Question 1

What is the SIR model?

Accepted Answer

The SIR model is a simple mathematical model of infectious disease spread. The population is divided into three compartments: Susceptible (S, can be infected), Infected (I, currently infectious), and Recovered (R, immune or deceased). The model uses coupled differential equations: dS/dt = −βSI/N, dI/dt = βSI/N − γI, dR/dt = γI. The parameters β (transmission rate) and γ (recovery rate) determine how the epidemic evolves.

Question 2

What is R₀ (basic reproduction number)?

Accepted Answer

R₀ (R-naught) is the average number of secondary infections produced by one infectious individual in a fully susceptible population. Mathematically R₀ = β/γ in the SIR model. If R₀ > 1, the epidemic grows; if R₀ < 1, it dies out. Measles has R₀ ≈ 12–18, flu ≈ 1.2–1.4, COVID-19 original strain ≈ 2.5–3, Ebola ≈ 1.5–2.5.

Question 3

What is herd immunity and how is it calculated?

Accepted Answer

Herd immunity occurs when enough of the population is immune (through infection or vaccination) that chains of transmission cannot be sustained, protecting those who cannot be vaccinated. The herd immunity threshold is HIT = 1 − 1/R₀. For measles (R₀ ≈ 15), HIT ≈ 93%. For flu (R₀ ≈ 1.3), HIT ≈ 23%. This means measles requires far higher vaccination coverage to achieve population-level protection.

Question 4

What is the difference between SIR, SEIR, and SIRS models?

Accepted Answer

SIR: Susceptible → Infected → Recovered (permanent immunity). SEIR adds an Exposed (E) compartment for the incubation period between infection and becoming infectious — important for diseases like COVID-19 (incubation ~5 days) and measles (~14 days). SIRS allows recovered individuals to lose immunity and return to susceptible — appropriate for flu-like diseases with short-lived immunity. SIS (no R compartment) models diseases like the common cold where no lasting immunity develops.

🧪 SIR Epidemic Model Simulator

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