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an increasing rate constant, supposedly caused by microbial growth" />
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<h1>Logistic kinetics</h1>
<div class="hidden name"><code>logistic.solution.Rd</code></div>
</div>
<div class="ref-description">
<p>Function describing exponential decline from a defined starting value, with
an increasing rate constant, supposedly caused by microbial growth</p>
</div>
<pre class="usage"><span class='fu'>logistic.solution</span>(<span class='no'>t</span>, <span class='no'>parent.0</span>, <span class='no'>kmax</span>, <span class='no'>k0</span>, <span class='no'>r</span>)</pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>t</th>
<td><p>Time.</p></td>
</tr>
<tr>
<th>parent.0</th>
<td><p>Starting value for the response variable at time zero.</p></td>
</tr>
<tr>
<th>kmax</th>
<td><p>Maximum rate constant.</p></td>
</tr>
<tr>
<th>k0</th>
<td><p>Minumum rate constant effective at time zero.</p></td>
</tr>
<tr>
<th>r</th>
<td><p>Growth rate of the increase in the rate constant.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>
<p>The solution of the logistic model reduces to the
<code><a href='SFO.solution.html'>SFO.solution</a></code> if <code>k0</code> is equal to
<code>kmax</code>.</p>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>The value of the response variable at time <code>t</code>.</p>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>FOCUS (2014) “Generic guidance for Estimating Persistence and
Degradation Kinetics from Environmental Fate Studies on Pesticides in EU
Registration” Report of the FOCUS Work Group on Degradation Kinetics,
Version 1.1, 18 December 2014
<a href='http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics'>http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a></p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'> <span class='co'># Reproduce the plot on page 57 of FOCUS (2014)</span>
<span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.2</span>),
<span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>100</span>),
<span class='kw'>xlab</span> <span class='kw'>=</span> <span class='st'>"Time"</span>, <span class='kw'>ylab</span> <span class='kw'>=</span> <span class='st'>"Residue"</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.4</span>),
<span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>2</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>2</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.8</span>),
<span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>3</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>3</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.001</span>, <span class='fl'>0.2</span>),
<span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>4</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>4</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.08</span>, <span class='fl'>0.2</span>),
<span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>5</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>5</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/legend'>legend</a></span>(<span class='st'>"topright"</span>, <span class='kw'>inset</span> <span class='kw'>=</span> <span class='fl'>0.05</span>,
<span class='kw'>legend</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/paste'>paste0</a></span>(<span class='st'>"k0 = "</span>, <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.001</span>, <span class='fl'>0.08</span>),
<span class='st'>", r = "</span>, <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.2</span>, <span class='fl'>0.4</span>, <span class='fl'>0.8</span>, <span class='fl'>0.2</span>, <span class='fl'>0.2</span>)),
<span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fl'>5</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fl'>5</span>)</div><div class='img'><img src='logistic.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='co'># Fit with synthetic data</span>
<span class='no'>logistic</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"logistic"</span>))
<span class='no'>sampling_times</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span>)
<span class='no'>parms_logistic</span> <span class='kw'><-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='kw'>kmax</span> <span class='kw'>=</span> <span class='fl'>0.08</span>, <span class='kw'>k0</span> <span class='kw'>=</span> <span class='fl'>0.0001</span>, <span class='kw'>r</span> <span class='kw'>=</span> <span class='fl'>0.2</span>)
<span class='no'>d_logistic</span> <span class='kw'><-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>logistic</span>,
<span class='no'>parms_logistic</span>, <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>),
<span class='no'>sampling_times</span>)
<span class='no'>d_2_1</span> <span class='kw'><-</span> <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_logistic</span>,
<span class='kw'>sdfunc</span> <span class='kw'>=</span> <span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'><a href='sigma_twocomp.html'>sigma_twocomp</a></span>(<span class='no'>x</span>, <span class='fl'>0.5</span>, <span class='fl'>0.07</span>),
<span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>reps</span> <span class='kw'>=</span> <span class='fl'>2</span>, <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>5</span>, <span class='kw'>LOD</span> <span class='kw'>=</span> <span class='fl'>0.1</span>, <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>123456</span>)<span class='kw'>[[</span><span class='fl'>1</span>]]
<span class='no'>m</span> <span class='kw'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"logistic"</span>, <span class='no'>d_2_1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>m</span>)</div><div class='img'><img src='logistic.solution-2.png' alt='' width='700' height='433' /></div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>m</span>)$<span class='no'>bpar</span></div><div class='output co'>#> Estimate se_notrans t value Pr(>t) Lower
#> parent_0 1.057896e+02 2.3743105248 44.5559374 6.656664e-16 1.006602e+02
#> kmax 6.398190e-02 0.0193490291 3.3067243 2.836921e-03 3.329058e-02
#> k0 1.612775e-04 0.0009640761 0.1672871 4.348592e-01 3.972250e-10
#> r 2.263946e-01 0.2822811886 0.8020181 2.184792e-01 1.531165e-02
#> Upper
#> parent_0 110.9190170
#> kmax 0.1229682
#> k0 65.4803698
#> r 3.3474197</div></pre>
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<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#arguments">Arguments</a></li>
<li><a href="#note">Note</a></li>
<li><a href="#value">Value</a></li>
<li><a href="#references">References</a></li>
<li><a href="#examples">Examples</a></li>
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