A dynamic neural network model for predicting risk of Zika in real time

Abstract

Background: In 2015, the Zika virus spread from Brazil throughout the Americas, posing an unprecedented challenge to the public health community. During the epidemic, international public health officials lacked reliable predictions of the outbreak's expected geographic scale and prevalence of cases, and were therefore unable to plan and allocate surveillance resources in a timely and effective manner.

Methods: In this work, we present a dynamic neural network model to predict the geographic spread of outbreaks in real time. The modeling framework is flexible in three main dimensions (i) selection of the chosen risk indicator, i.e., case counts or incidence rate; (ii) risk classification scheme, which defines the high-risk group based on a relative or absolute threshold; and (iii) prediction forecast window (1 up to 12 weeks). The proposed model can be applied dynamically throughout the course of an outbreak to identify the regions expected to be at greatest risk in the future.

Results: The model is applied to the recent Zika epidemic in the Americas at a weekly temporal resolution and country spatial resolution, using epidemiological data, passenger air travel volumes, and vector habitat suitability, socioeconomic, and population data for all affected countries and territories in the Americas. The model performance is quantitatively evaluated based on the predictive accuracy of the model. We show that the model can accurately predict the geographic expansion of Zika in the Americas with the overall average accuracy remaining above 85% even for prediction windows of up to 12 weeks.

Conclusions: Sensitivity analysis illustrated the model performance to be robust across a range of features. Critically, the model performed consistently well at various stages throughout the course of the outbreak, indicating its potential value at any time during an epidemic. The predictive capability was superior for shorter forecast windows and geographically isolated locations that are predominantly connected via air travel. The highly flexible nature of the proposed modeling framework enables policy makers to develop and plan vector control programs and case surveillance strategies which can be tailored to a range of objectives and resource constraints.

Keywords: Dynamic neural network; Epidemic risk prediction; Zika.

Fig. 1

Weekly distribution of case and connectivity-risk variables. a Zika cases, b incidence rates, c case-weighted travel risk $${CR}_{\mathbf{j}}^{\mathbf{t}}$$, and d incidence-weighted travel risk $${IR}_{\mathbf{j}}^{\mathbf{t}}$$, for top 10 ranked countries and territories in the Americas for each respective variable

Fig. 2

Schematic of NARX network with d_x input and d_y output delays: Each neuron produces a single output based on several real-valued inputs to that neuron by forming a linear combination using its input weights and sometimes passing the output through a nonlinear activation function: $\mathbf{z}\mathbf{=}\mathbf{\phi }\left(\sum _{\mathbf{i}\mathbf{=}\mathbf{1}}^{\mathbf{n}}{\mathbf{w}}_{\mathbf{i}}{\mathbf{u}}_{\mathbf{i}}\mathbf{+}\mathbf{b}\right)\mathbf{=}\mathbf{\phi }\left({\mathbf{w}}^{\mathbf{T}}\mathbf{x}\mathbf{+}\mathbf{b}\right)$, where w denotes the vector of weights, u is the vector of inputs, b is the bias, and φ is a linear or nonlinear activation function (e.g., linear, sigmoid, and hyperbolic tangent [82])

Fig. 3

Country prediction accuracy by relative risk level. Panel a illustrates the actual relative risk level assigned to each country at Epi week 40 for a fixed forecast window, N = 4. Panels b–e each correspond to a different classification scheme, specifically b R = 0.1, c R = 0.2, d R = 0.3, e R = 0.4, and f R = 0.5. The inset shown by the small rectangle highlights the actual and predicted risk in the Caribbean islands. For panels b–e, green indicates a correctly predicted low-risk country, light gray indicates an incorrectly predicted high-risk country, and dark gray indicates an incorrectly predicted low-risk country. The risk indicator used is case counts

Fig. 4

Country prediction accuracy by forecast window. Panel a illustrates the actual relative risk level assigned to each country at Epi week 40 for a fixed classification scheme, R = 0.2. Panels b–e each correspond to different forecast windows, specifically b N = 1, c N = 2, d N = 4, e N = 8, and f N = 12. The inset shown by the small rectangle highlights the actual and predicted risk in the Caribbean islands. For panels b–e, the red indicates a correctly predicted high-risk country and green indicates a correctly predicted low-risk country. Light gray indicates an incorrectly predicted high-risk country, and dark gray indicates an incorrectly predicted low-risk country. The risk indicator used is case counts

Fig. 5

Aggregate model performance measured by ACC (averaged over all locations and all weeks) for all combinations of relative risk classification schemes (i.e., R = 0.1, 0.2, 0.3, 0.4, and 0.5) and forecast windows (i.e., N = 1, 2, 4, 8, and 12), where the risk indicator is case counts

Fig. 6

Aggregate model performance measured by ROC AUC (averaged over all locations and all weeks) for a fixed relative risk classification scheme, i.e., R = 0.4, and forecast windows (i.e., N = 1, 2, 4, 8, and 12), where the risk indicator is case counts

Fig. 7

Model performance and robustness. ACC is averaged over all locations for selected epidemiological weeks when risk indicator is a case counts and b incidence rate, and a fixed forecast windows (i.e., N = 4). The error bars represent the variability in expected ACC across ten runs for each combination