Quantifying model evidence for yellow fever transmission routes in Africa

Abstract

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.

Fig 1. Diagram of models and data sources where R₀ denotes the basic reproduction number and λ, the force of infection.

Circles denote a product of calculation or inference; square boxes denote data sources.

Fig 2. Location of serological surveys used in the models.

The colour intensity indicates number of studies covering each province where grey = 0, pale blue = 1 and darker blue = 2 or more. Further details on serological surveys are available in Table A in S1 Text [, , –23]. Maps were produced from GADM version 2.0.

Fig 3. Diagram of model inference at one iteration.

Aspects relating the λ model are contained in the blue box. There are two main data sets that the models are estimated from, occurrence data, shown in white, and serological data, shown in black. Elements contained within circles denote families of model parameters with the vaccine efficacy (Ve) parameter common to both transmission model formulations. When a model is not activated (R₀ in this figure) the model-specific parameters are informed by pseudopriors, shown in purple. Solid arrows imply that the parameter is being informed by that data source or pseudoprior in this iteration; dashed arrows imply that the parameter family is currently not informed by that data source or pseudoprior in this iteration.

Fig 4. Geographical distribution of yellow fever occurrence.

Presence/ absence of yellow fever over 30 year period by province where white indicates absence and brown, presence (a). Median model predictions of the probability of at least one report of yellow fever (b). Countries not considered endemic for yellow fever are shown in black. The AUC of the shown fit is 0.9157. Maps were produced from GADM version 2.0.

Fig 5. Posterior predictive distributions of seroprevalence for each of the included serological studies.

Predictions from the λ model are shown in blue and from the R₀ model, red; paler red and blue regions indicate the 95% credible interval of the predictions. The data is shown with black dots with binomial 95% confidence ranges shown with black whiskers.

Fig 6. Estimated transmission intensity across the African endemic region for yellow fever.

Median posterior estimates of the GLM and transmission model parameters are used to calculate either (a) force of infection or (b) R₀ across the African endemic region. Countries not considered endemic for yellow fever are shown in grey. Maps were produced from GADM version 2.0.

Fig 7. Disease burden estimates for 2018 with equal model priors.

1,000 predictions of the burden in 2018 across the African endemic zone on log10 scale. The probability an infection is severe is drawn from a beta distribution with shape parameters 6.4 and 44.6 [39]. Predictions are drawn from each transmission model proportional to the model evidence under the assumption of equal model priors where pink points come from the λ model and blue points, from the R₀ model.