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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 25 (1987), S. 275-288 
    ISSN: 1432-1416
    Keywords: Chemical mass recruitment ; Quality recruitment ; Damping ; Ants ; Delayed differential equation ; Functional differential equation ; Monotonicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ant species on a “high evolutionary level” have evolved chemical recruitment systems such as mass recruitment or quality recruitment. The recruitment process from the nest to a food source may be damped by crowding effects at the source. For four patterns of behavior (mass/quality recruitment; with/without damping) we study mathematical models for the time development of the quantity of food at the source. Each of the models can be reduced to a second order time-delayed differential equation which will be studied in the equivalent form of a first order (nonlinear) functional differential equation. We discuss the complete exploitation of a given source. In case of mass recruitment there possibly remains a threshold quantity of food not worth exploiting. However, every source will be exploited completely (in finite time) provided that the volatility of the trail pheromone is small compared with the exploitation activities of the colony and the distance from the nest to the source. In addition, for the damped models the “capacity” of the crowded source must be large compared with the initial quantity of food offered. The efficiency of the exploitation activities of some species allows conclusions on their evolutionary development.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 21 (1985), S. 307-315 
    ISSN: 1432-1416
    Keywords: Recruitment ; mass recruitment ; ants ; differential equation ; delay
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The chemical mass recruitment of ants with a fixed rate of workers and scouts is described by a set of differential equations which can be reduced to one delayed first order equation. The model allows the description of the time-development of the quality of a food source. It depends on the proportion of workers and scouts in the population whether there remains a threshold quantity which is not worth exploiting. The more intensive the trail-laying efforts the more rapid and exhaustive the exploitation. The number of ants on the trail from the nest to the source will be maximal, if the trail-laying efforts are in equilibrium with the evaporating effects of the trail-pheromone.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Infection 15 (1987), S. 413-416 
    ISSN: 1439-0973
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Zusammenfassung Mit Hilfe von nichtlinearen, komplexen Fittingtechniken wird die AIDS-Inzidenz aus dem Datenmaterial über die registrierten kumulativen Voll-AIDS-Fälle ermittelt. Das computergestützte Verfahren gestattet gleichzeitig die Berechnung der Konversionsrate sowie der mittleren Inkubationszeit, die auf ca. 11 Jahre geschätzt wird, sofern nur die Beobachtungszeiträume hinreichend groß sind (≥45 Jahre). Für kürzere Beobachtungszeiträume wird — infolge der Überrepräsentierung von Patienten mit sehr kurzer Inkubationszeit — die mittlere beobachtete Inkubationszeit wesentlich kleiner sein. Nach den Modellrechnungen ergibt sich z. B. für eine Kohorte von gleichzeitig infizierten Personen im siebten Jahr nach dem Infektionszeitpunkt eine mittlere beobachtete Inkubationszeit von nur 5,3 Jahren.
    Notes: Summary Using a nonlinear curve fitting method we calculate the incidence of AIDS cases through a study of reported data on cumulative AIDS cases. The method allows one to estimate the expected value of the incubation time, which happens to be about 11 years, if the intervals of observation are sufficiently large (≥45 years). For smaller intervals of observation the mean observed incubation time will be much shorter in consequence of the overrepresentation of “quick runners”. The model predicts a mean observed incubation time of 5.3 years for an infected cohort in the first seven years after infection.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemie in unserer Zeit 22 (1988), S. 72-72 
    ISSN: 0009-2851
    Keywords: Chemistry ; Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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