Computer simulation of Clostridium botulinum strain 56A behavior at low spore concentrations.

It is generally assumed that spore behavior is independent of spore concentration, but recently published mathematical models indicate that this is not the case. A Monte Carlo simulation was employed in this study to further examine the independence assumption by evaluating the inherent variance in spore germination data. All simulations were carried out with @Risk software. A total of 500 to 4,000 iterations were needed for each simulation to reach convergence. Lag time and doubling time from a higher inoculum concentration were used to simulate the time to detection (TTD) at a lower inoculum concentration under otherwise identical environmental conditions. The point summaries of the simulated and observed TTDs were recorded for the 26 simulations, with kinetic data at the target inoculum concentration. The ratios of the median (R(m) = median(obs)/median(sim)) and 90% range (R(r) = 90% range(obs)/90% range(sim)) were calculated. Most R(m) and R(r) values were greater than one, indicating that the simulated TTDs were smaller and more homogeneous than the observed ones. R(r) values departed farther from one than R(m) values. Ratios obtained when simulating 1 spore with 10,000 spores deviated the farthest from one. Neither ratio was significantly different from the other when simulating 1 spore with 100 spores or simulating 100 spores with 10,000 spores. When kinetic data were not available, the percent positive observed at the 95th percentile of the simulated TTDs was obtained. These simulation results confirmed that the assumption of independence between spores is not valid.