https://ad25aderram.github.io/my-portfolio/tags/modelling/ModellingHugoBlox Kit (https://hugoblox.com)en-usSat, 01 Mar 2025 00:00:00 +0000https://ad25aderram.github.io/my-portfolio/media/icon_hu_b93c5070c370bd46.pnghttps://ad25aderram.github.io/my-portfolio/tags/modelling/https://ad25aderram.github.io/my-portfolio/projects/covid-sird/Sat, 01 Mar 2025 00:00:00 +0000https://ad25aderram.github.io/my-portfolio/projects/covid-sird/<p>An epidemiological modelling project simulating the spread of COVID-19 in Morocco using the SIRD compartmental model — applied mathematics meeting a real-world public health problem.</p> <h2 id="the-model">The model</h2> <p>The <strong>SIRD model</strong> divides a population into four compartments evolving over time:</p> <table> <thead> <tr> <th>Compartment</th> <th>Meaning</th> </tr> </thead> <tbody> <tr> <td><strong>S</strong></td> <td>Susceptible — not yet infected</td> </tr> <tr> <td><strong>I</strong></td> <td>Infected — currently infectious</td> </tr> <tr> <td><strong>R</strong></td> <td>Recovered</td> </tr> <tr> <td><strong>D</strong></td> <td>Deceased</td> </tr> </tbody> </table> <p>The dynamics are governed by a system of ordinary differential equations:</p> <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback"><span class="line"><span class="cl">dS/dt = -β·S·I/N </span></span><span class="line"><span class="cl">dI/dt = β·S·I/N - γ·I - μ·I </span></span><span class="line"><span class="cl">dR/dt = γ·I </span></span><span class="line"><span class="cl">dD/dt = μ·I </span></span></code></pre></div><p>Where β is the transmission rate, γ the recovery rate, and μ the mortality rate.</p> <h2 id="my-contribution">My contribution</h2> <ul> <li>Analysed and implemented the SIRD ODE system</li> <li>Solved numerically using SciPy to simulate population evolution over time</li> <li>Tuned β, γ, and μ parameters against observed Moroccan COVID-19 data</li> <li>Visualised S, I, R, D curves and interpreted dynamics — peak infection timing, convergence behaviour, and sensitivity to β changes</li> </ul> <h2 id="key-finding">Key finding</h2> <p>A small change in the transmission rate β shifts the infection peak by weeks — a concrete illustration of why epidemic modelling matters for policy decisions, and why early intervention has outsized impact.</p> <h2 id="tech-stack">Tech stack</h2> <ul> <li><strong>Language</strong>: Python</li> <li><strong>Libraries</strong>: NumPy, SciPy (ODE solving), Matplotlib (visualisation)</li> <li><strong>Focus</strong>: Applied mathematics, numerical methods, data visualisation</li> </ul>