Critical Community Size

Study-defined host-population size or range associated with a specified local infection fade-out versus persistence criterion over a stated horizon.

Version

v1 · 2026-10-07 · History

Domain-specific #

13846

Domain group

Applied Sciences & Engineering

Origin domain

Medicine & Healthcare

Subdomains

Stochastic Epidemics, Pathogen Persistence → Medicine & Healthcare

Core Idea

Critical community size (CCS) is a pathogen- and setting-specific host-population size or range associated with a declared criterion for local infection fade-out versus persistence over a stated period. It summarizes a stochastic relation, not a universal line guaranteeing extinction below or endurance above. Disease, immunity, vaccination, surveillance, and outside introductions shape the estimate.[^{ref-c585bc133710][}ref-ce7b082673a4]

Scope of Application

Bartlett's historical U.S. measles analysis used a post-epidemic fade-out criterion that was as likely as not, reporting roughly 250,000–300,000 people and a mean fade-out time near two years under his convention. Wearing and Rohani analyzed England–Wales pertussis with distinct pre-vaccine and vaccination-era conditions and reported different ranges. Neither number transfers automatically to a new pathogen or era.[^{ref-c585bc133710][}ref-ce7b082673a4]

Clarity

A numerical CCS claim needs a named pathogen, host-community unit, fade-out definition, risk or time criterion, and convention for outside introduction. Weeks with zero reported cases can be a surveillance proxy, not proof that no infection occurred. A later imported outbreak is not uninterrupted local persistence.[^{ref-c585bc133710][}ref-ce7b082673a4]

Manages Complexity

CCS organizes community size, transmission conditions, immunity, vaccination, stochastic low-case periods, and observation around one question: at what population size does the specified local fade-out outcome meet the stated criterion? A single reported number is compact, but it hides the graded size–risk relation and must travel with its study conditions.[^ref-ce7b082673a4]

Abstract Reasoning

Define the pathogen, community and observation window; choose a local fade-out rule; distinguish importation from internal persistence; and estimate the outcome's frequency against host size. Identify the size or range meeting that declared rule. If reporting, vaccination, or immunity assumptions change, reassess the estimate rather than carry the old count forward.[^{ref-c585bc133710][}ref-ce7b082673a4]

Knowledge Transfer

The size-versus-fade-out question transfers within infection epidemiology from measles to pertussis. Its numerical answer does not: the diseases, eras, and observation rules differ. The live Threshold Prime stresses a distinct or rapid transition; these sources also permit graded operational risk, so that Prime is not an established strict parent of this entry.[^{ref-c585bc133710][}ref-ce7b082673a4]

Example

Bartlett's U.S. measles summary uses an even-odds post-epidemic fade-out criterion and reports a historical size range. Mapped back: measles and the U.S. urban populations define infection and host unit; recurrent epidemic conditions supply the transmission setting without proving one exact birth-rate mechanism from the abstract; post-epidemic loss is the fade-out outcome; and the population range plus probability and roughly two-year convention form the operational boundary. Reintroduction is distinct.[^ref-c585bc133710]

Wearing and Rohani relate England–Wales pertussis zero-notification weeks to community size and report about 150,000–250,000 before vaccination versus 800,000–1,000,000 during the vaccination era. Mapped back: pertussis supplies the infection, model assumptions supply the transmission setting, zero reported weeks supply a fade-out proxy, and the era-specific ranges supply operational size boundaries. Reporting and outside infection pressure limit literal extinction claims.[^ref-ce7b082673a4]

Neighborhood in Abstraction Space

Critical Community Size sits in a sparse region of the domain-specific corpus (99^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Survival Analysis & Demographic Rates (16 abstractions)

Nearest neighbors

• Epidemic models on lattices — 0.76
• Infection rate — 0.76
• Clinical Case Definition — 0.75
• Attack rate — 0.73
• Uncertain geographic context problem — 0.73

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With

Basic Reproduction Number is a transmission ratio, not a host count. Minimum viable population concerns survival of the host species. Zero notifications need not mean zero infections, and a local chain that ends can later be reintroduced. A CCS range is a study-defined risk boundary, not a universal natural cliff.[^{ref-c585bc133710][}ref-ce7b082673a4]

References

[^ref-c585bc133710]: M. S. Bartlett, “The Critical Community Size for Measles in the United States,” Journal of the Royal Statistical Society: Series A 123, no. 1 (1960), pp. 37–44, original publisher Summary. https://academic.oup.com/jrsssa/article/123/1/37/7101793

[^ref-ce7b082673a4]: Helen J. Wearing and Pejman Rohani, “Estimating the Duration of Pertussis Immunity Using Epidemiological Signatures,” PLoS Pathogens 5, no. 10 (2009), e1000647, Results “Critical community size,” Methods, and Figures 3–4. https://journals.plos.org/plospathogens/article?id=10.1371/journal.ppat.1000647