Markovian Modeling and Monte Carlo Simulation of Bacterial Disinfection: Non-Linear Approach

摘要

The disinfection of bacterial populations in fluid media entails the elimination or attenuation of vast numbers of microorganisms. These microorganisms are discrete and mesoscopic, exhibiting incessant and irregular motion as well as convoluted non-linear behavior, and colliding frequently among themselves or with the surrounding vessel surfaces and/or mixing devices. Hence, it is highly likely that some of the attributes of the bacteria during disinfection, e.g., their number concentration, will exhibit random, or stochastic, fluctuations as time progresses. Such fluctuations are particularly pronounced at the termination stage of disinfection when the number of bacteria is minute. The exploration of the resultant random fluctuations via stochastic paradigms, tgerefirem, might be profoundly insightful; neyertheless, relatively little has been done hitherto in this regard. The current contribution aims at formulating a Markovian stochastic model for the rate of bacterial disinfection based on a highly non-linear intensity of transition. The resulting master equation of the model has been simulated via the Monte Carlo method to circumvent the complexity of solving it analytically or numerically by conventional numerical techniques. For illustration, the mean, variance (standard deviation), and coefficient of variation of the number concentration of bacteria during disinfection have been estimated through Monte Carlo simulation. The results of simulation are in line with the available experimental data as well as with those computed from the corresponding deterministic model.