CDC & WHO Epidemiological Model

Measles Transmission & Herd Immunity Threshold Simulator

Real-time airborne diffusion kinetics, containment boundaries, and clinical complication models.

🛡️ Herd Protection Active
💡 Tip: Click anywhere to introduce an index measles case
Day: 0 (Week 0.0)
Active Load: 0 cases
Susceptible: 0
Vaccinated: 0
Exposed: 0
Infectious: 0
Recovered: 0
Epidemic Trajectory (SEIR Curves over Time)
● Infectious ● Exposed ● Recovered ● Susceptible

Epidemiological Principles & Mathematical Foundations

Measles virus (Measles morbillivirus) is one of the most contagious human pathogens known, remaining viable as an airborne aerosol for up to two hours after an infectious person leaves an enclosed space.

1. Why is the Measles Threshold So High (93–95%)? Because the Basic Reproduction Number ($R_0$) of measles ranges between 12 and 18, each infected person would, on average, infect 12 to 18 non-immune people in a naive population. The mathematical threshold $HIT = 1 - 1/R_0$ dictates that even a slight drop from 95% to 88% causes the effective reproduction rate ($R_e$) to cross above 1.0, enabling explosive sustained community transmission.
2. Microscopic Spatial Kinetics vs Macro SEIR This simulator models micro-agent Brownian diffusion with aerosol cross-infection vectors combined with clinical latency periods (incubation period: 8–12 days; infectious window: 4 days before to 4 days after rash onset). Real-world clusters in schools and daycares exacerbate spread because unvaccinated individuals often cluster geographically rather than mixing uniformly.
3. Two-Dose Vaccine Durability (MMR) A single dose of the MMR vaccine confers approximately 93% protection against measles, while two doses achieve ~97% long-term neutralizing immunity. Breakthrough infections in fully vaccinated individuals are rare and typically exhibit substantially reduced viral shedding and milder clinical course.