dMafart_model: First Derivate of the Weibull-Mafart Model

In albgarre/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 δ_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

dN/dt = -N * p * (1/delta)^p * t^(p-1)

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

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