Introducing the Stochastic Simulation of Chemical Reactions Using the Gillespie Algorithm and MATLAB: Revisited and Augmented


  • A. Argoti Kansas State University
  • L.T. Fan Kansas State University
  • J. Cruz Kansas State University
  • S.T. Chou Kansas State University


The stochastic simulation of chemical reactions, specifically, a simple reversible chemical reaction obeying the first-order, i.e., linear, rate law, has been presented by Martínez-Urreaga and his collaborators in this journal. The current contribution is intended to complement and augment their work in two aspects. First, the simple reversible chemical reaction is explicitly modeled as a stochastic process—specifically, as a birth-death process. The resultant model yields the master, i.e., governing, equation of the process whose solution renders it possible to analytically obtain the process’ expected means and variances. Second, the master equation is stochastically simulated through the Monte Carlo method by resorting to the time-driven approach in addition to the event-driven approach adopted by Martínez-Urreaga and his collaborators on the basis of the Gillespie algorithm. The process’ means and variances have been numerically computed by implementing these approaches, the results from which are compared with the analytical solutions of the stochastic model for validation. In addition, they are compared with the solution of the deterministic model as presented by Martínez-Urreaga and his collaborators. The two approaches for stochastic simulation by the Monte Carlo method are further illustrated with the photoelectrochemical disinfection of bacteria also obeying the first-order rate law. The results are validated by comparing them with the available experimental data.

Author Biographies

A. Argoti, Kansas State University

Andres Argoti is a research associate in the Department of Chemical Engineering at Kansas State University. He received his B.S. in Chemical Engineering from Universidad Nacional de Colombia, Bogota, and his M.S. and Ph.D. from Kansas State University, both in Chemical Engineering. His major research interest is in the stochastic analysis, modeling, and simulation of chemical and biochemical processes.

L.T. Fan, Kansas State University

L. T. Fan, a University Distinguished Professor, holds the Mark H. and Margaret H. Hulings Chair in Engineering and is director of the Institute of Systems Design and Optimization at Kansas State University. He served as department head of the Department of Chemical Engineering between 1968 and 1998. Currently, his major research interests are in stochastic analysis and modeling and in process-network synthesis based on process graphs (P-graphs). Fan received his B.S. in chemical engineering from National Taiwan University, M.S. in chemical engineering from Kansas State University, and M.S. in Mathematics and Ph.D. in chemical engineering from West Virginia University.

J. Cruz, Kansas State University

Juan Cruz is a graduate research assistant in the Department of Chemical Engineering at Kansas State University where he is currently carrying out his doctoral studies. Cruz received his B.S. in chemical engineering from Universidad Nacional de Colombia, Bogota; subsequently, he had a twoyear stint performing research at University of Puerto Rico, Mayaguez. His major research interests include nonaqueous enzymology, biomolecular engineering, and molecular modeling and simulation.

S.T. Chou, Kansas State University

Song-tien Chou obtained his B.S. in chemical engineering from National Taiwan University, and earned M.S. degrees in both chemical engineering and statistics, and a Ph.D. in statistics, all from Kansas State University. He is teaching in the Department of Finance and Banking at Kun Shan University in Taiwan; he was the department chair between 2000 and 2002. His research interests include the application of stochastic processes, risk analysis, and environmental engineering.