[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Surveillance and outbreaks](https://durgical.com/en/epidemiology/areas/outbreaks/) › Basic reproduction number (R0) and herd immunity # Basic reproduction number (R0) and herd immunity - Measure R0 tells how many people one case infects in a population with no immunity; from it comes the share of immune people that stops spread. Updated Nov 5, 2026 ## Key points - R0 > 1: the infection spreads; R0 = 1: it stays stable; R0 On this page - The basics Key points - What it is - Formula and reading - Worked example - Markers - How to read it - Common pitfalls - Memory aid - Elsewhere in DurgiPedia - Study Test yourself - Connections Connections ## What it is The basic reproduction number (R0) is the average number of secondary cases that one case produces in a fully susceptible population. The effective reproduction number (Rt) is the same average at a given moment, with part of the population immune or control measures in place. If R is above 1 the epidemic grows; below 1, it dies out. The herd immunity threshold, 1 − 1/R0, is the share of immune people needed for each case to cause fewer than one new case. ## Formula and reading - Herd immunity threshold: H = 1 − 1/R0. - Critical vaccine coverage: Vc = (1 − 1/R0) / E, where E is vaccine effectiveness (0 to 1). - Rt ≈ R0 × s, where s is the share of the population still susceptible. - Reading: R above 1, growth; equal to 1, stable endemic level; below 1, the outbreak dies out. ## Worked example - Data (made up): a respiratory infection has R0 = 5; the available vaccine has 90 % effectiveness. - Herd immunity threshold: 1 − 1/5 = 1 − 0.2 = 0.8, that is, 80 % of the population must be immune. - Coverage needed: 0.80 / 0.90 = 0.889; rounding up, 89 % of the population vaccinated. - Current situation: coverage is 70 %; immune = 0.70 × 0.90 = 0.63 (63 %). - Susceptible: 1 − 0.63 = 0.37 (37 %). - Effective R: 5 × 0.37 = 1.85; since it is above 1, one imported case can start an outbreak. - To bring R below 1, fewer than 20 % must be susceptible: 5 × 0.20 = 1. - Reading: at 70 % coverage each case infects almost 2 people on average; raising coverage to 89 % breaks the chain. ## Markers - R0 - Rt - 1 − 1/R0 - Herd immunity ## How to read it - Every unvaccinated child adds susceptibles: coverage below the threshold in one municipality allows outbreaks even if the national average is high. - Herd immunity protects those who cannot be vaccinated (very young infants, immunosuppressed people) only if the rest of the population is vaccinated. ## Common pitfalls - Using the threshold as the coverage target without correcting for vaccine effectiveness: it underestimates the coverage needed. - Treating R0 as a biological constant: it changes with contact density and control measures. - Mixing up R0 (fully susceptible population) and Rt (the current situation). ## Memory aid One minus one over R: the more contagious the agent, the closer to 100 % the wall of immune people must be. ## Test yourself Think of the answer, then tap the question to see it. ## If R0 = 4, what share of the population must be immune to reach herd immunity? 1 − 1/4 = 0.75, that is, 75 %. ## How do R0 and Rt differ? R0 assumes a fully susceptible population with no control; Rt is the effective number at a given moment, with immune people and measures in place. ## Why is the vaccine coverage needed higher than the herd immunity threshold? Because no vaccine protects 100 %: the threshold must be divided by vaccine effectiveness. ## What happens to an outbreak when Rt falls below 1? Each case produces on average fewer than one new case, and the outbreak fades out. [Add to my cards (4)](https://durgical.app/estudiar/?add=/en/epidemiology/basic-reproduction-number-and-herd-immunity/) ## Elsewhere in DurgiPedia - [Herd immunity and outbreak control](https://durgical.com/en/immunology/herd-immunity-and-outbreak-control/) - [Colombia's PAI schedule (which vaccines, at what age)](https://durgical.com/en/immunology/colombia-s-pai-schedule/) - [Vaccine types: live, inactivated, subunit, toxoid, mRNA, vector](https://durgical.com/en/immunology/vaccine-types-live-inactivated-subunit-toxoid-mrna-vector/) ## Connections ## Related 5 - [Attack rate](https://durgical.com/en/epidemiology/attack-rate/) - [Endemic, epidemic, outbreak and pandemic](https://durgical.com/en/epidemiology/endemic-epidemic-outbreak-and-pandemic/) - [Epidemic curve](https://durgical.com/en/epidemiology/epidemic-curve/) - [The PAI as a public health programme](https://durgical.com/en/epidemiology/the-pai-as-a-public-health-programme/) - [Epidemiologic triad and chain of infection](https://durgical.com/en/epidemiology/epidemiologic-triad-and-chain-of-infection/) ## Related conditions 3 - [Measles](https://durgical.com/en/conditions/measles/) - [COVID-19](https://durgical.com/en/conditions/covid-19/) - [Influenza (flu)](https://durgical.com/en/conditions/influenza/) [← All of epidemiology](https://durgical.com/en/epidemiology/) Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources. Sources: [Coronavirus disease (COVID-19): Herd immunity, lockdowns and COVID-19](https://www.who.int/news-room/questions-and-answers/item/herd-immunity-lockdowns-and-covid-19) (World Health Organization, 2020); [Principles of Epidemiology | Lesson 1 - Section 11](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson1/section11.html) (Centers for Disease Control and Prevention, 2012). ## **Spotted a mistake?** We are always improving for the community. Tell us what is wrong and our team will review it. Report a mistake Representative model, for educational purposes only. --- Source: https://durgical.com/en/epidemiology/basic-reproduction-number-and-herd-immunity/ License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/basic-reproduction-number-and-herd-immunity/