TY - JOUR

T1 - Simulation of population dynamics using continuous-time finite-state Markov chains

AU - Yin, K. Karen

AU - Yang, Hongchuan

AU - Daoutidis, Prodromos

AU - Yin, G. George

PY - 2003/2/15

Y1 - 2003/2/15

N2 - This paper is concerned with the simulation of certain types of population dynamics using Markov chains. A brief review of the Markovian property, the Chapman-Kolmogorov equation, and the forward equation together with its solution is given. The essentials in simulating continuous-time Markov chains are provided and two case studies are presented for demonstration. The first is a process of drug delivery for which a closed-form solution of the forward equation can also be obtained. The second one deals with cell population dynamics, for which a Markovian model capturing birth, death, and growth is developed and simulated. The key to such simulation studies is to specify the generator Q, which in turn requires a thorough understanding of the properties of the underlying system. In return, one obtains not only the means and variances, but also the entire probability distributions, and the evolution of the random processes of interest.

AB - This paper is concerned with the simulation of certain types of population dynamics using Markov chains. A brief review of the Markovian property, the Chapman-Kolmogorov equation, and the forward equation together with its solution is given. The essentials in simulating continuous-time Markov chains are provided and two case studies are presented for demonstration. The first is a process of drug delivery for which a closed-form solution of the forward equation can also be obtained. The second one deals with cell population dynamics, for which a Markovian model capturing birth, death, and growth is developed and simulated. The key to such simulation studies is to specify the generator Q, which in turn requires a thorough understanding of the properties of the underlying system. In return, one obtains not only the means and variances, but also the entire probability distributions, and the evolution of the random processes of interest.

KW - Forward equation

KW - Infinitesimal generator

KW - Markov chain

KW - Particulate processes

KW - Population dynamics

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U2 - 10.1016/S0098-1354(02)00179-5

DO - 10.1016/S0098-1354(02)00179-5

M3 - Article

AN - SCOPUS:0037441352

VL - 27

SP - 235

EP - 249

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

SN - 0098-1354

IS - 2

ER -