Huang reparameterized Gompertz survival model

HuangRGS reparametrized Gompertz survival model for microbial inactivation. Returns the model parameters estimated according to data collected in microbial inactivation experiments.

Usage

HuangRGS(x, Y0, k, M)

Arguments

x

is a numeric vector indicating the heating time under a constant temperature of the experiment

Y0

is the initial microbial concentration (ln(cfu 1/g))

k

is the inactivation rate (1/s)

M

is a time constant (s)

Value

A numeric vector with the fitted values

Details

The model's inputs are:

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

Y(t): the natural logarithm of the bacterial concentration (ln(X(t))) measured at time t.

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

References

Huang L (2009). “Thermal inactivation of Listeria monocytogenes in ground beef under isothermal and dynamic temperature conditions.” Journal of Food Engineering, 90(3), 380-387. ISSN 0260-8774, doi:10.1016/j.jfoodeng.2008.07.011 .

Author

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

Examples

library(gslnls)
data(bixina)
initial_values <- list(Y0 = 5.6, k = 0.37, M = 6.8)
fit <- gsl_nls(lnN ~ HuangRGS(Time, Y0, k, M),
  data = bixina,
  start = initial_values
)
summary(fit)
#> 
#> Formula: lnN ~ HuangRGS(Time, Y0, k, M)
#> 
#> Parameters:
#>     Estimate Std. Error t value Pr(>|t|)    
#> Y0  5.502090   0.046071  119.43  < 2e-16 ***
#> k   0.182138   0.009672   18.83 7.53e-12 ***
#> M  12.053884   0.150299   80.20  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.1154 on 15 degrees of freedom
#> 
#> Number of iterations to convergence: 15 
#> Achieved convergence tolerance: 4.996e-16
#> 

plot(lnN ~ Time, data = bixina)
lines(bixina$Time, predict(fit), col = "blue")