🧫 Outbreak: Epidemiology & Disease Modeling

From John Snow's 1854 cholera map to global smallpox eradication and aerosol superspreading, public health rests on mathematical epidemiology. Can you model the transmission curves and halt the contagion?

How to play

Examine 8 historic and modern outbreak scenarios: Measles airborne aerosol dynamics, Influenza antigenic shift vs. drift, John Snow's Broad Street pump, Ebola ring vaccination, and Polio Salk IPV vs. Sabin OPV.
Calculate the Herd Immunity Threshold: apply H_c = 1 − (1 / R₀) to determine the critical vaccination coverage required to stop transmission.
Use the Interactive Epidemic Containment Console to adjust vaccination coverage and public health contact reductions in real time on the SIR Epidemic Curve canvas.
Understand superspreading dispersion (k) and non-pharmaceutical curve flattening below healthcare surge capacity.
Tap your answer or press 1–4. Right answers build a 🔥 streak bonus!

Scenario 1/8 ⭐ 0 pts 🔥 0

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High Transmissibility

Measles Virus: Airborne Transmissibility

R₀ = 12 – 18 H_c = 92 – 95%

Kermack-McKendrick SIR Compartmental Epidemic Curve

Pathogen: Morbillivirus Transmission: Airborne Aerosol

Susceptible S(t) Infected I(t) Recovered / Immune R(t) Healthcare Surge Capacity

🎛️ Interactive Epidemic Containment Console

💉 Vaccination / Prior Immunity (v) 0%

😷 Contact Reduction / Public Health NPIs (c) 0%

Effective R_e: 15.00 Herd Target H_c: 93.3% Peak Active I_max: 74.2%

⚠️ EPIDEMIC WAVE GROWING (Re = 15.00 > 1)

About Epidemiological Modeling, R₀ & Disease Containment

Modern infectious disease modeling was established in 1927 by Scottish biochemist William Ogilvy Kermack and military physician Anderson Gray McKendrick in their seminal paper "A Contribution to the Mathematical Theory of Epidemics". They formulated the differential equations dividing host populations into three compartments: Susceptible, Infectious, and Recovered (or immune).

The basic reproduction number, R₀, defines the expected secondary cases originating from one index patient in a fully susceptible population. When the effective reproduction rate R_t = R₀ · (S/N) drops below 1, transmission contracts and the epidemic wave recedes. From this principle emerges the fundamental herd immunity threshold: H_c = 1 − (1 / R₀). High-transmissibility viruses like measles (R₀ ≈ 15) demand 95%+ vaccination coverage, whereas smallpox (R₀ ≈ 4.5) required ~75–80%.

In 1854, Dr. John Snow founded modern spatial epidemiology during the Soho cholera outbreak in London. By cartographically plotting cholera fatalities and demonstrating that mortality clustered around the public water pump on Broad Street, Snow proved cholera was waterborne decades before Robert Koch isolated Vibrio cholerae.