Résumé
More than 100 years after its formal description, Chagas disease remains a major public health concern in Latin America with a yearly burden of 430,000 Disability-Adjusted Life Years (DALYs). The aetiological agent, a protozoan named Trypanosoma cruzi, is mainly transmitted to mammalian hosts by triatomine vectors. Multiple species of mammals and triatomines can harbour and transmit the parasite, and the feeding range of triatomine species typically includes many noncompetent hosts. Furthermore, the transmission of the pathogen can occur via several routes including the typical vector's faeces, but also oral, congenital and blood transfusion routes. These ecological and epidemiological complexities of the disease have hindered many control initiatives. In such a context, mathematical models provide invaluable tools to explore and understand the dynamics of T. cruzi transmission, and to design, optimize and monitor the efficacy of control interventions. We intend here to provide the first review of the mathematical models of Chagas disease, focussing on how they have contributed to our understanding of (1) the population dynamics and control of triatomine vectors, and (2) the epidemiology of T. cruzi infections. We also aim at suggesting promising lines of modelling that could further improve our understanding of the ecology, evolution, and control of the disease.