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A fully stochastic approach bridging the microscopic behavior of individual microorganisms with macroscopic ensemble dynamics in surface flow networks
Author(s) -
Yeghiazarian Lilit,
Samorodnitsky Gennady
Publication year - 2013
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/wrcr.20541
Subject(s) - randomness , statistical physics , markov process , stochastic process , markov chain , bridging (networking) , population , computer science , biological system , mathematical optimization , mathematics , physics , statistics , machine learning , computer network , biology , demography , sociology
Prediction of microbial surface water contamination is a formidable task because of the inherent randomness of environmental processes driving microbial fate and transport. In this article, we develop a theoretical framework of a fully stochastic model of microbial transport in watersheds, and apply the theory to a simple flow network to demonstrate its use. The framework bridges the gap between microscopic behavior of individual microorganisms and macroscopic ensemble dynamics. This scaling is accomplished within a single mathematical framework, where each microorganism behaves according to a continuous‐time discrete‐space Markov process, and the Markov behavior of individual microbes gives rise to a nonhomogeneous Poisson random field that describes microbial population dynamics. Mean value functions are derived, and the spatial and temporal distribution of water contamination risk is computed in a straightforward manner.