A fully stochastic approach bridging the microscopic behavior of individual microorganisms with macroscopic ensemble dynamics in surface flow networks

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.