SIR Epidemic Model

SIR Epidemic Model: SIR is the Geometry of Contagion. Intermediate Biometry visual proof at NICEFA.

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The Formal Theorem

dS/dt = -bSI

Analytical Intuition.

SIR is the Geometry of Contagion. Divides population into Susceptible, Infected, Recovered. Epidemic curve rises until susceptibles run low. R-naught determines if the fire spreads.

CAUTION

Institutional Warning.

Herd Immunity Threshold. You only need to vaccinate enough to drop R-naught below 1.

Academic Inquiries.

What does gamma represent?

The recovery rate?inverse of average infectious time.

Standardized References.

Definitive Institutional SourceMurray, J.D. (2002). Mathematical Biology.

Intermediate

Predator-Prey

Predator-Prey: Lotka-Volterra is the Pulse of Nature. Intermediate Biometry visual proof at NICEFA.

Advanced

Survival Analysis

Survival Analysis: Survival is Statistics of Duration. Advanced Biometry visual proof at NICEFA.

Advanced

Hodgkin-Huxley Model

Hodgkin-Huxley Model: Hodgkin-Huxley is the Geometry of the Spike. Advanced Biometry visual proof at NICEFA.

Intermediate

Chemical Kinetics

Chemical Kinetics: Chemical Kinetics is the Math of Reaction. Intermediate Biometry visual proof at NICEFA.

Institutional Citation

Reference this proof in your academic research or publications.

NICEFA Visual Mathematics. (2026). SIR Epidemic Model: Visual Proof & Intuition. Retrieved from https://www.nicefa.org/library/biometry/sir-epidemic-model-theory

Dominate the Logic.

"Abstract theory is just a movement we haven't seen yet."

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