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  • Epidemiological model  (1)
  • Key words: Epidemiologic modeling – SIS model – Delay – Threshold – Hopf bifurcation  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Disease transmission models with density-dependent demographics (1992)
    Springer
    Journal of mathematical biology 30 (1992), S. 717-731 
    Details
    ISSN: 1432-1416
    Keywords: Epidemiological model ; Density-dependent logistic growth ; Thresholds ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The models considered for the spread of an infectious disease in a population are of SIRS or SIS type with a standard incidence expression. The varying population size is described by a modification of the logistic differential equation which includes a term for disease-related deaths. The models have density-dependent restricted growth due to a decreasing birth rate and an increasing death rate as the population size increases towards its carrying capacity. Thresholds, equilibria and stability are determined for the systems of ordinary differential equations for each model. The persistence of the infectious disease and disease-related deaths can lead to a new equilibrium population size below the carrying capacity and can even cause the population to become extinct.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00173265
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Two SIS epidemiologic models with delays (2000)
    Springer
    Journal of mathematical biology 40 (2000), S. 3-26 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Epidemiologic modeling – SIS model – Delay – Threshold – Hopf bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  The SIS epidemiologic models have a delay corresponding to the infectious period, and disease-related deaths, so that the population size is variable. The population dynamics structures are either logistic or recruitment with natural deaths. Here the thresholds and equilibria are determined, and stabilities are examined. In a similar SIS model with exponential population dynamics, the delay destabilized the endemic equilibrium and led to periodic solutions. In the model with logistic dynamics, periodic solutions in the infectious fraction can occur as the population approaches extinction for a small set of parameter values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050003
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    Paper (German National Licenses)
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