Medicine & Health ★★☆ Moderate

💉 Herd Immunity

When enough people are immune, an infectious disease can no longer spread — even unvaccinated individuals are protected. The herd immunity threshold is pc = 1 − 1/R₀. Higher R₀ demands higher vaccine coverage. Explore how vaccination halts epidemics with the SIRV model.

❌ Herd immunity NOT reached — epidemic possible
R₀: 3.0 Threshold pc: 66.7% Vaccinated: 50% Peak infected: —% Final immune: —%

💉 How Herd Immunity Works

Each infected person infects on average R₀ others in a fully susceptible population. If a fraction p is already immune, the effective reproduction number drops to Rₑ = R₀(1−p). The epidemic shrinks when Rₑ < 1:

p_c = 1 − 1/R₀    (herd immunity threshold)

Measles (R₀ ≈ 12–18) requires ~95% coverage. COVID-19 (R₀ ≈ 2–4) needs ~50–75%. Influenza (R₀ ≈ 1.3–2) needs only ~25–50%. The SIRV model splits the population into Susceptible, Infected, Recovered, and Vaccinated compartments, tracking flows between them over time.

About Herd Immunity Simulator

Herd immunity occurs when a sufficient proportion of a population has become immune to an infection — through vaccination or prior illness — so that the disease can no longer spread efficiently. Even individuals who are not themselves immune benefit because the chains of transmission are broken before the pathogen can reach them. This indirect protection is critical for people who cannot be vaccinated, such as newborns and immunocompromised patients.

The herd immunity threshold (HIT) is determined by the basic reproduction number R₀: HIT = 1 - 1/R₀. For measles with R₀ ≈ 15, approximately 93% of the population must be immune to halt transmission. For COVID-19 with R₀ ≈ 2.5–3, the threshold is around 60–70%. The simulator models this using SIR (Susceptible–Infected–Recovered) compartmental dynamics.

Maintaining herd immunity requires sustained vaccination coverage. Vaccine hesitancy, waning immunity, and the emergence of new variants can erode it. Public health campaigns, booster programmes, and outbreak monitoring are essential tools for keeping community immunity above the threshold and preventing resurgent epidemics.

Frequently Asked Questions

What is the herd immunity threshold and how is it calculated?

The herd immunity threshold (HIT) is the minimum immune fraction needed to stop an epidemic: HIT = 1 - 1/R₀. For R₀ = 4, HIT = 75%; for R₀ = 10, HIT = 90%. Higher transmission diseases require higher immunity coverage.

Can herd immunity be achieved through natural infection alone?

Technically yes, but natural infection herd immunity comes at enormous cost in illness, death, and long-term complications. Vaccination achieves the same protective threshold safely and quickly, which is why it is the recommended public health strategy.

Why do some diseases fail to achieve herd immunity despite high vaccination rates?

Some diseases persist because vaccine coverage is uneven (creating pockets of susceptible individuals), immunity wanes over time, or new variants can partially escape immunity. Measles outbreaks have occurred even in high-coverage countries when local vaccination rates drop below 95%.

Does herd immunity protect vaccinated individuals too?

Yes. Even vaccinated individuals benefit from herd immunity because lower community transmission reduces exposure. No vaccine is 100% effective, so fewer circulating pathogens mean vaccinated people face less risk of breakthrough infections.

What is the SIR model used in epidemiology?

The SIR model divides a population into Susceptible, Infected, and Recovered compartments, described by differential equations. It captures how infection spreads and wanes over time, and forms the foundation for more complex models including SEIR (with an Exposed class) and agent-based simulations.