Suppose we introduce a small number of infecteds into a
large population of susceptibles. Then 
.
Looking at (5a), if
the coefficient of Y in (5a) is greater than one;
consequently 
is positive and the number of
infecteds must increase. Alternatively, if the quantity
in (7) is less than one, the coefficient of Y in
(5a) is negative and the number of infecteds must
decrease. Thus
is a threshold for growth or decay of the epidemic. We call
the basic reproduction number for the epidemic. Consider
what it means. One can show that
is the mean duration of infectivity
of infecteds. Since c is the mean contact rate, cD
is the total number of contacts made by an infective
person and if all contacts are with susceptibles, 
must be the number of susceptibles infected per
infective at the start of the process. Obviously, if
that number is greater than one, the number of
infectives must grow and if it is less than one, the
number of infectives must decrease.
Thus a fundamental concept of epidemiology is brought out by these simple models. But the basic idea holds for much more complicated processes. If on the average, an infective gives rise to more than one new infective, the epidemic grows. If on the average, an infective gives rise to less than one new infective, the epidemic decreases.
Finally, the definition of provides insight into
defining public health measures to control a disease.
Clearly we want to decrease 
and that can
be done by decreasing 
, c and/or D. For
example, decreasing contact rates during the period of
infectiousness clearly would decrease , and that
could be done by isolation of patients during the highly
infectious period.