dPeleg_model: First Derivate of the Weibull-Peleg Model

In albgarre/bioinactivation: Mathematical Modelling of (Dynamic) Microbial Inactivation

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

d(log10(S))/dt = -b * n *( - log10(S)/b )^( (n-1)/n)

b(T) = 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.

See Also

predict_inactivation

albgarre/bioinactivation documentation built on Nov. 27, 2022, 9:19 a.m.