Analytical models approximating individual processes: a validation method.

Upscaling population models from fine to coarse resolutions, in space, time and/or level of description, allows the derivation of fast and tractable models based on a thorough knowledge of individual processes. The validity of such approximations is generally tested only on a limited range of parameter sets. A more general validation test, over a range of parameters, is proposed; this would estimate the error induced by the approximation, using the original model's stochastic variability as a reference. This method is illustrated by three examples taken from the field of epidemics transmitted by vectors that bite in a temporally cyclical pattern, that illustrate the use of the method: to estimate if an approximation over- or under-fits the original model; to invalidate an approximation; to rank possible approximations for their qualities. As a result, the application of the validation method to this field emphasizes the need to account for the vectors' biology in epidemic prediction models and to validate these against finer scale models.

Early determination of the reproductive number for vector-borne diseases: the case of dengue in Brazil.

OBJECTIVE: To evaluate a new method of deriving the reproductive number for vector-borne diseases from the early epidemic curves for vector-borne diseases with incubations in the vectors and in the hosts. METHOD: We applied the model to several dengue epidemics in different climatic regions of Brazil: Brasilia, Belém, Fortaleza, Boa Vista. RESULTS: The new method leads to higher estimates of the reproductive number than previous models. CONCLUSION: At present, Aedes aegypti densities, the meeting of more compatible strains of viruses and mosquitoes, may lead to re-emergence of urban yellow fever epidemics.