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| Endeemsed kompartmentaalsed mudelid (SIS, SIRS, SIRV)× | Paljunemisarv (R0 ja Rt)× | SEIR-mudel× | |
|---|---|---|---|
| Valdkond | Epidemioloogia | Epidemioloogia | Epidemioloogia |
| Perekond | Regression model | Regression model | Regression model |
| Tekkeaasta≠ | 2000 | 1990 | 1991 |
| Looja≠ | Herbert Hethcote | Diekmann, Heesterbeek & Metz | Kermack & McKendrick; Anderson & May |
| Tüüp≠ | Compartmental ODE model | Threshold parameter for epidemic spread | Deterministic compartmental ODE model |
| Algallikas≠ | Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4), 599–653. DOI ↗ | 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 ↗ | Anderson, R. M., & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press. ISBN: 978-0-19-854040-3 |
| Rööpnimetused | SIS Model, SIRS Model, SIRV Model, Endemic Disease Models | 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 |
| Seotud≠ | 3 | 2 | 3 |
| Kokkuvõte≠ | 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 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. |
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