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

Abstract

Vector-borne diseases are becoming increasingly widespread in a growing number of countries and it has the potential to invade new areas and habitats, either associated to changes in vectors habitats, human circulation or climate changes. From the dynamical point of view, the spatial-temporal interaction of models that try to adjust to such events are rich and challenging. The first challenges are to address the dynamics of the vectors (very fast and local) and the dynamics of humans (very heterogeneous and non-local). The objective of the present paper is to use the well-known Ross-Macdonald models, incorporating spatial movements, identifying different times scales and estimate in a suitable way the parameters. We will concentrate in a practical example, a simplified space model, and apply to Dengue's spread in the state of Rio de Janeiro, Brazil..