| dPeleg_model {bioinactivation} | R Documentation |
First Derivate of the Weibull-Peleg Model
Description
Calculates the first derivative of Weibull-Peleg model at a given time for the model parameters provided and the environmental conditions given.
Usage
dPeleg_model(t, x, parms, temp_profile)
Arguments
t |
numeric vector indicating the time of the experiment. |
x |
list with the value of logS at t. |
parms |
parameters for the secondary model. No explicit check of their validity is performed (see section Model Parameters). |
temp_profile |
a function that provides the temperature at a given time. |
Details
The model is developed from the isothermal Weibull model without
taking into
account in the derivation the time dependence of b for
non-isothermal temperature profiles.
This function is compatible with the function
predict_inactivation.
Value
The value of the first derivative of logS at time t as a list.
Model Equation
\frac{d(\mathrm{log}_{10}(S))}{dt}=-b(T) \cdot n \cdot
(- log10(S)/b(T))^{(n-1)/n)}
b(T) = \mathrm{ln}(1 + exp( k_b*(T - T_{crit}) ))
Model Parameters
temp_crit: Temperature below which there is inactivation.
k_b: slope of the b ~ temp line for temperatures above the critical one.
n: shape factor of the Weibull distribution.
Note
For logS=0, dlogS = 0 unless n=1. Hence, a small shift needs to be introduced to logS.