Title of article :
Hopf bifurcation in models for pertussis epidemiology
Author/Authors :
Hethcote، نويسنده , , H.W. and Yi، نويسنده , , Li and Zhujun، نويسنده , , Jing، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 1999
Pages :
17
From page :
29
To page :
45
Abstract :
Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two of the models. Periods of about four years are found for epidemiologically reasonable parameter values in two of these models.
Keywords :
pertussis , Epidemiology , Periodic Solutions , Hopf bifurcation , differential equations
Journal title :
Mathematical and Computer Modelling
Serial Year :
1999
Journal title :
Mathematical and Computer Modelling
Record number :
1591451
Link To Document :
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