A model of microbial survival curves in water treated with a volatile disinfectant

Aim: To develop a method to calculate microbial survival parameters in water treated with a dissipating disinfectant and predict the inactivation patterns under different agent concentrations and decay rate regimes. Methods and Results: It has been assumed that the survival curves of the organism, under (hypothetical) constant agent concentration conditions, follow the power law model log [N(t)/N-0] = -bt(n) with a concentration independent exponent, eta. The concentration dependence of the rate parameter, beta, has been assumed to obey a log logistic relationship. Under changing disinfectant concentration, the survival curve is constructed so that its local slope, i.e. momentary logarithmic inactivation rate of the organism, is the slope of the momentary constant concentration curve at the momentary agent concentration, at the time which corresponds to the momentary survival ratio. The resulting differential equation was used to retrieve the survival parameters by numerical minimization procedures. Once these are calculated, the equation is solved numerically to produce the survival curve for almost any conceivable agent concentration history. The predictive ability of the method is demonstrated by using the survival parameters, calculated from published data obtained under one concentration profile, to predict survival curves under very different decay patterns. Conclusions: It is possible to calculate microbial survival parameters from data obtained in treatments where the unstable or volatile disinfectant progressively dissipates and use them to predict the outcome of different treatments. Significance and Impact of the Study: The proposed mathematical method will enable the prediction of microbial inactivation patterns in water treated with unstable and/or volatile chemical agents.