How a disease travels through contact networks, and why social structure is as important as the pathogen itself.
Disease follows the contours of contact. The architecture of social networks — who knows whom and how often they meet — determines the trajectory of an outbreak.
In a network model, each person is a node, each contact an edge. The disease hops node to node. The central question is whether a single case fizzles out or ignites a self-sustaining epidemic.
The SIR model divides the population into Susceptible, Infected, and Recovered.
Each step, an infected node transmits to each susceptible neighbor with probability and recovers with probability .
Click a node to infect it, or use the seed buttons. Then press Play.
Figure 1. The geography of contagion. The SIR model demonstrates how an outbreak depends on both local transmission rules and the global connectivity of the network. Raise the immune fraction to see the herd-immunity threshold: when roughly 1 − 1/R0 of the population is immune, most outbreaks fizzle.
is the average number of new infections caused by one infected person in a fully susceptible population. : epidemic can grow exponentially. : transmission breaks.
The transition at is sharp. Near it, outcomes are bimodal: the disease dies quickly or infects a large fraction of the network. The phase transition makes early-stage outbreaks hard to predict.
Figure 2. Criticality and the tipping point. Near the threshold , the epidemic outcome is unpredictable, often resulting in either a minor event or a major outbreak.
The same disease behaves differently on different networks. Random graphs spread it steadily. Small-world networks let it jump between distant clusters through shortcut edges. Scale-free networks have a few high-degree hubs that act as superspreaders.
Figure 3. The influence of topology. Even with identical disease parameters, different network structures (random, small-world, and scale-free) show markedly different levels of vulnerability.
Targeted vaccination of highly connected hubs can halt an epidemic with far fewer doses than random vaccination. The network structure is the vulnerability.