Deterministic and stochastic survival models of injured ozonated Giardia cysts

Giardia cysts exposed to short sublethal ozonation in lake waters continue to die-off well after the ozone complete dissipation. This delayed inactivation can be the manifestation of injured cysts' mortality, which the traditional Chick-Watson-Hom type models of disinfection do not account for. But it can be described by a slightly modified version of a general microbial survival model adapted for injured cysts or other targeted microorganisms surviving disinfection. The downward concavity of the cysts' semi-logarithmic survival ratio vs. time relationships suggests that the cysts' deaths had unimodal temporal distribution. Indeed, the cumulative (CDF) forms of the Weibull and lognormal distribution functions both had excellent fit to the experimental survival data. Such a survival pattern can also be described by a fully probabilistic model devised from the injured cysts' Markov chain, where the mortality's probability rate rises linearly with time. The stochastic model explains the ubiquitous observation that microbial survival curves become increasingly irregular and irreproducible as the number of survivors dwindles, regardless of their concavity degree and direction. Although based on ozonated Giardia cyst data, the concept should be applicable to the delayed mortality of other microorganisms surviving sublethal treatments of other kinds but unable to recover and/or multiply. KEY POINTS: • Deterministic and stochastic survival models can describe delayed inactivation. • The Weibull and lognormal distributions can describe cysts' times to mortality. • Stochastic model explains the progressively growing scatter in survival curves.