dGeeraerd_model {bioinactivation} R Documentation

## First Derivate of Geeraerd's Model

### Description

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

### Usage

dGeeraerd_model(t, x, parms, temp_profile)


### Arguments

 t numeric vector indicating the time of the experiment. x list with the values of the variables at time 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

This function is compatible with the function predict_inactivation.

### Value

A list with the value of the first derivatives of N and C_c at time t.

### Model Equation

\frac{dN}{dt} = -N \cdot k_{max} \cdot \alpha \cdot \gamma

\frac{dC_c}{dt} = - C_c \cdot k_{max}

\alpha = \frac {1}{1+C_c}

\gamma = 1 - \frac{N_{res}}{N}

k_{max} = \frac{1}{D_T}

log_{10}D_T = log_{10}D_R + \frac{T_R-T}{z}

### Model Parameters

• temp_ref: Reference temperature for the calculation,

• D_R: D-value at the reference temperature,

• z: z value,

• N_min: Minimum value of N (defines the tail).

### Notes

To define the Geeraerd model without tail, assign N_min = 0. For the model without shoulder, assign C_0 = 0

predict_inactivation