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  • 1
    Electronic Resource
    Electronic Resource
    Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models (1986)
    Springer
    Journal of mathematical biology 23 (1986), S. 187-204 
    Details
    ISSN: 1432-1416
    Keywords: Epidemiology ; nonlinear incidence rates ; Hopf bifurcation ; periodicities ; infectious diseases
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifurcations, and homoclinic loop bifurcations. These may be important epidemiologically in that they demonstrate the possibility of infection outbreak and collapse, or autonomous periodic coexistence of disease and host. The possible mechanisms leading to nonlinear incidence rates are discussed. Finally, a modified general criterion for supercritical or subcritical Hopf bifurcation of 2-dimensional systems is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276956
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  • 2
    Electronic Resource
    Electronic Resource
    Dynamical behavior of epidemiological models with nonlinear incidence rates (1987)
    Springer
    Journal of mathematical biology 25 (1987), S. 359-380 
    Details
    ISSN: 1432-1416
    Keywords: Epidemiological models ; Nonlinear incidence rates ; Hopf bifurcation ; Homoclinic-loop bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Epidemiological models with nonlinear incidence rates λI pSqshow a much wider range of dynamical behaviors than do those with bilinear incidence rates λIS. These behaviors are determined mainly by p and λ, and secondarily by q. For such models, there may exist multiple attractive basins in phase space; thus whether or not the disease will eventually die out may depend not only upon the parameters, but also upon the initial conditions. In some cases, periodic solutions may appear by Hopf bifurcation at critical parameter values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277162
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    Paper (German National Licenses)
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