The aim of this paper is to evaluate the effectiveness of control strategies for diseases transmitted by the Aedes albopictus mosquito (the ‘Asian tiger’) and spread by human travel. This mosquito, which has become established in southern Europe in recent years, is a vector for many diseases. For example, an outbreak of chikungunya, hitherto regarded as a tropical disease, occurred in Italy in 2007. The initial case was a person who had acquired the disease overseas. Mosquito‐borne infections can only be spread over large distances by human travel, as the flight range of mosquitos is very limited. A system dynamics model has been developed which describes the mosquito life‐cycle, the natural history of mosquito‐borne disease in humans and mosquitos, and human behaviour including travel. Potential disease control strategies include chemical treatments to destroy either larvae or adult mosquitos, campaigns to influence human behaviour, or quarantine of infectious people. In this paper, which is based on the Italian chikungunya outbreak, this model is used to study and compare the effect of different control strategies, where the various actions are combined in different ways and implemented for different time periods.