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copied!<p>In some ways, you are encountering the difference between <a href="http://reference.wolfram.com/mathematica/ref/Set.html?q=Set&lang=en" rel="nofollow"><code>Set</code></a> (<code>=</code>) and <a href="http://reference.wolfram.com/mathematica/ref/SetDelayed.html?q=SetDelayed&lang=en" rel="nofollow"><code>SetDelayed</code></a> (<code>:=</code>). For instance, if you wrote <code>f = 7</code>, <code>f</code> becomes <code>7</code> in all occurrences of <code>f</code> after it was initialized. But, if you wrote <code>f = 7 t</code> instead, and tried to use it as you would a function, i.e. <code>f[8]</code>, you'd get <code>(7 t)[8]</code> because <code>Set</code> says that the value of <code>f</code> is unchanging. <code>SetDelayed</code>, however, implies that the value of <code>f</code> will change and must be reevaluated every time it occurs. Your initial case, though, is special.</p> <p>When you wrote</p> <pre><code>Beta = Piecewise[{{0.01, Inf[t] > 20}, {.06, Inf[t] <= 20}}] </code></pre> <p><code>Inf[t]</code> was undefined, so that it remained unevaluated. But, every occurence of <code>Beta</code> in your differential equations was replaced by the above formula, courtesy of <code>Set</code>, so <code>NDSolve</code> only saw the <code>Piecewise</code> functions. In your second case, you wrote</p> <pre><code>Beta = UpdateTransmission[Inf[t]] </code></pre> <p>Here the problem is that <code>UpdateTransmission</code> is executed only when <code>Beta</code> is initially defined, and while <code>Piecewise</code> remains unevaluated, <code>UpdateTransmission</code> most likely still gives a result for a purely symbolic input. I'd try one of three things, </p> <ol> <li>replace every occurrence of <code>Beta</code> in you equations with <code>UpdateTransmission[Inf[t]]</code>,</li> <li><p>redefine <code>Beta</code> using <code>SetDelayed</code>, e.g. </p> <pre><code>Beta := UpdateTransmission[Inf[t]] </code></pre> <p>so that it will be reevaluated every time it is encountered, or</p></li> <li><p>redefine <code>UpdateTransmission</code> to not accept symbols via either </p> <pre><code>UpdateTransmission[x_?(Head[#]=!=Symbol&)] := ... </code></pre> <p>or</p> <pre><code>UpdateTransmission[x_] /; Head[x]=!= Symbol := ... </code></pre></li> </ol> <p>Option 3 works by forcing <code>UpdateTransmission[Inf[t]]</code> to remain unevaluated, and effectively does the same thing as option 1. But, it requires a minimum of change. Personally, I'm in favor of options 1 or 3, as I don't know how many times <code>Beta</code> will need to be reevaluated as <code>NDSolve</code> operates.</p>

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