dGeeraerd_model: 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)

Value

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

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.

Model Equation

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

 \deqn{\frac{dC_c}{dt} = - C_c \cdot k_{max}}{
           dC_c/dt = - C_c * k_max}
 \deqn{\alpha = \frac {1}{1+C_c}}{
           \alpha = 1/(1+C_c)}
 \deqn{\gamma = 1 - \frac{N_{res}}{N}}{
           \gamma = 1 - N_res/N}
 \deqn{k_{max} = \frac{1}{D_T}}{k_max = 1/D_T}
 \deqn{log_{10}D_T = log_{10}D_R + \frac{T_R-T}{z}}{
            log(D_T) = log(D_R) + (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

Details

This function is compatible with the function predict_inactivation.