Monte carlo simulation of bacterial disinfection: Nonlinear and time‐explicit intensity of transition

Abstract

in Wiley Online Library (wileyonlinelibrary.com).Bacteria being disinfected in fluid media are discrete entities and mesoscopic in size; moreover, they are incessantly as well as irregularly in motion and in collision among themselves or with the surrounding solid surfaces. As such, it is highly likely that some of the attributes of the bacterial population, for example, their number concentration, will fluctuate randomly. This is especially the case at the tail-end of disinfection when the population of bacteria is sparse. It might be effectual, therefore, to explore the resultant random fluctuations via a stochastic paradigm. Proposed herein is a Markovian stochastic model for the rate of bacterial disinfection, whose intensity of transition takes into account the contact time of the bacteria with the disinfecting agent to eliminate any given percentage of the bacteria in terms of a nonlinear function of time. The model's master equation has been simulated by resorting to the Monte Carlo method to circumvent the undue complexities in solving it analytically or numerically via conventional numerical techniques. For illustration, the mean, the variance (standard deviation), and the coefficient of variation of the number concentration of bacteria during disinfection have been estimated through Monte Carlo simulation. The results of simulation compare favorably with the available experimental data as well as with those computed from the corresponding deterministic model.

A generalized model for bacterial disinfection: Stochastic approach

“…For comparison, the master equation's linear and non-linear cases have also been solved numerically via simulation by resorting to the Monte Carlo method, often regarded as numerical experiments. The analytical and numerical results obtained for a set of linear cases of the generalized stochastic model have been validated by comparing them to those derived in our earlier works [21,23,24]; the comparison indicates that they are in excellent agreement. Moreover, the analytical and simulated results for a number of non-linear cases of the generalized stochastic model have been validated with the experimental observations for a specific instance of bacterial disinfection [25].…”

“…Moreover, the analytical and simulated results for a number of non-linear cases of the generalized stochastic model have been validated with the experimental observations for a specific instance of bacterial disinfection [25]. In this regard, a particular non-linear case appears to describe these experimental data more accurately than those linear cases of the generalized stochastic model equivalent to the models elaborated in two of our earlier works [23,24]. In light of these results, it is expected that the generalized stochastic model could be applied to the mathematical description of a variety of instances of bacterial disinfection performed at 6 distinct ambient conditions and settings.…”

“…The system under consideration can be modeled as a pure-death process, a particular instance of the Markovian birth-and-death process [22], as described in our earlier contributions [21,23,24]. The death event of this pure-death process is identified as the elimination of a single bacterium by means of a disinfecting agent.…”

“…The master equation for the pure-death process of concern is obtained as [21][22][23][24] n n 1 n 1 n n 0 0 d p (t) (t)p (t) (t)p (t), n = n , n 1, ..., 2, 1, 0 dt…”

“…Naturally, it is expected that the generalized model's performance in representing any specific set of experimental data could be enhanced in view of the flexible nature of its intensity of transition. In addition, the models developed in our earlier works [21,23,24] are embodied by the generalized stochastic model proposed herein: They presented stochastic models for bacterial disinfection each based on an intensity of transition given by the product of the first power of number concentration of bacteria and a power function of time t whose values were constrained to positive, integer numbers. 5 The proposed model yields the master equation of the process under consideration, which can be linear or non-linear depending on the power of the number concentration of bacteria, i.e., the process' random variable, in the intensity of transition.…”