Unsupervised dogs in cities are a serious environmental problem in most developing countries. Although this problem is of a high priority, there is always a great deal of debate on its solution and a scarce management based on information from the basic ecology of this problem. In the city of Santiago de Chile, there is a population of one million of dogs, between owned and stray dogs, with the resulting problems of public health and safety. In fact, this serious problem has produced strong ethical controversies in the public opinion on the measures applied for controlling this population. In this study, we performed an analysis of existing information about the size and the structure of the dog population at Santiago city, Chile. Based on these results, we developed a population dynamic model that captures the growth of the street dog population. The model is a system of equations coupled in four states: owned dogs and street dogs (supervised and stray) and both divided between fertile and sterile states. These four states were chosen because it gives much more flexibility when evaluating management actions and allows the exclusion of time as an explicit variable (autonomous equation). The results strongly suggest a source-sink population structure, where the population of street dogs is strongly subsidised by individuals migrating from the state of ownedr dogs, which are abandoned or escape. Therefore, different scenarios are proposed in the population dynamics model that consider the potential strategies to be applied as public policies.