The net and basic reproduction numbers are among the most widely-applied
concepts in
infectious disease epidemiology. A net reproduction number (the average
number of secondary
infectious cases resulting from each case in a given population) of above
1 is conventionally
associated with an increase in incidence; the basic reproduction number
(defined analogously
for a ‘totally susceptible’ population) provides a
standard measure of the ‘transmission
potential’ of an infection. Using a model of the
epidemiology of tuberculosis in England and
Wales since 1900, we demonstrate that these measures are difficult to apply
if disease can
follow reinfection, and that they lose their conventional interpretations
if important
epidemiological parameters, such as the rate of contact between individuals,
change over the
time interval between successive cases in a chain of transmission (the
serial interval).
The net reproduction number for tuberculosis in England and Wales appears
to have been
approximately 1 from 1900 until 1950, despite concurrent declines in morbidity
and mortality
rates, and it declined rapidly in the second half of this century. The
basic reproduction number
declined from about 3 in 1900, reached 2 by 1950, and first fell below
1 in about 1960.
Reductions in effective contact between individuals over this period, measured
in terms of the
average number of individuals to whom each case could transmit the infection,
meant that the
conventional basic reproduction number measure (which does not consider
subsequent changes
in epidemiological parameters) for a given year failed to reflect the ‘actual
transmission
potential’ of the infection. This latter property is better described
by a variant of the
conventional measure which takes secular trends in contact into account.
These results are
relevant for the interpretation of trends in any infectious disease for
which epidemiological
parameters change over time periods comparable to the infectious period,
incubation period or
serial interval.