WOLFRAM|DEMONSTRATIONS PROJECT

Probabilistic Model for Microbial Mortality

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generate new data at same settings
seed repeatable random numbers
seed
0
no. of pts.
200
n
0
1000
model
constant
linear
sigmoid I
sigmoid II
constant probability rate
P
m
0.05
linear parameters
P
m
0
0.02
a
0.002
stretched exponential parameters
P
m init
0.03
P
m asym
0.03
τ
50.
m
5.
axes maxima
survival ratio s(t)
t
max
100.
P
m max
0.08
The semi-logarithmic survival curves of microbial cells and spores exposed to a lethal agent have a variety of shapes. A stochastic model based on the inactivation probability of each individual cell or spore can reproduce these shapes. If the underlying probability is constant, the survival curve is log-linear (“first-order kinetics”) and if it rises or falls, the semi-logarithmic survival curve has downward or upward concavity, respectively. If the underlying probability rate function is sigmoid, the semi-logarithmic survival curve can exhibit residual survival or a prominent flat shoulder. This Demonstration also shows that as the initial microbial population size grows, the corresponding survival curve becomes smoother and more deterministic.