2005
DOI: 10.1002/aic.10534
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Abstract: Thermal treatment under controlled conditions results in almost complete destruction, or disinfection, of cell or bacterial populations. Medical needs and public health concerns often demand that such disinfection be as complete as possible. The bacteria, particulate and mesoscopic in size, undergo complex motion and behavior, and thus, they die off at irregular rates during disinfection. Hence, in addition to the average death rates of bacteria, the fluctuations around these average rates must be known, espec… Show more

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Cited by 4 publications
(3 citation statements)
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“…When the distribution of X(1) is difficult to obtain, the closed-form results provided by Theorem 1 inherit this lack of tractability, which, in the most extreme case, can force the use of approximations in both univariate and multivariate settings. An example of a distribution that is difficult to handle is that of non-linear death processes with λ X (x) = x(d 0 − x) I{x < d 0 } , which is of current interest in the context of bacterial disinfection (Chou et al, 2005) and for which Theorem 3 in Billard et al (1979) gives intricate closed-form expressions for P X(1) = s + k | X(0) = s . In this case, results can be obtained without the need of any approximation.…”
Section: Applications: Making Time Change More Appealing To Model Ovementioning
confidence: 99%
“…When the distribution of X(1) is difficult to obtain, the closed-form results provided by Theorem 1 inherit this lack of tractability, which, in the most extreme case, can force the use of approximations in both univariate and multivariate settings. An example of a distribution that is difficult to handle is that of non-linear death processes with λ X (x) = x(d 0 − x) I{x < d 0 } , which is of current interest in the context of bacterial disinfection (Chou et al, 2005) and for which Theorem 3 in Billard et al (1979) gives intricate closed-form expressions for P X(1) = s + k | X(0) = s . In this case, results can be obtained without the need of any approximation.…”
Section: Applications: Making Time Change More Appealing To Model Ovementioning
confidence: 99%
“…In fact, numerous works offer unambiguous discourses on the need for the stochastic treatment of bacterial behavior, especially the bacteria's population dynamics [13][14][15][16]. Naturally, many of these works deal with the stochastic modeling of the inactivation, or disinfection, of bacterial populations [17][18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…Soboleva and Pleasants6 and May8 have presented a compelling argument for the paramount importance of incorporating the inherent stochastic and nonlinear features in modeling and simulating the behavior of biological populations in general and bacterial populations in particular. In fact, the growth or decline of populations of bacteria has been increasingly formulated according to nonlinear rate laws mainly deterministically9–15 and also stochastically 6, 7, 16…”
Section: Introductionmentioning
confidence: 99%