Epidemic Network — Watts-Strogatz

Small-world network generation and SIR epidemic spread

NETWORK

40
4
0.10

NETWORK STATS

Avg path length L—
Clustering C—
Small-world?—

SIR EPIDEMIC

0.30
6
Susceptible
Infected
Recovered
Total infected—
About: Watts and Strogatz (1998) showed that real networks — neural, social, power grids — exhibit "small-world" properties: high clustering (like regular lattices) yet short average path lengths (like random graphs). Starting from a ring lattice where each node connects to K nearest neighbors, randomly rewiring edges with probability β interpolates between order (β=0) and randomness (β=1). The small-world regime at intermediate β has C≈C(0) but L≈L(1), enabling efficient epidemic spread. SIR epidemics on small-world networks spread faster than on regular lattices but can be modeled with effective R₀ depending on network topology.