مقایسهٔ روش‌ها

	مدل همه‌گیرِ سازه‌ایِ SIR (بیمار-مبتلا-بهبودیافته)	معادلات دیفرانسیل تصادفی (SDEs)
حوزه	اپیدمیولوژی	شبیه‌سازی
خانواده	Regression model	Process / pipeline
سال پیدایش	1927	1944 (theory); 1992 (numerical framework)
پدیدآور	Kermack & McKendrick	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
نوع	Deterministic compartmental ODE model	Continuous-time stochastic process model
منبع بنیادین	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.	Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer.
نام‌های دیگر	Kermack–McKendrick Model, Susceptible-Infectious-Recovered Model, Compartmental Epidemic Model, SIR Epidemiyoloji Modeli	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
مرتبط	3	4
خلاصه	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.