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  • 1
    Electronic Resource
    Electronic Resource
    The saturating contact rate in marriage- and epidemic models (1993)
    Springer
    Journal of mathematical biology 31 (1993), S. 529-539 
    Details
    ISSN: 1432-1416
    Keywords: Contact rate ; Time-scale arguments ; Mass-action kinetics ; Epidemic models ; Marriage models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note we show how to derive, by a mechanistic argument, an expression for the saturating contact rate of individual contacts in a population that mixes randomly. The main assumption is that the individual interaction times are typically short as compared to the time-scale of changes in, for example, individual-type, but that the interactions yet make up a considerable fraction of the time-budget of an individual. In special cases an explicit formula for the contact rate is obtained. The result is applied to mathematical epidemiology and marriage models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00173891
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations (1990)
    Springer
    Journal of mathematical biology 28 (1990), S. 365-382 
    Details
    ISSN: 1432-1416
    Keywords: Epidemic models ; Heterogeneous populations ; Basic reproductive number ; Invasion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00178324
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    Paper (German National Licenses)
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