Volume 6, Number 1, Spring 1998
OSCILLATIONS IN AN ENDEMIC MODEL
FOR PERTUSSIS
HERBERT W. HETHCOTE
Abstract. An epidemiologic model for the spread of pertussis
(whooping cough) is built from a demographic model
with an equilibrium age distribution. Computer simulations
of the mathematical model are used to study pertussis in the
United States. Both before and after vaccination began in
1940, the reported incidence of pertussis has been cyclical
with a period of 3 to 4 years. Because a seasonal contact
rate in models for measles leads to subharmonic oscillations
with a period of two years, it is plausible that a seasonal contact
rate could produce similar multiyear oscillations in the
pertussis model. But this does not happen, since the resulting
oscillations in incidence have a 1year period. However,
yearly stochasticity in the contact rate does lead to irregular
oscillations in the pertussis simulation model with a period of
about 4 years. Thus stochasticity is a new possible mechanism
leading to multiyear oscillations.
(Subscribers Only)
