dPeleg_model {bioinactivation} | R Documentation |

## First Derivate of the Weibull-Peleg Model

### Description

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

### Usage

```
dPeleg_model(t, x, parms, temp_profile)
```

### Arguments

`t` |
numeric vector indicating the time of the experiment. |

`x` |
list with the value of logS at t. |

`parms` |
parameters for the secondary model. No explicit check of their validity
is performed (see section |

`temp_profile` |
a function that provides the temperature at a given time. |

### Details

The model is developed from the isothermal Weibull model without
taking into
account in the derivation the time dependence of `b`

for
non-isothermal temperature profiles.

This function is compatible with the function
`predict_inactivation`

.

### Value

The value of the first derivative of logS at time `t`

as a list.

### Model Equation

```
\frac{d(\mathrm{log}_{10}(S))}{dt}=-b(T) \cdot n \cdot
(- log10(S)/b(T))^{(n-1)/n)}
```

`b(T) = \mathrm{ln}(1 + exp( k_b*(T - T_{crit}) ))`

### Model Parameters

temp_crit: Temperature below which there is inactivation.

k_b: slope of the b ~ temp line for temperatures above the critical one.

n: shape factor of the Weibull distribution.

### Note

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

### See Also

*bioinactivation*version 1.2.3 Index]