Time-Scale Analysis and Parameter Fitting for Vector-Borne Diseases with Spatial Dynamics

Vector-borne diseases are progressively spreading in a growing number of countries, and it has the potential to invade new areas and habitats. From the dynamical perspective, the spatial–temporal interaction of models that try to adjust to such events is rich and challenging. The first challenge is to address the dynamics of vectors (very fast and local) and the dynamics of humans (very heterogeneous and non-local). The objective of this work is to use the well-known Ross–Macdonald models, identifying different time scales, incorporating human spatial movements and estimate in a suitable way the parameters. We will concentrate on a practical example, a simplified space model, and apply it to dengue spread in the state of Rio de Janeiro, Brazil.