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+ <img src="../logo.svg" class="logo" alt=""><h1>Incidence Decay and Exponential Adjustment (IDEA)</h1>
+ <small class="dont-index">Source: <a href="https://github.com/MI2YorkU/Rnaught/blob/master/R/idea.R" class="external-link"><code>R/idea.R</code></a></small>
+ <div class="d-none name"><code>idea.Rd</code></div>
+ </div>
+
+ <div class="ref-description section level2">
+ <p>This function implements a least squares estimation method of R0 due to
+Fisman et al. (PloS One, 2013). See details for implementation notes.</p>
+ </div>
+
+ <div class="section level2">
+ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">idea</span><span class="op">(</span><span class="va">cases</span>, <span class="va">mu</span><span class="op">)</span></span></code></pre></div>
+ </div>
+
+ <div class="section level2">
+ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-cases">cases<a class="anchor" aria-label="anchor" href="#arg-cases"></a></dt>
+<dd><p>Vector of case counts. The vector must be of length at least two
+and only contain positive integers.</p></dd>
+
+
+<dt id="arg-mu">mu<a class="anchor" aria-label="anchor" href="#arg-mu"></a></dt>
+<dd><p>Mean of the serial distribution. This must be a positive number.
+The value should match the case counts in time units. For example, if case
+counts are weekly and the serial distribution has a mean of seven days,
+then <code>mu</code> should be set to <code>1</code>. If case counts are daily and the serial
+distribution has a mean of seven days, then <code>mu</code> should be set to <code>7</code>.</p></dd>
+
+</dl></div>
+ <div class="section level2">
+ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+ <p>An estimate of the basic reproduction number (R0).</p>
+ </div>
+ <div class="section level2">
+ <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
+ <p>This method is closely related to that implemented in <code><a href="id.html">id()</a></code>. The method is
+based on an incidence decay model. The estimate of R0 is the value which
+minimizes the sum of squares between observed case counts and case counts
+expected under the model.</p>
+<p>This method is based on an approximation of the SIR model, which is most
+valid at the beginning of an epidemic. The method assumes that the mean of
+the serial distribution (sometimes called the serial interval) is known. The
+final estimate can be quite sensitive to this value, so sensitivity testing
+is strongly recommended. Users should be careful about units of time (e.g.,
+are counts observed daily or weekly?) when implementing.</p>
+ </div>
+ <div class="section level2">
+ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
+ <p><a href="https://doi.org/10.1371/journal.pone.0083622" class="external-link">Fisman et al. (PloS One, 2013)</a></p>
+ </div>
+ <div class="section level2">
+ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+ <div class="dont-index"><p><code><a href="id.html">id()</a></code> for a similar method.</p></div>
+ </div>
+
+ <div class="section level2">
+ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Weekly data.</span></span></span>
+<span class="r-in"><span><span class="va">cases</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">1</span>, <span class="fl">4</span>, <span class="fl">10</span>, <span class="fl">5</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">19</span>, <span class="fl">3</span>, <span class="fl">3</span>, <span class="fl">14</span>, <span class="fl">4</span><span class="op">)</span></span></span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Obtain R0 when the serial distribution has a mean of five days.</span></span></span>
+<span class="r-in"><span><span class="fu">idea</span><span class="op">(</span><span class="va">cases</span>, mu <span class="op">=</span> <span class="fl">5</span> <span class="op">/</span> <span class="fl">7</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#></span> [1] 1.419546</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Obtain R0 when the serial distribution has a mean of three days.</span></span></span>
+<span class="r-in"><span><span class="fu">idea</span><span class="op">(</span><span class="va">cases</span>, mu <span class="op">=</span> <span class="fl">3</span> <span class="op">/</span> <span class="fl">7</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#></span> [1] 1.233927</span>
+</code></pre></div>
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