ABSTRACT
Epidemiological models often must balance between accurate description of the disease dynamics, the different scales of modelling, and the associated levels of complexity which allow for establishing tractable causal relationships in the health problems at hand. Ordinary differential equations describe the changes in the sizes of the different compartments. Mechanisms included in epidemic models are transmission, i.e. contact either between susceptible and infected or, in the case of vector-borne diseases, between humans and vectors, infection of susceptible hosts/vectors, recovery, development of temporary or lifelong immunity, development of cross-immunity, possibility of reinfection by a virus of a different serotype. In the study of disease dynamics described by a dynamical system one seeks to perform a qualitative analysis of the states where the system is at rest, namely the equilibria. Mathematical models for vector-borne diseases are natural candidates for time scale separation analysis based on singular perturbation theory.
