Stochastic Modeling of Thermal Death Kinetics of a Cell Population Revisited


  • L.T. Fan Kansas State University
  • A. Argoti Caicedo Kansas State University
  • S.T. Chou Kansas State University
  • W.Y. Chen Kansas State University


Microorganisms as well as plant and animal cells involved in various biochemical processes are discrete entities whose sizes are mesoscopic. Thus, their number concentration (density) continually fluctuates, especially when it is small; such is the case at the tail end of thermal disinfection. It is, therefore, highly desirable and even essential to introduce the concept and methodology of stochastic processes in the instruction of biochemical engineering. It is indeed appropriate for major textbooks in the field to include these subjects. In fact, the thermal disinfection is commonly adopted to illustrate the application of stochastic processes in these textbooks, but only the mean (the first moment) of the fluctuating number concentration is analytically obtained and numerically presented in the majority of such textbooks; apparently, only one presents the variance (the second moment about the mean). 

To gain deeper insight into the stochastic nature of any phenomenon or process of interest, as manifested in fluctuations of the characteristic property of concern, it would be immensely useful to evaluate the quantities defined in terms of the moments of the distribution of this fluctuating property higher than the second order. In this contribution, the skewness (third moment about the mean over the third power of the standard deviation) and kurtosis (fourth moment about the mean over the fourth power of the standard deviation) of the distribution of fluctuations in the number concentration of cells are evaluated for the same example of thermal disinfection; these results would supplement what is given in the currently available textbooks.

Author Biographies

L.T. Fan, Kansas State University

L.T. Fan is University Distinguished Professor, holds the Mark H. and Margaret H. Hulings Chair in Engineering, and is Director of Institute of Systems Design and Optimization at Kansas State University He served as Department Head of Chemical Engineering between 1968 and 1998. He received a BS from National Taiwan University, his MS from Kansas State University, and his PhD from West Virginia University, all in chemical engineering, in addition to an MS in mathematics from West Virginia University

A. Argoti Caicedo, Kansas State University

Andres Argoti Caicedo is a graduate research assistant in the Department of Chemical Engineering at Kansas State University He received his BS in Chemical Engineering from the Universidad Nacional de Colombia, Bogota. His research interest is in the application of stochastic processes in chemical engineering.

S.T. Chou, Kansas State University

Song-tien Chou obtained his BS in Chemical Engineering from National Taiwan University, MS's in Chemical Engineering and Statistics and PhD in Statistics from Kansas State University His research interests include the application of stochastic processes, risk analysis, and environmental engineering.

W.Y. Chen, Kansas State University

Wei-Yin Chen received his PhD in Chemical Engineering from the City University of New York, his MS in Chemical Engineering from the Polytechnic Institute of New York, an MS in Applied Mathematics and Statistics from the State University of New York at Stony Brook, and a BS in Chemical Engineering from Tunghai University He is presently a Professor of Chemical Engineering at the University of Mississippi.