Linganisha mbinu

	Miundo Mfumo wa Magonjwa Endemiki (SIS, SIRS, SIRV)	Namba ya Uzazi (R0 na Rt)	Mfumo wa Mlipuko wa Magonjwa wa SIR
Nyanja	Epidemiolojia	Epidemiolojia	Epidemiolojia
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2000	1990	1927
Mwanzilishi	Herbert Hethcote	Diekmann, Heesterbeek & Metz	Kermack & McKendrick
Aina	Compartmental ODE model	Threshold parameter for epidemic spread	Deterministic compartmental ODE model
Chanzo asilia	Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4), 599–653.	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.
Majina mbadala	SIS Model, SIRS Model, SIRV Model, Endemic Disease Models	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
Zinazohusiana	3	2	3
Muhtasari	Endemic compartmental models extend the classical SIR framework to capture diseases that persist indefinitely in a population rather than burning out after a single epidemic wave. The SIS model allows recovered individuals to return to susceptibility immediately; SIRS introduces temporary immunity before loss; SIRV adds a vaccinated compartment. Together these models are foundational tools for studying diseases such as influenza, gonorrhea, and seasonal pathogens where reinfection or waning immunity is epidemiologically central.	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.