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Selected Works of Yi Li
Article
Hopf Bifurcation in Models for Pertussis Epidemiology
Mathematical and Computer Modelling (1999)
  • Herbert W. Hethcote
  • Yi Li, Wright State University - Main Campus
  • Zhujun Jing
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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,
  • Differential equations,
  • Hopf bifurcation,
  • Periodic solutions
Disciplines
Publication Date
December 1, 1999
Publisher Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Mathematical and Computer Modelling. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematical and Computer Modelling, 30, 11-12, (December 1999) DOI# 10.1016/S0895-7177(99)00196-X
Citation Information
Herbert W. Hethcote, Yi Li and Zhujun Jing. "Hopf Bifurcation in Models for Pertussis Epidemiology" Mathematical and Computer Modelling Vol. 30 Iss. 11-12 (1999)
Available at: http://works.bepress.com/yi_li/76/