ε (eV)

during a short time interval dt is proportional with the bacteria population. This
is, if dN bacteria dies during a time dt from an initial population of N bacteria,
then with 2N bacteria, the number of inactivations in the same time interval dt
will be 2dN. This means that, for short time intervals, bacteria die independently
of each other, since the inactivation rate is not influenced by the proximity of
one bacterium to others. Given the above observation, the inactivation speed r,
defined by Eq. (2.2), can be written as
r = α · N, (2.4)
where the proportionality constant α is called the decay coefficient of the bacteria
population. The quantity α is thus independent of t and N, and depends only on
the type of bacteria and on the type of the inactivation agent used for sterilization.
Introducing Eq .(2.4) in (2.3), the variation rate of the viable bacteria with
time can be expressed by the following differential equation
dN
dt
= −α · N. (2.5)
Separating the variables, integrating, and using the initial condition
N(t =0)=N0, (2.6)
the evolution of the number N of viable microorganisms ones, and with the treat-
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