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| Modèle épidémique compartimental SIR× | Nombre de reproduction (R0 et Rt)× | |
|---|---|---|
| Domaine | Épidémiologie | Épidémiologie |
| Famille | Regression model | Regression model |
| Année d'origine≠ | 1927 | 1990 |
| Auteur d'origine≠ | Kermack & McKendrick | Diekmann, Heesterbeek & Metz |
| Type≠ | Deterministic compartmental ODE model | Threshold parameter for epidemic spread |
| Source fondatrice≠ | Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society A, 115(772), 700–721. DOI ↗ | Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R0. Journal of Mathematical Biology, 28(4), 365–382. link ↗ |
| Alias | Kermack–McKendrick Model, Susceptible-Infectious-Recovered Model, Compartmental Epidemic Model, SIR Epidemiyoloji Modeli | Basic Reproduction Ratio, Effective Reproduction Number, Net Reproduction Number, Temel Üreme Sayısı |
| Apparentées≠ | 3 | 2 |
| Résumé≠ | The SIR model is a foundational mathematical framework for describing the spread of infectious diseases through a population. Introduced by William Ogilvy Kermack and Anderson Gray McKendrick in 1927, it partitions a closed population of size N into three mutually exclusive compartments: Susceptible (S), Infectious (I), and Recovered (R). A system of ordinary differential equations governs the flow of individuals between compartments, capturing epidemic dynamics with two key parameters — the transmission rate β and the recovery rate γ. | The basic reproduction number R0 is the expected number of secondary infections produced by a single infectious individual introduced into a fully susceptible population. Formally defined and computationally grounded by Diekmann, Heesterbeek, and Metz in 1990 using the next-generation matrix approach, R0 serves as the central threshold parameter in mathematical epidemiology: if R0 > 1, an epidemic can establish itself; if R0 < 1, the outbreak dies out. The effective reproduction number Rt extends this to partially immune or partially susceptible populations over time. |
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