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| Reproduktionszahl (R0 und Rt)× | Stochastische Differentialgleichungen (SDGLn)× | |
|---|---|---|
| Fachgebiet≠ | Epidemiologie | Simulation |
| Familie≠ | Regression model | Process / pipeline |
| Entstehungsjahr≠ | 1990 | 1944 (theory); 1992 (numerical framework) |
| Urheber≠ | Diekmann, Heesterbeek & Metz | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) |
| Typ≠ | Threshold parameter for epidemic spread | Continuous-time stochastic process model |
| Wegweisende Quelle≠ | 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 ↗ | Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗ |
| Aliasnamen≠ | Basic Reproduction Ratio, Effective Reproduction Number, Net Reproduction Number, Temel Üreme Sayısı | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) |
| Verwandt≠ | 2 | 4 |
| Zusammenfassung≠ | 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. | 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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