The deterioration of drinking-water quality within distribution systems is a serious cause for concern. Extensive water-quality deterioration often results in violations against regulatory standards and has been linked to water-borne disease outbreaks. The causes for the deterioration of drinking water quality inside distribution systems are not yet fully understood. Mathematical models are often used to analyze how different biological, chemical, and physical phenomena interact and cause water quality deterioration inside distribution systems. In this dissertation research I developed a mathematical model, the Expanded Comprehensive Disinfection and Water Quality (CDWQ-E) model, to track water quality changes in chloraminated water. I then applied CDWQ-E to forecast water quality deterioration trends and the ability of Naegleria fowleri (N.fowleri), a protozoan pathogen, to thrive within drinking-water distribution systems. When used to assess the efficacy of substrate limitation versus disinfection in controlling bacterial growth, CDWQ-E demonstrated that bacterial growth is more effectively controlled by lowering substrate loading into distribution systems than by adding residual disinfectants. High substrate concentrations supported extensive bacterial growth even in the presence of high levels of chloramine. Model results also showed that chloramine decay and oxidation of organic matter increase the pool of available ammonia, and thus have potential to advance nitrification within distribution systems. Without exception, trends predicted by CDWQ-E matched trends observed from experimental studies. When CDWQ-E was used to evaluate the ability N. fowleri to survive in finished drinking water, the model predicted that N. fowleri can survive for extended periods of time in distribution systems. Model results also showed that N. fowleri growth depends on the availability of high bacterial densities in the 105 CFU/mL range. Since HPC levels this high are rarely reported in bulk water, it is clear that in distribution systems biofilms are the prime reservoirs N. fowleri because of their high bacterial densities. Controlled laboratory experiments also showed that drinking water can be a source of N. fowleri, and the main reservoir appeared to be biofilms dominated by bacteria. When introduced to pipe-loops N. fowleri successfully attached to biofilms and survived for 5 months.