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| SEIRモデル× | 確率微分方程式 (SDE)× | |
|---|---|---|
| 分野≠ | 疫学 | シミュレーション |
| 系統≠ | Regression model | Process / pipeline |
| 提唱年≠ | 1991 | 1944 (theory); 1992 (numerical framework) |
| 提唱者≠ | Kermack & McKendrick; Anderson & May | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) |
| 種類≠ | Deterministic compartmental ODE model | Continuous-time stochastic process model |
| 原典≠ | Anderson, R. M., & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press. ISBN: 978-0-19-854040-3 | Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗ |
| 別名≠ | Susceptible-Exposed-Infectious-Recovered Model, SEIR Compartmental Model, Latent Period Epidemic Model, SEIR Bulaşıcı Hastalık Modeli | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) |
| 関連≠ | 3 | 4 |
| 概要≠ | The SEIR model is a deterministic compartmental model that partitions a closed population into four epidemiological states: Susceptible (S), Exposed (E), Infectious (I), and Recovered (R). It extends the classic SIR framework by explicitly incorporating a latent period during which individuals have been infected but are not yet infectious. The model was systematically formalized by Anderson and May (1991) and remains a cornerstone of mathematical epidemiology for diseases with non-negligible incubation periods. | 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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