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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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  • 2
    Electronic Resource
    Electronic Resource
    Stability analysis for models of diseases without immunity (1981)
    Springer
    Journal of mathematical biology 13 (1981), S. 185-198 
    Details
    ISSN: 1432-1416
    Keywords: Epidemiology ; Deterministic models ; Distributed delays ; Thresholds ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary A cyclic, constant parameter epidemiological model is described for a closed population divided into susceptible, exposed and infectious classes. Distributed delays are introduced and the model is formulated as two coupled Volterra integral equations. The delays do not change the general nature of thresholds or asymptotic stability; in all cases considered the disease either dies out, or approaches an endemic steady state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275213
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  • 3
    Electronic Resource
    Electronic Resource
    Integral equation models for endemic infectious diseases (1980)
    Springer
    Journal of mathematical biology 9 (1980), S. 37-47 
    Details
    ISSN: 1432-1416
    Keywords: Epidemiology ; Endemic infectious diseases ; Deterministic models ; Thresholds ; Distributed delays ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (births and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276034
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