Quantifying model evidence for yellow fever transmission routes in Africa

Yellow fever is a vector-borne disease endemic in tropical regions of Africa, where 90% of the global burden occurs, and Latin America. It is notoriously under-reported with uncertainty arising from a complex transmission cycle including a sylvatic reservoir and non-specific symptom set. Resulting estimates of burden, particularly in Africa, are highly uncertain. We examine two established models of yellow fever transmission within a Bayesian model averaging framework in order to assess the relative evidence for each model’s assumptions and to highlight possible data gaps. Our models assume contrasting scenarios of the yellow fever transmission cycle in Africa. The first takes the force of infection in each province to be static across the observation period; this is synonymous with a constant infection pressure from the sylvatic reservoir. The second model assumes the majority of transmission results from the urban cycle; in this case, the force of infection is dynamic and defined through a fixed value of R0 in each province. Both models are coupled to a generalised linear model of yellow fever occurrence which uses environmental covariates to allow us to estimate transmission intensity in areas where data is sparse. We compare these contrasting descriptions of transmission through a Bayesian framework and trans-dimensional Markov chain Monte Carlo sampling in order to assess each model’s evidence given the range of uncertainty in parameter values. The resulting estimates allow us to produce Bayesian model averaged predictions of yellow fever burden across the African endemic region. We find strong support for the static force of infection model which suggests a higher proportion of yellow fever transmission occurs as a result of infection from an external source such as the sylvatic reservoir. However, the model comparison highlights key data gaps in serological surveys across the African endemic region. As such, conclusions concerning the most prevalent transmission routes for yellow fever will be limited by the sparsity of data which is particularly evident in the areas with highest predicted transmission intensity. Our model and estimation approach provides a robust framework for model comparison and predicting yellow fever burden in Africa. However, key data gaps increase uncertainty surrounding estimates of model parameters and evidence. As more mathematical models are developed to address new research questions, it is increasingly important to compare them with established modelling approaches to highlight uncertainty in structures and data.
Author summary Yellow fever (YF) is notoriously under reported due to non-specific symptom spectrum and the true burden is highly uncertain as a result of a complex transmission cycle. As such, estimates surrounding YF burden are highly uncertain and the mechanisms behind transmission are often unclear. We assess these mechanisms and the resulting uncertainty by estimating two existing models of YF transmission within a product space framework. This allows us to produce updated estimates of transmission intensity and to compare the relative support for each model given the data. We find strong support for a model assuming a static force of infection, approximating the constant infection pressure from the sylvatic reservoir of YF. We also highlight areas where data is sparse, often the same areas estimated to have especially high transmission intensity. This is the first robust multi-model approach to applied YF modelling and provides a framework that could be extended to other disease models.