natural logarithm of the initial microbial concentration (ln(N0)) at time=0

MUmax

is the maximum specific growth rate given in time units

lag

is the duration of the lag phase in time units

Value

An object of nls class with the fitted parameters of the model

Details

Model's inputs are:

t: time, assuming time zero as the beginning of the experiment.

Y(t): the natural logarithm of the microbial concentration (ln(N(t)) measured at time t.

Users should make sure that the microbial concentration input is entered in natural logarithm, Y(t) = ln(N(t)).

References

Baranyi J, Roberts TA (1995). “Mathematics of predictive microbiology.” International Journal of Food Microbiology, 26, 199-218.

Author

Vasco Cadavez, vcadavez@ipb.pt and Ursula Gonzales-Barron, ubarron@ipb.pt

Examples

## Example: Baranyi reduced model
library(gslnls)
data(growthred)  # simulated data set.
initial_values = list(Y0=0.1, MUmax=1.7, lag=5) # define the initial values
fit <- gsl_nls(lnN ~ BaranyiRM(Time, Y0, MUmax, lag),
           data=growthred,
           start =  initial_values)
summary(fit)
#> 
#> Formula: lnN ~ BaranyiRM(Time, Y0, MUmax, lag)
#> 
#> Parameters:
#>       Estimate Std. Error t value Pr(>|t|)    
#> Y0    -0.01690    0.24928  -0.068    0.948    
#> MUmax  1.84523    0.05189  35.560  3.3e-08 ***
#> lag    9.29338    0.68563  13.555  1.0e-05 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.4117 on 6 degrees of freedom
#> 
#> Number of iterations to convergence: 6 
#> Achieved convergence tolerance: 1.426e-12
#>