dPeleg_model

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

Functions for modelling microbial inactivation under
isothermal or dynamic conditions. The calculations are based on several mathematical models broadly
used by the scientific community and industry. Functions enable to make predictions for cases where the
kinetic parameters are known. It also implements functions for parameter estimation for isothermal and
dynamic conditions. The model fitting capabilities include an Adaptive Monte Carlo method for a Bayesian
approach to parameter estimation.

Alberto Garre

bioinactivation

Mathematical Modelling of (Dynamic) Microbial Inactivation

Pablo S. Fernandez

Jose A. Egea

dPeleg_model function

<dl><dt>t</dt>
<dd>numeric vector indicating the time of the experiment.</dd>
<dt>x</dt>
<dd>list with the value of logS at t.</dd>
<dt>parms</dt>
<dd>parameters for the secondary model. No explicit check of their validity
is performed (see section Model Parameters).</dd>
<dt>temp_profile</dt>
<dd>a function that provides the temperature at a given time.</dd></dl>

Arguments

$$\frac{d(\mathrm{log}_{10}(S))}{dt}=-b(T) \cdot n \cdot
 (- log10(S)/b(T))^{(n-1)/n)} $$
<div class="sourceCode"></div><pre><code> \deqn{b(T) = \mathrm{ln}(1 + exp( k_b*(T - T_{crit}) ))}{
 b(T) = ln( 1 + exp( k_b*(T - T_crit) ) )}
</code></pre>

Model Equation

<ul>
<li>temp_crit: Temperature below which there is inactivation.</li>
<li>k_b: slope of the b ~ temp line for temperatures above the
critical one.</li>
<li>n: shape factor of the Weibull distribution.</li>
</ul>

Model Parameters

First Derivate of the Weibull-Peleg Model — dPeleg_model

<dl>

<dt>t</dt>
<dd>numeric vector indicating the time of the experiment.</dd>


<dt>x</dt>
<dd>list with the value of logS at t.</dd>


<dt>parms</dt>
<dd>parameters for the secondary model. No explicit check of their validity
is performed (see section Model Parameters).</dd>


<dt>temp_profile</dt>
<dd>a function that provides the temperature at a given time.</dd>

</dl>

$$\frac{d(\mathrm{log}_{10}(S))}{dt}=-b(T) \cdot n \cdot
 (- log10(S)/b(T))^{(n-1)/n)} $$
<div class="sourceCode"><pre><code> \deqn{b(T) = \mathrm{ln}(1 + exp( k_b*(T - T_{crit}) ))}{
 b(T) = ln( 1 + exp( k_b*(T - T_crit) ) )}
</code></pre></div>

<ul>
<li>temp_crit: Temperature below which there is inactivation.</li>
<li>k_b: slope of the b ~ temp line for temperatures above the
critical one.</li>
<li>n: shape factor of the Weibull distribution.</li>
</ul>

dPeleg_model: First Derivate of the Weibull-Peleg Model

Description

Usage

Value

Arguments

Model Equation

Model Parameters

Details

See Also