Paper Title
Mathematical Study to Detect Contamination in Small Water Pipelines

Transporting drinking water through water pipelines is vulnerable to contamination. After contamination event, non-native microbes interact with the native one in biofilms attach to pipes surfaces. Under the assumption that the flow is constant in time, we analyze the concentration of the pathogenic microbes within the water and the biofilms in a single pipe, and we provide the conditions of persisting of pathogenic microbes in a small water pipelines using Lyapunov stability.