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Epiverse-TRACE Initiative, London School of Hygiene and Tropical Medicine, UK
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London School of Hygiene and Tropical Medicine, UK
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<pclass="date">2025-09-02</p>
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<pclass="date">2025-09-03</p>
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</section><sectionid="TOC">
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<h2id="toc-title">Table of contents</h2>
@@ -680,7 +681,12 @@ <h3 id="understanding-or-explaining-disease-dynamics">Understanding or explainin
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<h3id="some-key-milestones-in-infectious-disease-modelling">Some key milestones in infectious disease modelling</h3>
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<p><ahref="images/model_milestones.png" class="lightbox" data-gallery="quarto-lightbox-gallery-8"><imgdata-src="images/model_milestones.png" data-fig-cap="Milestones in mathematical modeling and modeling to inform public policy. Source: [Lesslar et al., 2016](10.1093/aje/kww021)"></a></p>
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<divclass="quarto-figure quarto-figure-center">
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<figure>
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<p><ahref="images/model_milestones.png" class="lightbox" data-gallery="quarto-lightbox-gallery-8" title="Milestones in mathematical modeling and modeling to inform public policy. Source: Lesslar et al., 2016"><imgdata-src="images/model_milestones.png" alt="Milestones in mathematical modeling and modeling to inform public policy. Source: Lesslar et al., 2016"></a></p>
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<figcaption>Milestones in mathematical modeling and modeling to inform public policy. Source: <ahref="10.1093/aje/kww021">Lesslar et al., 2016</a></figcaption>
<h3id="the-modelling-for-decision-making-process">The modelling for decision-making process</h3>
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<p><ahref="images/modelling_process.png" class="lightbox" data-gallery="quarto-lightbox-gallery-10" title="The modelling process involves balancing realism, tractability, and generality. Source: Heesterbeek et al, 2015"><imgdata-src="images/modelling_process.png" alt="The modelling process involves balancing realism, tractability, and generality. Source: Heesterbeek et al, 2015"></a></p>
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<p><ahref="images/modelling_process.png" class="lightbox" data-gallery="quarto-lightbox-gallery-10" title="The modelling process involves balancing realism, tractability, and generality. Source: Heesterbeek et al, 2015"><imgdata-src="images/modelling_process.png" style="width:70.0%" alt="The modelling process involves balancing realism, tractability, and generality. Source: Heesterbeek et al, 2015"></a></p>
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<figcaption>The modelling process involves balancing realism, tractability, and generality. Source: <ahref="10.1126/science.aaa4339">Heesterbeek et al, 2015</a></figcaption>
<li>Let’s do a code walk through in R using the script <ahref="https://github.com/jamesmbaazam/mppr_r_practicals/tree/main/model_implementation_practicals"><code>sir.Rmd</code></a>.</li>
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<li>Let’s do a code walk through in R using the script <ahref="https://github.com/jamesmbaazam/mppr_r_practicals/tree/main/model_implementation_practicals"><code>sir.Rmd</code></a>.
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<li><p>Beyond the SIR model, calculating <spanclass="math inline">\(R0\)</span> for more complex models can be challenging due to the presence of multiple compartments.</p></li>
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<li><p>For complex models, we use the <spanstyle="color:tomato;">next generation matrix</span> approach <spanclass="citation" data-cites="diekmann1990definition diekmann2010construction">(<ahref="#/references" role="doc-biblioref" onclick="">Diekmann, Heesterbeek, and Metz 1990</a>; <ahref="#/references" role="doc-biblioref" onclick="">Diekmann, Heesterbeek, and Roberts 2010</a>)</span>.</p></li>
<p>Using the next generation matrix approach, we can show that the SEIR model with constant births and deaths has <spanclass="math display">\[R0 = \dfrac{\beta \sigma}{(\gamma + \mu)(\sigma + \mu)}\]</span>.</p>
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<p>Using the next generation matrix approach, we can show that the SEIR model with constant births and deaths has <spanclass="math display">\[R0 = \dfrac{\beta \sigma}{(\gamma + \mu)(\sigma + \mu)}\]</span></p>
<li><p>We can use the same approach as the SIR model to simulate the SEIR model.</p></li>
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<li><p>Modify the <ahref="https://github.com/jamesmbaazam/mppr_r_practicals/tree/main/model_implementation_practicals"><code>sir.Rmd</code></a> script to simulate the SEIR model.</p></li>
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<li><p>Modify the <ahref="https://github.com/jamesmbaazam/mppr_r_practicals/tree/main/model_implementation_practicals"><code>sir.Rmd</code></a> script to simulate the SEIR model.</p>
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<h5id="r-practicals-3">R Practicals</h5>
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<li>We can use the same approach as the SIR model to simulate the model with isolation.</li>
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<li>Modify the SIR model in <ahref="https://github.com/jamesmbaazam/mppr_r_practicals/tree/main/model_implementation_practicals"><code>sir.Rmd</code></a> to incorporate the isolated compartment, <spanclass="math inline">\(Q\)</span> and the relevant parameters.</li>
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<li>Modify the SIR model in <ahref="https://github.com/jamesmbaazam/mppr_r_practicals/tree/main/model_implementation_practicals"><code>sir.Rmd</code></a> to incorporate the isolated compartment, <spanclass="math inline">\(Q\)</span> and the relevant parameters.
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