Peter Rashkov
Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Sofia, Bulgaria

Dengue fever's epidemiology is characterised by co-circulating multiple variants of the pathogen, the dengue virus. Mathematical modelling of dengue faces the challenges of finding a balance between accurate description of the disease dynamics, the different time scales of the dynamics of the human host and the mosquito vector populations, and the associated levels of complexity which allow for establishing tractable causal relationships.

One approach in modelling vector-borne diseases like dengue has been to use host-only models that include the vector dynamics in an implicit fashion. We present the theoretical rationale that allows us to reduce the complexity of host-vector model via time-scale separation and rigorously derive the quasi-steady state approximation. Then we discuss some issues which emerge repeatedly in the mathematical models of dengue: differences in structure (host-only vs. host-vector models), ecological effects due to seasonal changes in the vector population, immunological effects such as disease severity, and which have an effect on the model's dynamic behaviour.

Numerical bifurcation analysis is used to compare the structure of a host-vector model for dengue (with two variants and reinfection) and its variant resulting from a quasi-steady state approximation to that of a host-only model.