قارن الطرق

	نموذج SIR الوبائي التقسيمي	رقم التكاثر (R0 و Rt)	نموذج SEIR
المجال	علم الأوبئة	علم الأوبئة	علم الأوبئة
العائلة	Regression model	Regression model	Regression model
سنة النشأة	1927	1990	1991
صاحب الطريقة	Kermack & McKendrick	Diekmann, Heesterbeek & Metz	Kermack & McKendrick; Anderson & May
النوع	Deterministic compartmental ODE model	Threshold parameter for epidemic spread	Deterministic compartmental ODE model
المصدر التأسيسي	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.	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.	Anderson, R. M., & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press. ISBN: 978-0-19-854040-3
الأسماء البديلة	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	Susceptible-Exposed-Infectious-Recovered Model, SEIR Compartmental Model, Latent Period Epidemic Model, SEIR Bulaşıcı Hastalık Modeli
ذات صلة	3	2	3
الملخص	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.	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.