SummaryDengue, similar to other arboviral diseases, exhibits complex spatiotemporal dynamics. Even at town or village level, individual-based spatially explicit models are required to correctly reproduce epidemic curves. This makes modelling at the regional level (province, country or continent) very difficult and cumbersome. We propose here a first step to build a hierarchized model by constructing a simple analytical expression which reproduces the model output from macroscopic parameters describing each 'village'. It also turns out to be a good approximation of real urban epidermic outbreaks. Subsequently, a regional model could be built by coupling these equations on a lattice.keywords dengue, urban epidermics, multi-scale models, Easter Island, Brazil, Lima

During the initial phase of an epidemic, individual displacements between different regions modify the contact patterns. Understanding mobility processes and their consequences is necessary to predict the subsequent spread of the disease in order to optimize control policies. The basic reproduction number is commonly used to determine the threshold between extinction and expansion of the disease. Once it is derived for an epidemic model that includes the travel of population between distinct localities, the dependence of the diseases dynamics upon travel rates becomes explicit. In this study, we examine the effects of travel on the epidemic threshold for a model of two communities. The travel rates are treated as varying subject to two scenarios. We show theoretically that if the transmission potentials within communities are moderate, the epidemic threshold can be modified by travel. The conditions for the presence of the threshold induced by travel is determined and the critical values of travel at which the basic reproduction number is equal to one are derived. We show further that these results can also be applied to a model of three communities under specific travel patterns and that the derived basic reproduction number has a form similar to that of the two communities problem.