Understanding the effect of vector dynamics in epidemic models using center manifold analysis

In vector borne diseases the human hosts' epidemiology often acts on a much slower time scales than the one of the mosquitos which transmit the disease as a vector from human to human, due to their vastly different life cycles. We investigate in a model with susceptible (S), infected (I) and recovered (R) humans and susceptible (U) and infected (V) mosquitoes 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. This analysis of the SIRUV model is qualitatively in agreement with a previously investigated simpler SISUV model, hence a feature of vector-borne diseases in general.