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SIR Epidemic Dynamics on Network Structures

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About This MicroSim

The SIR model divides a population into Susceptible, Infected, and Recovered compartments. In a well-mixed population the trajectory is determined by the reproduction number \(R_0 = \beta/\gamma\). On an explicit network, structure matters enormously: hubs accelerate early spread, while peripheral nodes may never be reached.

This MicroSim runs both models in parallel. On the left is the ODE trajectory; on the right is the network simulation. Sliders control the infection rate \(\beta\) and recovery rate \(\gamma\). You can pre-load different network topologies (random, scale-free, lattice) to compare epidemic outcomes.

Learning objective (Bloom's Analyze (Level 4)): Compare SIR epidemic spread on a well-mixed population (classical ODE model) vs. an explicit network, and see how network heterogeneity — especially hubs — dramatically alters epidemic behavior.

How to Use

  1. Choose a network — click a topology preset (Erdős–Rényi, Barabási–Albert, grid).
  2. Set \(\beta\) and \(\gamma\) — sliders on the bottom control transmission and recovery rates.
  3. Seed infection — click a node to infect it, or use "Infect Hub" to start at the highest-degree node.
  4. Run simulation — click "Start" to animate. The left panel shows live SIR curves for the network simulation vs. the ODE prediction.
  5. Compare outcomes — observe when the ODE overestimates or underestimates peak infection.

Iframe Embed Code

You can embed this MicroSim in any web page with the following HTML:

<iframe src="https://AnvithPothula.github.io/graph-neural-networks-textbook/sims/ch05-sir-epidemic-network/main.html"
        height="557"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

Undergraduate / Graduate (College Level)

Duration

20–30 minutes

Prerequisites

Differential equations (basic ODE intuition). Graph degree and connectivity (Chapter 1). Optionally: reproduction number \(R_0\).

Activities

  1. Set \(\beta = 0.3\), \(\gamma = 0.1\) (\(R_0 = 3\)) on both a random graph and a scale-free graph of the same size. Compare peak infection size and outbreak duration.
  2. Infect a hub vs. a leaf node on the same Barabási–Albert graph. Quantify the difference in final recovered fraction.
  3. Find the critical threshold \(\beta/\gamma\) below which the epidemic dies out without reaching the giant component.

Assessment Question

Derive the basic reproduction number \(R_0\) for the SIR ODE model. Explain why the network-based SIR can show an epidemic even when the ODE \(R_0 < 1\).

References

  1. Kermack & McKendrick (1927). A contribution to the mathematical theory of epidemics. Proc. R. Soc.
  2. Pastor-Satorras & Vespignani (2001). Epidemic spreading in scale-free networks. PRL.

Part of Chapter 5: Label Propagation and Semi-Supervised Learning. Return to the chapter page or browse all MicroSims.