In industrialized nations, the availability of potable water is often provided through sophisticated water distribution systems that consist a network of pipes, pumping stations, reservoirs, and other components that deliver safe drinking water to consumers. Biological contamination of the water distribution system, due to factors such as a breach in a pipe or other causes, can have an adverse effect on water quality.

In this talk, we discuss the development and analysis of a mathematical model of the release of pathogenic bacterial species into the water distribution system. Bacteria within a water distribution system frequently form biofilms on the interior surfaces of pipes that pathogens can attach to and grow, possibly leading to the persistence of the pathogens within the network. This mathematical model is studied under time-constant and time-periodic flow regimes using Lyapunov stability and Floquet theory for various network types. Frequently, water distribution networks have a significant number of components, making direct calculations prohibitively expensive so we developed and analyzed an efficient approach for predicting the long-time behavior of the pathogen population for large water-distribution networks. The analytical results are validated using numerical simulations of the full non-linear system on a range of water distribution network sizes.