WOLFRAM|DEMONSTRATIONS PROJECT

Pathogen Dose-Response Curves with the Beta Poisson and Lognormal Models

​
dose-response curves
x axis
linear
log
b
15.
a
0.5
seed repeatable random numbers
seed value
1
noise amplitude (% of full scale)
5.
number of points to generate
20
ingested number axis maximum
500000.
fitted parameters: μ
L
= 4.035
σ
L
= 2.314
r
2
= 0.999
1
10
100
1000
10
4
10
5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
ingested number of pathogens
probability of infection
scattered dose-response data fitted with lognormal model
1
10
100
1000
10
4
10
5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
ingested number of pathogens
probability of infection
beta Poisson function used to generate the data

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. It has been frequently described by the beta Poisson model and less often by other models, including the cumulative form of the lognormal distribution. The purpose of this Demonstration is to show that for all practical purposes, the beta Poisson and lognormal distribution models can be used interchangeably over a large range of the ingested pathogen's numbers.