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   3 Fisman et al. (PloS One, 2013). See details for implementation notes."><meta property="og:description" content="This function implements a least squares estimation method of R0 due to
   4 Fisman et al. (PloS One, 2013). See details for implementation notes."><meta property="og:image" content="https://MI2YorkU.github.io/Rnaught/logo.svg"></head><body>
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  36   <main id="main" class="col-md-9"><div class="page-header">
  37       <img src="../logo.svg" class="logo" alt=""><h1>Incidence Decay (ID)</h1>
  38       <small class="dont-index">Source: <a href="https://github.com/MI2YorkU/Rnaught/blob/master/R/id.R" class="external-link"><code>R/id.R</code></a></small>
  39       <div class="d-none name"><code>id.Rd</code></div>
  40     </div>
  41
  42     <div class="ref-description section level2">
  43     <p>This function implements a least squares estimation method of R0 due to
  44 Fisman et al. (PloS One, 2013). See details for implementation notes.</p>
  45     </div>
  46
  47     <div class="section level2">
  48     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
  49     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">id</span><span class="op">(</span><span class="va">cases</span>, <span class="va">mu</span><span class="op">)</span></span></code></pre></div>
  50     </div>
  51
  52     <div class="section level2">
  53     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
  54
  55
  56 <dl><dt id="arg-cases">cases<a class="anchor" aria-label="anchor" href="#arg-cases"></a></dt>
  57 <dd><p>Vector of case counts. The vector must be non-empty and only
  58 contain positive integers.</p></dd>
  59
  60
  61 <dt id="arg-mu">mu<a class="anchor" aria-label="anchor" href="#arg-mu"></a></dt>
  62 <dd><p>Mean of the serial distribution. This must be a positive number.
  63 The value should match the case counts in time units. For example, if case
  64 counts are weekly and the serial distribution has a mean of seven days,
  65 then <code>mu</code> should be set to <code>1</code>. If case counts are daily and the serial
  66 distribution has a mean of seven days, then <code>mu</code> should be set to <code>7</code>.</p></dd>
  67
  68 </dl></div>
  69     <div class="section level2">
  70     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
  71     <p>An estimate of the basic reproduction number (R0).</p>
  72     </div>
  73     <div class="section level2">
  74     <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
  75     <p>The method is based on a straightforward incidence decay model. The estimate
  76 of R0 is the value which minimizes the sum of squares between observed case
  77 counts and cases counts expected under the model.</p>
  78 <p>This method is based on an approximation of the SIR model, which is most
  79 valid at the beginning of an epidemic. The method assumes that the mean of
  80 the serial distribution (sometimes called the serial interval) is known. The
  81 final estimate can be quite sensitive to this value, so sensitivity testing
  82 is strongly recommended. Users should be careful about units of time (e.g.,
  83 are counts observed daily or weekly?) when implementing.</p>
  84     </div>
  85     <div class="section level2">
  86     <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
  87     <p><a href="https://doi.org/10.1371/journal.pone.0083622" class="external-link">Fisman et al. (PloS One, 2013)</a></p>
  88     </div>
  89     <div class="section level2">
  90     <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
  91     <div class="dont-index"><p><code><a href="idea.html">idea()</a></code> for a similar method.</p></div>
  92     </div>
  93
  94     <div class="section level2">
  95     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
  96     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Weekly data.</span></span></span>
  97 <span class="r-in"><span><span class="va">cases</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><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>
  98 <span class="r-in"><span></span></span>
  99 <span class="r-in"><span><span class="co"># Obtain R0 when the serial distribution has a mean of five days.</span></span></span>
 100 <span class="r-in"><span><span class="fu">id</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>
 101 <span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1.245734</span>
 102 <span class="r-in"><span></span></span>
 103 <span class="r-in"><span><span class="co"># Obtain R0 when the serial distribution has a mean of three days.</span></span></span>
 104 <span class="r-in"><span><span class="fu">id</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>
 105 <span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1.14092</span>
 106 </code></pre></div>
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