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Expanded Fermi Solutions in Pathogens' Dose-Response Curves

​
ingested number m
250
pathogens neededto infect, n
25
x axis
linear
log
m & n multiplier
1
10
100
1,000
10,000
minima
maxima
p
1
0.1
0.5
p
2
0.6
0.8
p
3
0.7
0.9
p
4
0.5
0.8
p
5
1.
1.
p
6
1.
1.
x axis maximum (linear)
500.
x axis maximum (log)
5.×
7
10
A foodborne or waterborne pathogen's dose-response curve is a plot of the probability of acute infection or death as a function of its ingested number. This Demonstration generates hypothetical plots based on the expanded Fermi solution concept, that is, that the probability of infection is determined by the number ingested and a set of probabilities that a given number of the pathogens will survive during their passage through the digestive system. Unlike in the "standard Fermi solution" where the probabilities are specified by single values, in the expanded version the probabilities are specified by their ranges. These allow analytical calculation of the lognormal distribution's logarithmic mean and standard deviation whose cumulative form represents the dose-response curve. The Demonstration also calculates and displays the hypothetical pathogen's dose that will result in 5, 50, and 95 percent probability of infection or death.
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