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Zbl 0993.92033
Hethcote, Herbert W.
The mathematics of infectious diseases. (English)
[J] SIAM Rev. 42, No.4, 599-653 (2000). ISSN 0036-1445; ISSN 1095-7200/e

Summary: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models.\par Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

MSC 2000:: *92D30 Epidemiology
34C60 Applications of qualitative theory of ODE
34C23 Bifurcation (periodic solutions)
35Q80 Appl. of PDE in areas other than physics
35B32 Bifurcation (PDE)

Keywords: thresholds; basic reproduction number; contact number; infectious diseases

Cited in: Zbl 1211.34062

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