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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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  • 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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  • 3
    Electronic Resource
    Electronic Resource
    Selection for biennial life histories in plants (1987)
    Springer
    Plant ecology 70 (1987), S. 149-156 
    Details
    ISSN: 1573-5052
    Keywords: Biennial ; Cirsium vulgare ; Density-dependent selection ; Fitness criterion ; Life history ; Monocarpic perennial
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The applicability of traditional models of life-history evolution is restricted because models assume constant environments without density-dependence. In these models the geometric growth rate (λ) of a lineage is the natural choice for the fitness criterion. Because in growing populations λ is very sensitive to changes in generation time, biennials appear at a disadvantage when compared to species with annual reproduction. We propose an alternative fitness criterion for the situation in which recruitment is limited by both the availability of seeds and the (constant) rate at which ‘safe sites’ for establishment are created by small-scale disturbances. Under the assumptions of the model the evolutionarily stable strategy is to maximize expected seed production, irrespective of the length of the life cycle. For monocarpic plants, this implies that delay of flowering is favourable if the increased seed production compensates for the death of rosettes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00039328
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    Paper (German National Licenses)
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