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.
- 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.
- 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.
- 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.
- 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.
- 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.
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