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| SIR Kompartmentalizált Járványügyi Modell× | Sztochasztikus differenciálegyenletek (SDE)× | |
|---|---|---|
| Tudományterület≠ | Epidemiológia | Szimuláció |
| Módszercsalád≠ | Regression model | Process / pipeline |
| Keletkezés éve≠ | 1927 | 1944 (theory); 1992 (numerical framework) |
| Megalkotó≠ | Kermack & McKendrick | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) |
| Típus≠ | Deterministic compartmental ODE model | Continuous-time stochastic process model |
| Alapmű≠ | 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 ↗ | Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗ |
| Alternatív nevek≠ | Kermack–McKendrick Model, Susceptible-Infectious-Recovered Model, Compartmental Epidemic Model, SIR Epidemiyoloji Modeli | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) |
| Kapcsolódó≠ | 3 | 4 |
| Összefoglaló≠ | 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. | Stochastic differential equations (SDEs) are differential equation models that combine a deterministic drift term — governing the average tendency of a system — with a stochastic diffusion term driven by a Wiener process (Brownian motion). Pioneered through Itô calculus by Kiyosi Itô in 1944 and given a comprehensive numerical treatment by Kloeden and Platen in 1992, SDEs are the standard modelling language for continuous-time systems subject to random noise, including financial asset prices, population dynamics, and physical processes. |
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