Risk Assessment for Safe Drinking Water Supplies - Global Drinking Water Management and Conservation - page 125

It can be shown that the combined probability of exposure and infection can be
stated as

Þ¼ 1
n ¼ 0

P inf j l ð Pn jð XP inf j n ð Þ ð 6 : 1 Þ

where
P inf jð Þ is the probability of infection given the mean pathogen density
Pn jðÞ is the probability of exposure to n organisms, given the mean pathogen
density

;
P inf jð Þ is probability of infection given exposure to n organisms
We need one more probability: the probability of the organism successfully over-
coming host barriers. Let that probability be r. If the organisms are randomly
distributed, the probability of infection P inf is

μ

P inf ¼ 1 exp r ð l Þ ð 6 : 2 Þ

assuming the randomly distributed organisms can be represented as a Poisson
distribution.
A property of this type of model is that it can now be shown that a maximum risk
curve exists and it takes the shape shown in Fig. 6.4 , drawn for the pathogen
Campylobacter.

6.3.4.1 Risk Characterization

The objective of risk characterization is to integrate information from exposure and
dose response models to express public health outcomes, which requires predicting

the number of infections from multiple exposures. The number of infections may be
described as a binomial random variable X. The probability that the number of
infections will equal a given number k is given as

-

p k

P ð X ¼ k Þ¼ X

n

n
k

n k

ð 1 p Þ ð 6 : 3 Þ

k ¼ 0

where k is the number of infections
n is the number of infections per year for an individual; n = 365 for the number of

infections per year

p is the probability of infection.

This equation can be maximized to find the most likely infections based on the

calculation of P inf given in Eq. 6.2 .
If we assume that the consecutive exposures are independent of each other, we
can find the annual probability of one or more infections by assuming a binomial

process. If the probability of infection is P inf , then the probability of NOT being