Mathematical modeling and statistical inference to better understand arbovirus dynamics

Arboviruses such as the dengue and Zika viruses are expanding worldwide and mo- deling their dynamics can help to better understand and predict their propagation, as well as experiment control scenarios. These mosquito-borne diseases are influenced by a multiplicity of human and environmental factors that are complex to include in parsimonious epidemiological models. In parallel, statistical and computational tools are nowadays available to confront theore- tical models to the observed data. The objective of this PhD work is therefore to study arbovirus propagation models in the light of data. Firstly, in order to identify the most important elements to incorporate in models for dengue dynamics in a rural setting, several dengue models are com- pared using data from the Kampong Cham region in Cambodia. Models incorporate increasing complexity both in the details of disease life history and in the account for several forms of sto- chasticity. In the deterministic framework, including serotype interactions proved decisive, whereas explicit modeling of mosquito vectors and asymptomatic infections had limited added value, when seasonality and underreporting are already accounted for. Moreover, including several forms of un- certainties highlighted that a large part of the disease dynamics is only captured by stochasticity and not by the elements of the deterministic skeleton. Therefore, secondly, we explore other aspects of transmission, such as seasonality and spatial structure, in the case of dengue epidemics in Rio de Janeiro (Brazil). Finally, the models and estimation methods are applied to study an emerging arbovirus, the Zika virus. Using data from epidemics in the Pacific, we estimate the key parameters of disease propagation in the stochastic framework and explore their variability in terms of geogra- phic setting and model formulation by comparing four islands and two models with vector-borne transmission. In addition, potential interactions with the dengue virus are explored.