dMafart_model: First Derivate of the Weibull-Mafart Model

In bioinactivation: Mathematical Modelling of (Dynamic) Microbial Inactivation

First Derivate of the Weibull-Mafart Model

Description

Calculates the first derivative of Weibull-Mafart model at a given time for the model parameters provided and the environmental conditions given.

Usage

dMafart_model(t, x, parms, temp_profile)

Arguments

t	numeric vector indicating the time of the experiment.
x	list with the value of N 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-Mafart model without taking into account in the derivation the time dependence of \delta_T for non-isothermal temperature profiles.

This function is compatible with the function predict_inactivation.

Value

The value of the first derivative of N at time t as a list.

Model Equation

 \deqn{\frac{dN}{dt} = -N \cdot p \cdot (1/\delta)^p \cdot t^{p-1} }{
           dN/dt = -N * p * (1/delta)^p * t^(p-1)}

 \deqn{\delta(T) = \delta_{ref} \cdot 10^{- (T-T_ref)/z} }{
           delta(T) = delta_ref * 10^(- (T-T_ref)/z )}

Model Parameters

• temp_ref: Reference temperature for the calculation.

• delta_ref: Value of the scale factor at the reference temperature.

• z: z-value.

• p: shape factor of the Weibull distribution.

Note

For t=0, dN = 0 unless n=1. Hence, a small shift needs to be introduced to t.

See Also

predict_inactivation

bioinactivation documentation built on April 11, 2025, 5:53 p.m.