Abdelrahman Said
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275 lines
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<div class="chapter">
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<div class="titlepage"><div><div><h1 class="title">
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<a name="igraph-Processes"></a>Chapter 30. Processes on graphs</h1></div></div></div>
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<div class="toc"><dl class="toc"><dt><span class="section"><a href="igraph-Processes.html#epidemic-models">1. Epidemic models</a></span></dt></dl></div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="epidemic-models"></a>1. Epidemic models</h2></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="igraph-Processes.html#igraph_sir">1.1. <code class="function">igraph_sir</code> — Performs a number of SIR epidemics model runs on a graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Processes.html#igraph_sir_t">1.2. <code class="function">igraph_sir_t</code> — The result of one SIR model simulation.</a></span></dt>
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<dt><span class="section"><a href="igraph-Processes.html#igraph_sir_destroy">1.3. <code class="function">igraph_sir_destroy</code> — Deallocates memory associated with a SIR simulation run.</a></span></dt>
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</dl></div>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="igraph_sir"></a>1.1. <code class="function">igraph_sir</code> — Performs a number of SIR epidemics model runs on a graph.</h3></div></div></div>
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<a class="indexterm" name="id-1.31.2.2.2"></a><p>
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</p>
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<div class="informalexample"><pre class="programlisting">
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igraph_error_t igraph_sir(const igraph_t *graph, igraph_real_t beta,
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igraph_real_t gamma, igraph_int_t no_sim,
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igraph_vector_ptr_t *result);
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</pre></div>
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<p>
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</p>
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<p>
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The SIR model is a simple model from epidemiology. The individuals
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of the population might be in three states: susceptible, infected
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and recovered. Recovered people are assumed to be immune to the
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disease. Susceptibles become infected with a rate that depends on
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their number of infected neighbors. Infected people become recovered
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with a constant rate. See these parameters below.
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</p>
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<p>
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This function runs multiple simulations, all starting with a
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single uniformly randomly chosen infected individual. A simulation
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is stopped when no infected individuals are left.
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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The graph to perform the model on. For directed graphs
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edge directions are ignored and a warning is given.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>beta</code></em>:</span></p></td>
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<td><p>
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The rate of infection of an individual that is
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susceptible and has a single infected neighbor.
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The infection rate of a susceptible individual with n
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infected neighbors is n times beta. Formally
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this is the rate parameter of an exponential distribution.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>gamma</code></em>:</span></p></td>
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<td><p>
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The rate of recovery of an infected individual.
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Formally, this is the rate parameter of an exponential
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distribution.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>no_sim</code></em>:</span></p></td>
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<td><p>
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The number of simulation runs to perform.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>result</code></em>:</span></p></td>
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<td><p>
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The result of the simulation is stored here,
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in a list of <a class="link" href="igraph-Processes.html#igraph_sir_t" title="1.2. igraph_sir_t — The result of one SIR model simulation."><code class="function">igraph_sir_t</code></a> objects. To deallocate
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memory, the user needs to call <a class="link" href="igraph-Processes.html#igraph_sir_destroy" title="1.3. igraph_sir_destroy — Deallocates memory associated with a SIR simulation run."><code class="function">igraph_sir_destroy</code></a> on
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each element, before destroying the pointer vector itself
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using <a class="link" href="igraph-Data-structures.html#igraph_vector_ptr_destroy_all" title="2.17.5. igraph_vector_ptr_destroy_all — Frees all the elements and destroys the pointer vector."><code class="function">igraph_vector_ptr_destroy_all()</code></a>.
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</p></td>
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</tr>
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</tbody>
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</table></div>
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<p>
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</p>
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<p><b>Returns: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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Error code.
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</p></td>
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</tr></tbody>
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</table></div>
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<p>
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Time complexity: O(no_sim * (|V| + |E| log(|V|))).
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</p>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="igraph_sir_t"></a>1.2. <code class="function">igraph_sir_t</code> — The result of one SIR model simulation.</h3></div></div></div>
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<a class="indexterm" name="id-1.31.2.3.2"></a><p>
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</p>
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<pre class="programlisting">
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typedef struct igraph_sir_t {
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igraph_vector_t times;
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igraph_vector_int_t no_s, no_i, no_r;
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} igraph_sir_t;
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</pre>
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<p>
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</p>
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<p>
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</p>
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<p>Data structure to store the results of one simulation
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of the SIR (susceptible-infected-recovered) model on a graph.
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It has the following members. They are all (real or integer)
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vectors, and they are of the same length.
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</p>
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<p><b>Values: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><code class="constant">times</code>:</span></p></td>
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<td><p>
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A vector, the times of the events are stored here.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><code class="constant">no_s</code>:</span></p></td>
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<td><p>
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An integer vector, the number of susceptibles in
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each time step is stored here.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><code class="constant">no_i</code>:</span></p></td>
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<td><p>
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An integer vector, the number of infected individuals
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at each time step, is stored here.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><code class="constant">no_r</code>:</span></p></td>
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<td><p>
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An integer vector, the number of recovered individuals
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is stored here at each time step.</p></td>
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</tr>
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</tbody>
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</table></div>
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<p>
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</p>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="igraph_sir_destroy"></a>1.3. <code class="function">igraph_sir_destroy</code> — Deallocates memory associated with a SIR simulation run.</h3></div></div></div>
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<a class="indexterm" name="id-1.31.2.4.2"></a><p>
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</p>
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<div class="informalexample"><pre class="programlisting">
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void igraph_sir_destroy(igraph_sir_t *sir);
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</pre></div>
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<p>
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</p>
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<p>
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code>sir</code></em>:</span></p></td>
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<td><p>
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The <a class="link" href="igraph-Processes.html#igraph_sir_t" title="1.2. igraph_sir_t — The result of one SIR model simulation."><code class="function">igraph_sir_t</code></a> object storing the simulation.</p></td>
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</tr></tbody>
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</table></div>
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<p>
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</p>
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