Basic reproduction number

The basic reproduction number, R₀, is the average number of secondary infections caused by one infected person in a fully susceptible population, under specified conditions.

Next-generation matrix: A matrix whose entries describe expected new infections in each group caused by an infected person in another group. Its dominant eigenvalue gives R₀ in models that divide populations into groups.
Effective reproduction number: The average number of secondary infections generated under current conditions, including existing immunity and interventions. Unlike R₀, it changes as susceptibility and control measures change.
Epidemiological modeling: The use of mathematical models to describe and predict patterns of health and disease in populations. Models estimate R₀ from transmission assumptions or epidemic data.
Ronald Ross: A British physician who demonstrated mosquito transmission of malaria and developed mathematical models of its spread. His malaria models helped establish threshold reasoning in infectious-disease control.
Generation interval: The time between infection of an infector and infection of a person they infect. It shapes how quickly an epidemic grows, even when R₀ is unchanged.
Susceptible population: People who can acquire a particular infection because they lack sufficient immunity or other protection. R₀ is defined against a population assumed fully susceptible.
COVID-19 pandemic: The global pandemic caused by SARS-CoV-2, beginning in 2019. Early estimates of R₀ helped characterize the virus's transmission potential.
Kermack–McKendrick theory: A mathematical framework explaining epidemic waves through interactions among susceptible, infected, and removed people. It formalized epidemic thresholds underlying the modern interpretation of R₀.
Contact rate: The frequency of potentially infectious contacts made by a person over a specified period. More effective contacts can raise the number of secondary infections.
Herd immunity threshold: The immune fraction above which sustained transmission is expected to decline in a simplified homogeneous population. It is commonly derived from R₀ under restrictive assumptions.

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