Time-scale separation and centre manifold analysis describing vector-borne disease dynamics

Abstract

In vector-borne diseases, the human hosts’ epidemiology often acts on a much slower time scales than the one of the mosquitos transmitting as a vector from human to human, due to their vastly different life cycles. We investigate in how far the fast time scale of the mosquito epidemiology can be slaved by the slower human epidemiology, so that for the understanding of human disease data mainly the dynamics of the human time scale is essential and only slightly perturbed by the mosquito dynamics.

Keywords:

• time-scale separation
• centre manifold approximation
• vector-borne diseases
• dengue fever
• stochastic processes

2010 AMS Subject Classifications::

• 92B05
• 34N05
• 32L10
• 34C45
• 37A50

Acknowledgements

This work has been supported by the European Union under FP7 in the projects EPIWORK and DENFREE and by FCT, Portugal, in various ways, especially via the project PTDC/MAT/115168/2009. We thank Hyun Mo Yang, Campinas, for useful discussions on mosquito dynamics and dengue fever.