Modeling and simulation of microbial survival during treatments with a dissipating lethal chemical agent

Abstract

In chemical preservation or disinfection by agents such as sulfite, chlorine, ozone and hydrogen dioxide, the effective agent's concentration diminishes with time as a result of reactivity, instability or evaporation. If it can be assumed that the momentary inactivation rate of the targeted microorganism only or primarily depends on the momentary agent concentration and survival ratio, then, theoretically, it is possible to estimate the survival curve during a treatment with a dissipating agent from inactivation data obtained under a set of constant agent concentrations, provided that both the survival parameters and the dissipation pattern can be expressed algebraically. This can be done by solving, numerically, a cumbersome differential equation, whose coefficients are terms which describe the changes in the survival parameters as a result of the agent dissipation. Solutions of this differential equation, obtained for hypothetical microorganisms treated with hypothetical dissipating agents are shown in the form of survival curves plotted on semi logarithmic coordinates. They demonstrate how the agent's decay pattern can affect the survival ratio and how the response of different organisms to the same treatment can be compared. A survival curve generated by the proposed model presents a theoretical limiting case. Whether it is also a satisfactory estimate of the actual response of organisms to a given chemical treatment remains to be demonstrated experimentally. In practice, the agent dissipation can be accompanied by regular or random fluctuations. But since the concentration cannot increase spontaneously, the dissipating rate must always be smaller or equal to zero. A mathematical model of such dissipation patterns was developed, and used to reveal the theoretical effects of the oscillations on the shape of microbial survival curves. A similar model was developed for scenarios in which the agent is periodically replenished.