Measles Outbreak Risk & Herd Immunity Lab

Simulate how drops in community MMR vaccination coverage breach the critical herd immunity threshold ($R_0 \approx 12\text{--}18$), fueling rapid transmission cascades across social networks.

Community Parameters

Epidemiological Scenarios

MMR Coverage Rate (V) 95%

Measles herd immunity requires $V_c \ge 1 - 1/R_0 \approx 93.3\%\text{--}95\%$.

Measles Virulence ($R_0$) 15

Basic reproduction number: average secondary infections in a fully susceptible population.

Network Clustering Index Medium

Unvaccinated individuals often cluster geographically or socially (e.g. specific schools).

Simulation Control

Direct Inoculation

Or click anywhere directly on the interactive community map to infect that individual.

Live Community Network (N = 600)

Aerosol transmission radius & contact paths under active airborne spread

🛡️ Herd Immunity Protected

Effective R ($R_e$)

0.75

< 1.0 (Outbreak decays)

Total Infected

0.0% of population

Threshold Gap ($V - V_c$)

+1.7%

Safety margin vs $R_0$

Susceptible at Risk

570 vaccinated

Vaccinated Susceptible Exposed (Incubating) Infectious Plume

Epidemic Curve Timeline

Active infections over transmission generations

Ready. Click 'Start Transmission' or tap an individual to inoculate.

Stochastic SEIR Micro-Lattice Model

Why Measles is the Strictest Test of Herd Immunity

Measles virus (genus Morbillivirus) remains infectious suspended in the air for up to two hours after an infected person leaves a room. Because its basic reproduction number ($R_0$) averages between 12 and 18, it is among the most transmissible respiratory pathogens known to science.

Critical Vaccination Threshold: $V_c = \frac{1 - 1/R_0}{E}$

Where $E$ is vaccine clinical efficacy (~97% for two MMR doses). When community coverage slips from 95% down to 85%, effective reproduction ($R_e$) jumps from below 1.0 to well above 2.2, transforming an isolated imported case into a self-sustaining outbreak.

Spatial Clustering & The "Pocket" Effect

National or statewide vaccination averages often mask hyper-localized non-medical exemption pockets. An 88% overall county rate frequently contains individual elementary schools or neighborhoods where coverage is under 70%.

In this simulator, toggling the Network Clustering Index demonstrates how clustered susceptible populations enable exponential transmission chains even when surrounding districts maintain high overall vaccination.