On modeling and simulating transitions between microbial growth and inactivation or vice versa

Resumed growth of the survivors of a heat or chemical treatment after cooling or a disinfectant dissipation is not an uncommon phenomenon. Similarly, the inverse, the onset of mortality in a growing microbial population as a result of exposure to increasing temperature or concentration of an antimicrobial agent, is also a familiar scenario. Provided that in either regime, the organism has no time to adapt biologically, the continuous transition from growth to inactivation or vice versa can be simulated with conventional growth and inactivation models, whose rate constant is allowed to change sign. Where both the growth and inactivation follow first-order kinetics, the sign change has no effect on the model equation's solutions. The same applies when the growth and inactivation patterns are described by a rate model, like the differential logistic equation or its various variants. However, determination of such models' coefficients from experimental isothermal growth and inactivation data can be difficult for technical reasons, unless the model can be integrated analytically. If not, or when the model itself is unknown a priori, then the rate equation would have to be derived from the fit of empirical models like the Weibull, modified versions of the logistic function and the like. But this may create a new kind of problem as a result of that the log and certain power operations cannot be used for negative numbers. For certain models at least, the problem can be solved through modification of the procedure by which the rate equation is solved numerically. This is demonstrated in simulated transitions between growth and inactivation and between inactivation and growth based on the log linear and Weibullian-power law models and three logistic patterns based on a shifted logistic function, the Baranyi-Roberts model and a shifted arctan model.