Abstract
Overtourism is an increasingly relevant problem for tourist destinations, and some cities are starting to take extreme measures to counter it. In this paper, we introduce a simple mathematical model that analyzes the dynamics of the populations of residents and tourists when there is a competition for the access to local services and resources, since the needs of the two populations are partly mutually incompatible. We study under what conditions a stable equilibrium where residents and tourists coexist is reached, and what are the conditions for tourists to take over the city and to expel residents, among others. Even small changes in key parameters may bring about very different outcomes. Policymakers should be aware that a sound knowledge of the structural properties of the dynamics is important when taking measures, whose effect could otherwise be different than expected and even counterproductive.