Disinfection of some microorganisms is characterized by a lag-phase (a minimum required ozone exposure until disinfection occurs). This phenomenon is easy to model in laboratory batch reactors but not in continuous flow mixed reactors. This paper introduces a stochastic disinfection model where individual microorganisms are followed on their paths through full-scale reactors. Combining exponentially distributed transport processes with delayed exponential disinfection kinetics for large populations of microorganisms (up to 10,000 individuals) yields predictions which can be evaluated statistically. It could be shown that deterministic models work well for systems with good disinfection performance (more than 2 log units reduction of active microorganisms), for reactors with poor performance stochastic models have to be applied. It could be demonstrated for real reactors that Bacillus subtilis spores are poor surrogates for Cryptosporidium parvum oocysts. The differences between the two microorganisms are large for reactors that deviate significantly from plug-flow behaviour.