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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
    Amsterdam : Elsevier
    Insurance Mathematics and Economics 13 (1993), S. 149 
    ISSN: 0167-6687
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Insurance Mathematics and Economics 13 (1993), S. 152-153 
    ISSN: 0167-6687
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Langenbeck's archives of surgery 375 (1990), S. 259-265 
    ISSN: 1435-2451
    Keywords: Islets of Langerhans transplantation ; Pig
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Zusammenfassung Grenzen und Möglichkeiten der Transplantation von Langerhans-Inseln wurden am Schwein erprobt. Nach totaler Pankreatektomie wurden durch intraduktale Kollagenaseandauung zwischen 6mal 104 and 3mal 106 Inseln and inseltragende Fragmente pro Pankreas gewonnen. Nach Injektion des Transplantates in die Milz oder wahlweise in die Leber konnte bei den Tieren ein normoglykämischer Zustand mit normalen intravenösen Glukosetoleranztesten und ein Überleben bis zu 1 Jahr erreicht werden. Apankreatische Kontrollen verstarben im diabetischen Koma 10–12 Tage postoperativ. Eine gute Korrelation zwischen der Anzahl transplantierter Inseln und Normoglykämie nach Transplantation konnte demonstriert werden. Darüber hinaus war die synchrone In-vitro-Stimulation der Inseln mit Glukose und die daraus resultierende Inselsekretion ein wichtiger Indikator für die funktionelle Integrität der Inseln nach der Transplantation. Das Schwein bietet somit auch aufgrund der dem Menschen sehr ähnlichen immunologischen, physiologischen und anatomischen Eigenschaften bezüglich des Pankreas und der Ernährung ein gutes Modell zur weiteren präklinischen Erforschung der Inseltransplantation als Therapie des Diabetes mellitus.
    Notes: Summary Limits and possibilities of the transplantation of islets of Langerhans in pigs were studied. 6 × 104 to 3 × 106 islets and insulin producing fragments per pancreas were obtained by intraductal collagenase digestion of the pancreatic gland following total pancreatectomy. Islets grafted into the spleen or liver rendered normoglycemia to the pancreatectomized animals as demonstrated by normal fasting blood sugars and normal intravenous glucose tolerance tests as compared to not operated animals permitting a survival time of up to one year. Apancreatic controls died of ketoacidosis and diabetic coma 10 to 12 days posttransplant. The number of isolated and transplanted islets correlated well to the normoglycemic state of the animal. Beyond that the in vitro challenge of the islets with glucose and resulting insulin secretion was a very important indicator for the functional status and integrity of the islets after transplantation. Thus the pig appears to be a suitable model for the preclinical studying of islet transplantation especially since immunologic, physiologic and anatomic features of the pig are similar to those in the human regarding pancreas and nutrition.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1439-0973
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Zusammenfassung Aufgrund epidemiologischer Überlegungen wird geschlossen, daß Voll-AIDS möglicherweise nur dann auftritt, wenn der entsprechende Patient mit dem humanen Immundefizienzvirus (HIV) und außerdem mit einem weiteren infektiösen Koagens infiziert ist. Da sich die Ausbreitungsdynamik der AIDS-Fälle mit Manifestation von Kaposi-Sarkom wesentlich von der der Fälle ohne Kaposi-Sarkom unterscheidet, wird vermutet, daß für die Ausprägung von AIDS mit bzw. ohne Beteiligung von Kaposi-Sarkom jeweils eigenständige Koagenzien verantwortlich sind. Unsere formalen epidemiologischen Argumente scheinen durch neuere mikrobiologische Ergebnisse gestützt zu werden.
    Notes: Summary Through epidemiological considerations we conclude that full-blown AIDS may occur only if the index patient is infected by the human immunodeficiency virus (HIV) and, in addition, by some other infectious coagent. Since the dynamical behaviour of the spread of AIDS cases with manifestation of Kaposi's sarcoma differs fundamentally from that of the non-Kaposi cases, we conjecture that two independent coagents (together with HIV) are responsible for the outbreak of full-blown AIDS with or without manifestation of Kaposi's sarcoma, respectively. Our formal epidemiological considerations appear to be supported by recent microbiological findings.
    Type of Medium: Electronic Resource
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  • 7
    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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  • 8
    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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  • 9
    Publication Date: 2014-02-26
    Description: Die Autoren sind sich dar{ü}ber im klaren, daß zahlreiche Imponderabilien die Ergebnisse der vorgelegten Modellrechnungen beeinflussen k{ö}nnen. Immerhin repräsentiert jedoch das vorgelegte mathematische Modell die Summe unserer derzeitigen Kenntnisse zur Fragestellung AIDS--Epidemie; neu hinzukommende Erkenntnisse lassen sich rasch einarbeiten und in ihren Konsequenzen überschauen. Die Entwicklung neuer effizienter numerischer Methoden spielte eine Schlüsselrolle bei der tatsächlichen Simulation dieses umfangreichen realitätsnahen mathematischen Modells.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 10
    Publication Date: 2014-03-06
    Description: The rapidly increasing number of AIDS cases requires a realistic estimation of the future development of the HIV/AIDS disease. For that purpose we develop a large system of coupled nonlinear differential equations describing simultaneously the dynamics of the development of the disease, the population size, the gender and age structure. A set of 1650 coupled equations are linked by balanced parameters. The balancing procedure is described by a set of (formally) 2,178,000 additional algebraic conditions. As the considered system is stiff, it requires new special extrapolation methods combined with techniquees of dynamical sparsing for the solution of sparsely filled systems. According to our simulations we expect 19,0,000 deaths caused by AIDS in the Federal Republic of Germany (former territories) in the year 2000. Such an epidemical spread would tie up about 4-7 percent of the actual health care workers.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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