The problem of sewage pollution in waterways has been one of public concern for many years, and much work has been carried out on ways of lessening the problem. Nevertheless, some sewage still reaches waterways where it can cause environmental problems. Once sewage has been discharged, it is important to be able to ascertain as to how long it is likely to remain a hazard. One way of addressing this issue is by devising mathematical models to follow the time-evolution of faecal coliform indicator bacteria concentration. The aim of this paper is to propose a realistic, simple model, for use with the symbolic algebra computer program Mathematica, with which to follow the sequence of events after coliform discharge into a waterway. First, the mathematics of the model is outlined. Next, the parameters describing various modes of input to the system, and death due to irradiation, temperature, and sedimentation are discussed. Finally, results are presented which show that the model is useful in accurately predicting the system and is flexible enough to be easily adapted so as to handle different physical and environmental situations.