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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