dMetselaar_model: First Derivate of the Metselaar Model

In bioinactivation: Mathematical Modelling of (Dynamic) Microbial Inactivation

Description

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

Usage

dMetselaar_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 Metselaar 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/D)^p * (t/Delta)^(p-1)

D(T) = D_R * 10^(- (T-T_ref)/z )

Model Parameters

• temp_ref: Reference temperature for the calculation.

• D_R: D-value at the reference temperature.

• z: z-value.

• p: shape factor of the Weibull distribution.

• Delta: Scaling parameter

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 Aug. 1, 2019, 5:05 p.m.