A Contribution to the Mathematical Theory of Epidemics.¶
Kermack, W. O., & McKendrick, A. G. (1927). A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London, Series A, 115(772), 700-721.
Cited by¶
6 citations across 6 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Contagion
- The defining commitment is that propagation is contact-mediated and self-reproducing across a network, governed by a transmission rate and a contact topology, with a critical threshold separating two qualitatively different fates: a self-sustaining outbreak when each case produces on average more than one new case (R > 1), and burnout to extinction when it produces fewer (R < 1).
This sourceFounding mass-action model of disease spread; derives the threshold theorem in which a self-sustaining outbreak occurs only above a critical susceptible density, and supplies the susceptible/infected/removed partition with per-contact transmission and removal rates.
Supported in partVerified against the publisher's abstract
The 1927 abstract poses the epidemic threshold as an open question — whether an epidemic ends only when susceptibles are exhausted or while many remain — but states no R>1/R<1 criterion and no contact topology.
“One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population.”
- The defining commitment is that propagation is contact-mediated and self-reproducing across a network, governed by a transmission rate and a contact topology, with a critical threshold separating two qualitatively different fates: a self-sustaining outbreak when each case produces on average more than one new case (R > 1), and burnout to extinction when it produces fewer (R < 1).
- Critical Mass
- The prime's distinctive content is the discontinuity in fate at R = 1: effort spent pushing a system from R = 0.5 to R = 0.9 buys no self-sustenance at all, while the last increment from 0.99 to 1.01 changes the qualitative regime.
This sourceFounding mass-action model of disease spread; derives the threshold theorem in which an epidemic occurs only above a critical susceptible density, supplying the sharp 'no epidemic below threshold' discontinuity the prime invokes.
Supported in partVerified against the publisher's abstract
Supplies the founding mass-action SIR model and the question whether an epidemic can end with susceptibles still present, but the readable abstract states no threshold theorem and no discontinuity at R = 1.
“One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population.”
- The prime's distinctive content is the discontinuity in fate at R = 1: effort spent pushing a system from R = 0.5 to R = 0.9 buys no self-sustenance at all, while the last increment from 0.99 to 1.01 changes the qualitative regime.
- Logistic Growth
- In epidemiology, cumulative infections in a closed, well-mixed susceptible pool follow a logistic curve under the simplest assumptions, because new infections require both an infected source and a remaining susceptible.
This sourceFounds the compartmental epidemic model in which cumulative infections in a closed susceptible pool trace a logistic-type curve whose inflection is the epidemic peak and whose ceiling is the herd-immunity / susceptible-depletion threshold.
Supported in partVerified against the publisher's abstract
The paper's own abstract supplies the contact-infection mechanism the claim's 'because' clause rests on, but says nothing about cumulative infections tracing a logistic curve.
“The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death.”
- In epidemiology, cumulative infections in a closed, well-mixed susceptible pool follow a logistic curve under the simplest assumptions, because new infections require both an infected source and a remaining susceptible.
- Propagation
- Epidemiology & public health: Disease propagation modeling (SIR, SEIR models), basic reproduction number (R₀), pandemic forecasting, contact tracing as interruption of propagation, superspreader events as amplification, vector-borne propagation (mosquitoes, ticks), all tracing back to the foundational SIR formulation of Kermack and McKendrick (1927).
This sourceFounding mass-action model of disease spread; derives the threshold theorem in which a self-sustaining outbreak occurs only above a critical susceptible density, and supplies the susceptible/infected/removed partition with per-contact transmission and removal rates.
Supported in partVerified against the publisher's abstract
The abstract attests the founding mass-action contact-infection model with a susceptible/infected/removed flow and a threshold question, but not SIR/SEIR naming, R-zero, forecasting, contact tracing, superspreaders or vector-borne spread.
“The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death.”
- Epidemiology & public health: Disease propagation modeling (SIR, SEIR models), basic reproduction number (R₀), pandemic forecasting, contact tracing as interruption of propagation, superspreader events as amplification, vector-borne propagation (mosquitoes, ticks), all tracing back to the foundational SIR formulation of Kermack and McKendrick (1927).
- Reservoir-Flux Network
- Epidemiology. SIR/SEIR models partition a population into Susceptible, Infected, and Recovered reservoirs with infection, recovery, and death fluxes; total population is conserved, and interventions read as perturbations on the flux constants.
This sourceOriginates the SIR compartmental model with population conservation and flux constants for infection and recovery.
Supported in partVerified against the publisher's abstract
The 1927 abstract backs the SIR partition (susceptible to infected to removed by recovery or death) and a constant population, but says nothing of SEIR, reservoirs, or interventions as flux perturbations.
“Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death.”
- Epidemiology. SIR/SEIR models partition a population into Susceptible, Infected, and Recovered reservoirs with infection, recovery, and death fluxes; total population is conserved, and interventions read as perturbations on the flux constants.
- Threshold
- Listed in the references but not attached to a specific claim.
Verification¶
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