Drinking Water Distribution Systems (DWDSs) play a key role in sustainable development of modern society. They are classified as critical infrastructure systems. This imposes a large set of highly demanding requirements on the DWDS operation and requires dedicated algorithms for on-line monitoring and control to tackle related problems. Requirements on DWDS availability restrict the usability of the real plant in the design phase. Thus, a proper model is crucial. Within this paper a DWDS multi-species quality model for simulation and design is derived. The model is composed of multiple highly inter-connected modules which are introduced to represent chemical and biological species and (above all) their interactions. The chemical part includes the processes of chloramine decay with additional bromine catalysis and reaction with nitrogen compounds. The biological part consists of both heterotrophic and chemo-autotrophic bacteria species. The heterotrophic bacteria are assumed to consume assimilable organic carbon. Autotrophs are ammonia oxidizing bacteria and nitrite oxidizing bacteria species which are responsible for nitrification processes. Moreover, Disinfection By-Products (DBPs) are also considered. Two numerical examples illustrate the derived model's behaviour in normal and disturbance operational states.