M. Van Boven et al., Waning immunity and sub-clinical infection in an epidemic model: implications for pertussis in The Netherlands, MATH BIOSCI, 164(2), 2000, pp. 161-182
In The Netherlands, an epidemic outbreak of pertussis took place in 1996-19
97. Understanding of the causes of the epidemic is hampered by the fact tha
t many eases of infection with Bordetella pertussis go by unnoticed, and by
the fact that immunity against infection does not last lifelong. Motivated
by these observations, we develop and analyze an age-structured epidemic m
odel that takes these factors into account. A distinction is made between i
nfection in immunologically naive individuals, and infection in individuals
whose immune system has been primed before by infection or vaccination. Wh
ile the former often lead to severe symptoms and thus are more often diagno
sed and notified, the latter are largely sub-clinical. The main questions a
re: (1) to what extent do sub-clinical infections contribute to the circula
tion of B. pertussis; and (2) what might be the causes for the recent epide
mic? To answer these questions, we first present a new method to estimate t
he force of infection from notification data. The method is applied to the
1988-1995 case notification data from The Netherlands. Estimates of the for
ce of infection vary greatly, depending on the rate at which immunity is lo
st, and on the fraction of sub-clinical infections. For the 1988-1995 perio
d, our analysis indicates that if immunity is lost at a small rate and if a
majority of infections is sub-clinical, the contribution of infection in a
dults to the transmission process cannot be neglected. Our results furtherm
ore indicate that a decrease in the duration of protection after vaccinatio
n due to a change in the pathogen is the most likely factor to account for
the 1996-1997 epidemic. (C) 2000 Elsevier Science Inc. All rights reserved.