Linganisha mbinu

	SEIR Model	Namba ya Uzazi (R0 na Rt)	Mfumo wa Mlipuko wa Magonjwa wa SIR	Milinganyo ya Tofauti ya Stokastiki (SDEs)
Nyanja	Epidemiolojia	Epidemiolojia	Epidemiolojia	Uigaji
Familia	Regression model	Regression model	Regression model	Process / pipeline
Mwaka wa asili	1991	1990	1927	1944 (theory); 1992 (numerical framework)
Mwanzilishi	Kermack & McKendrick; Anderson & May	Diekmann, Heesterbeek & Metz	Kermack & McKendrick	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
Aina	Deterministic compartmental ODE model	Threshold parameter for epidemic spread	Deterministic compartmental ODE model	Continuous-time stochastic process model
Chanzo asilia	Anderson, R. M., & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press. ISBN: 978-0-19-854040-3	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.	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.
Majina mbadala	Susceptible-Exposed-Infectious-Recovered Model, SEIR Compartmental Model, Latent Period Epidemic Model, SEIR Bulaşıcı Hastalık Modeli	Basic Reproduction Ratio, Effective Reproduction Number, Net Reproduction Number, Temel Üreme Sayısı	Kermack–McKendrick Model, Susceptible-Infectious-Recovered Model, Compartmental Epidemic Model, SIR Epidemiyoloji Modeli	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
Zinazohusiana	3	2	3	4
Muhtasari	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.	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 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.