How it Works
The simulation builds a contact network with the chosen topology and runs a discrete-time SIR epidemic on it. Each time step, each infected node attempts to transmit to each susceptible neighbor with probability β·dt. Each infected node recovers with probability γ·dt per step.
Node sizes are proportional to degree (number of connections). Scale-free networks have a few very high-degree hubs that act as super-spreaders. The epidemic curve is shown in the top-right corner.
Node i recovers: prob γ·dt per step
R₀ = β/γ · ⟨k²⟩/⟨k⟩ (heterogeneous network correction)
Scale-free: P(k) ∝ k⁻², grown by preferential attachment
Frequently Asked Questions
What is the SIR model?
The SIR model divides a population into Susceptible (S), Infected (I), and Recovered (R) compartments. People move from S→I at rate β·S·I/N, and from I→R at rate γ·I, capturing the essential dynamics of many infectious diseases.
What is a contact network in epidemiology?
A contact network represents individuals as nodes and their social contacts as edges. Disease spreads along edges from infected to susceptible nodes. The network structure profoundly influences epidemic dynamics, speed, and final size.
What is a scale-free network?
A scale-free network has a degree distribution that follows a power law P(k) ∝ k⁻ᵞ. Most nodes have few connections, but rare hubs have very high degree. The internet and many social networks are approximately scale-free.
Why do hubs accelerate epidemic spread?
Hubs (high-degree nodes) connect to many others. When a hub becomes infected, it can rapidly infect many neighbors. Epidemics on scale-free networks spread faster and have no epidemic threshold in the infinite network limit.
What is the basic reproduction number R₀?
R₀ = β/γ is the average number of secondary infections caused by one infected individual in a fully susceptible population. If R₀ > 1 an epidemic can occur; if R₀ < 1 the infection dies out.
What is a small-world network?
A small-world network (Watts-Strogatz model) has high local clustering like a lattice but short average path lengths like a random graph. Most pairs of nodes are connected by a surprisingly short chain — the 'six degrees of separation'.
How does vaccinating hubs affect epidemic spread?
Targeted vaccination of high-degree nodes (hubs) is far more effective on scale-free networks than random vaccination. Removing hubs fragments the network into smaller components, greatly reducing epidemic spread even at low vaccination coverage.
What is herd immunity?
Herd immunity occurs when a sufficient fraction of the population is immune (recovered or vaccinated) so that the effective reproduction number R_eff < 1. For a homogeneous population, the threshold is 1 - 1/R₀.
How does network clustering affect epidemics?
High clustering creates local cliques where the virus can spread quickly among tight-knit groups but may then become locally exhausted. Clustering can slow global spread by reducing the number of long-range transmission pathways.
What is superspreading in epidemics?
Superspreading occurs when a single infected individual infects many more than average (like a hub in a contact network). Superspreading events (SSEs) account for a disproportionate fraction of transmission and are characteristic of heterogeneous contact networks.