Time-Scale Analysis Nonlocal Diffusion Systems, Applied To Disease Models

The objective of the present paper is to use the well-known Ross-Macdonald models as a prototype, incorporating spatial movements, identifying different time scales and proving a singular perturbation result using a system of local and nonlocal diffusion. This results can be applied to the prototype model, where the vector has a fast dynamics, local in space, and the host has a slow dynamics, nonlocal in space.