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-an increasing rate constant, supposedly caused by microbial growth"><meta name="robots" content="noindex"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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- <h1>Logistic kinetics</h1>
- <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/parent_solutions.R" class="external-link"><code>R/parent_solutions.R</code></a></small>
- <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>
-
- <div id="ref-usage">
- <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">logistic.solution</span><span class="op">(</span><span class="va">t</span>, <span class="va">parent_0</span>, <span class="va">kmax</span>, <span class="va">k0</span>, <span class="va">r</span><span class="op">)</span></span></code></pre></div>
- </div>
-
- <div id="arguments">
- <h2>Arguments</h2>
- <dl><dt>t</dt>
-<dd><p>Time.</p></dd>
-
-
-<dt>parent_0</dt>
-<dd><p>Starting value for the response variable at time zero.</p></dd>
-
-
-<dt>kmax</dt>
-<dd><p>Maximum rate constant.</p></dd>
-
-
-<dt>k0</dt>
-<dd><p>Minimum rate constant effective at time zero.</p></dd>
-
-
-<dt>r</dt>
-<dd><p>Growth rate of the increase in the rate constant.</p></dd>
-
-</dl></div>
- <div id="value">
- <h2>Value</h2>
-
-
-<p>The value of the response variable at time <code>t</code>.</p>
- </div>
- <div id="note">
- <h2>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>
- </div>
- <div id="references">
- <h2>References</h2>
- <p>FOCUS (2006) “Guidance Document on Estimating Persistence
-and Degradation Kinetics from Environmental Fate Studies on Pesticides in
-EU Registration” Report of the FOCUS Work Group on Degradation Kinetics,
-EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
-<a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>
-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" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a></p>
- </div>
- <div id="see-also">
- <h2>See also</h2>
- <div class="dont-index"><p>Other parent solutions:
-<code><a href="DFOP.solution.html">DFOP.solution</a>()</code>,
-<code><a href="FOMC.solution.html">FOMC.solution</a>()</code>,
-<code><a href="HS.solution.html">HS.solution</a>()</code>,
-<code><a href="IORE.solution.html">IORE.solution</a>()</code>,
-<code><a href="SFO.solution.html">SFO.solution</a>()</code>,
-<code><a href="SFORB.solution.html">SFORB.solution</a>()</code></p></div>
- </div>
-
- <div id="ref-examples">
- <h2>Examples</h2>
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
-<span class="r-in"><span> <span class="co"># Reproduce the plot on page 57 of FOCUS (2014)</span></span></span>
-<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu">logistic.solution</span><span class="op">(</span><span class="va">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="op">)</span>,</span></span>
-<span class="r-in"><span> from <span class="op">=</span> <span class="fl">0</span>, to <span class="op">=</span> <span class="fl">100</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">100</span><span class="op">)</span>,</span></span>
-<span class="r-in"><span> xlab <span class="op">=</span> <span class="st">"Time"</span>, ylab <span class="op">=</span> <span class="st">"Residue"</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu">logistic.solution</span><span class="op">(</span><span class="va">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="op">)</span>,</span></span>
-<span class="r-in"><span> from <span class="op">=</span> <span class="fl">0</span>, to <span class="op">=</span> <span class="fl">100</span>, add <span class="op">=</span> <span class="cn">TRUE</span>, lty <span class="op">=</span> <span class="fl">2</span>, col <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu">logistic.solution</span><span class="op">(</span><span class="va">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="op">)</span>,</span></span>
-<span class="r-in"><span> from <span class="op">=</span> <span class="fl">0</span>, to <span class="op">=</span> <span class="fl">100</span>, add <span class="op">=</span> <span class="cn">TRUE</span>, lty <span class="op">=</span> <span class="fl">3</span>, col <span class="op">=</span> <span class="fl">3</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu">logistic.solution</span><span class="op">(</span><span class="va">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="op">)</span>,</span></span>
-<span class="r-in"><span> from <span class="op">=</span> <span class="fl">0</span>, to <span class="op">=</span> <span class="fl">100</span>, add <span class="op">=</span> <span class="cn">TRUE</span>, lty <span class="op">=</span> <span class="fl">4</span>, col <span class="op">=</span> <span class="fl">4</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu">logistic.solution</span><span class="op">(</span><span class="va">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="op">)</span>,</span></span>
-<span class="r-in"><span> from <span class="op">=</span> <span class="fl">0</span>, to <span class="op">=</span> <span class="fl">100</span>, add <span class="op">=</span> <span class="cn">TRUE</span>, lty <span class="op">=</span> <span class="fl">5</span>, col <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/legend.html" class="external-link">legend</a></span><span class="op">(</span><span class="st">"topright"</span>, inset <span class="op">=</span> <span class="fl">0.05</span>,</span></span>
-<span class="r-in"><span> legend <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"k0 = "</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</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="op">)</span>,</span></span>
-<span class="r-in"><span> <span class="st">", r = "</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</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="op">)</span><span class="op">)</span>,</span></span>
-<span class="r-in"><span> lty <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fl">5</span>, col <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">)</span></span></span>
-<span class="r-plt img"><img src="logistic.solution-1.png" alt="" width="700" height="433"></span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span> <span class="co"># Fit with synthetic data</span></span></span>
-<span class="r-in"><span> <span class="va">logistic</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"logistic"</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span> <span class="va">sampling_times</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</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="op">)</span></span></span>
-<span class="r-in"><span> <span class="va">parms_logistic</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>kmax <span class="op">=</span> <span class="fl">0.08</span>, k0 <span class="op">=</span> <span class="fl">0.0001</span>, r <span class="op">=</span> <span class="fl">0.2</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="va">d_logistic</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">logistic</span>,</span></span>
-<span class="r-in"><span> <span class="va">parms_logistic</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fl">100</span><span class="op">)</span>,</span></span>
-<span class="r-in"><span> <span class="va">sampling_times</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="va">d_2_1</span> <span class="op">&lt;-</span> <span class="fu"><a href="add_err.html">add_err</a></span><span class="op">(</span><span class="va">d_logistic</span>,</span></span>
-<span class="r-in"><span> sdfunc <span class="op">=</span> <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu"><a href="sigma_twocomp.html">sigma_twocomp</a></span><span class="op">(</span><span class="va">x</span>, <span class="fl">0.5</span>, <span class="fl">0.07</span><span class="op">)</span>,</span></span>
-<span class="r-in"><span> n <span class="op">=</span> <span class="fl">1</span>, reps <span class="op">=</span> <span class="fl">2</span>, digits <span class="op">=</span> <span class="fl">5</span>, LOD <span class="op">=</span> <span class="fl">0.1</span>, seed <span class="op">=</span> <span class="fl">123456</span><span class="op">)</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span></span></span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span> <span class="va">m</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"logistic"</span>, <span class="va">d_2_1</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-in"><span> <span class="fu"><a href="plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m</span><span class="op">)</span></span></span>
-<span class="r-plt img"><img src="logistic.solution-2.png" alt="" width="700" height="433"></span>
-<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Estimate se_notrans t value Pr(&gt;t) Lower</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 1.057896e+02 1.9023449590 55.610120 3.768360e-16 1.016451e+02</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> kmax 6.398190e-02 0.0143201029 4.467978 3.841828e-04 3.929235e-02</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> k0 1.612775e-04 0.0005866813 0.274898 3.940351e-01 5.846688e-08</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> r 2.263946e-01 0.1718110662 1.317695 1.061043e-01 4.335843e-02</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 5.332935e+00 0.9145907310 5.830952 4.036926e-05 3.340213e+00</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Upper</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 109.9341588</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> kmax 0.1041853</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> k0 0.4448749</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> r 1.1821120</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 7.3256566</span>
-<span class="r-in"><span> <span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m</span><span class="op">)</span><span class="op">$</span><span class="va">distimes</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> DT50 DT90 DT50_k0 DT50_kmax</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> parent 36.86533 62.41511 4297.853 10.83349</span>
-<span class="r-in"><span></span></span>
-</code></pre></div>
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