(317d) Stochastic Modeling and Monte Carlo Simulation of Bacterial Disinfection: Generalized Approach

A generalized stochastic model for bacterial disinfection is introduced herein; its formulation is based on a highly non-linear intensity of transition given in terms of the product of the number concentration of bacteria and a power function of time. The exhaustive disinfection of bacteria is of paramount importance in various industries, especially those involving food and pharmaceuticals or those involving cattle-feeding operations; it is essential in eliminating pathogenic bacteria to guard against their deleterious effects on humans and animals. The disinfection of bacterial populations in fluid media entails the elimination or attenuation of vast numbers of microorganisms, which are discrete and mesoscopic in nature. These microorganisms exhibit incessant and irregular motion as well as complex non-linear behavior: Their motion is self-propelled due to their motility and is strongly affected by the flow of the surrounding fluid media and also by collision among themselves as well as with the surrounding vessel surfaces, and mixing devices. Consequently, various attributes of the bacteria during disinfection, such as their number concentration and size, will exhibit random, or stochastic, fluctuations as time progresses. These fluctuations will tend to be especially intense at the tail end, or termination period, of disinfection when the number of bacteria becomes exceedingly small. It is, therefore, highly desirable that the resultant random fluctuations be explored via stochastic paradigms; however, relatively little has been accomplished so far in this regard. The generalized, non-linear stochastic model proposed in the current contribution for bacterial disinfection aims at filling such a void. The model leads the master equation, which can be analytically solved for particular instances by conventional mathematical approaches or by rational approximation methods, e.g., system-size expansion. Nevertheless, the master equation has been simulated most frequently via the Monte Carlo method to circumvent the inherent complexity of solving it analytically or numerically by conventional techniques. To illustrate, the mean, variance (standard deviation), and coefficient of variation of the number concentration of bacteria during disinfection have been evaluated from their analytical expressions whenever possible and/or through Monte Carlo simulation otherwise. The results are in line with the available experimental data as well as with those computed from the corresponding deterministic models.