Ensemble forecast and parameter inference of childhood diarrhea in Chobe District, Botswana

Abstract

Diarrheal disease is the second largest cause of mortality in children younger than 5, yet our ability to anticipate and prepare for outbreaks remains limited. Here, we develop and test an epidemiological forecast model for childhood diarrheal disease in Chobe District, Botswana. Our prediction system uses a compartmental susceptible-infected-recovered-susceptible (SIRS) model coupled with Bayesian data assimilation to infer relevant epidemiological parameter values and generate retrospective forecasts. Our model inferred two system parameters and accurately simulated weekly observed diarrhea cases from 2007-2017. Accurate retrospective forecasts for diarrhea outbreaks were generated up to six weeks before the predicted peak of the outbreak, and accuracy increased over the progression of the outbreak. Many forecasts generated by our model system were more accurate than predictions made using only historical data trends. Accurate real-time forecasts have the potential to increase local preparedness for coming outbreaks through improved resource allocation and healthcare worker distribution.

Keywords: Bayesian inference; Childhood diarrhea; Dynamic modeling; Forecasting.

Figure 1.

Data smoothing and model system structure. (A) Weekly cases of under-5 diarrhea (after correction for missing data) in the dry seasons (weeks 20–51) in 2007–2016 are shown as grey points. Blue lines show under-5 diarrhea data after smoothing and subtraction of a baseline (see text for more details). (B) as for (A) but in the wet seasons (weeks 50–20) from 2007–2008 to 2016–2017. (C) Diagram of the model-system structure and outcomes. We use an SIRS model structure and weekly syndromic observations of under-5 diarrhea. The data assimilation system combines syndromic observations with SIRS model states and parameters to (1) infer syndromic epidemiological parameters, and (2) generate updated SIRS model states and parameters. The updated SIRS model states and parameters are then used to either (1) propagate the SIRS model forward one week, after which the assimilation process is repeated, or (2) generate forecasts by propagating the SIRS model forward until the end of the season.

Figure 2.

Parameter estimates across seasons. Estimates in both the wet season and dry season are shown in (A) for duration of immunity (1/δ) and (B) for the basic reproduction number R₀. The boxplots show variation in estimates from 10 simulations run each year.

Figure 3.

Estimates of the duration of immunity (1/δ) in days across years and seasons. Estimates for duration of immunity (1/δ) are shown for the dry season (A) and wet season (B) across years. Here we are modeling diarrheal disease as a syndrome caused by multiple pathogens, so 1/δ can be interpreted as the typical period between infections rather than waning immunity. Boxplots show variability in estimates across the 10 simulations run each year.

Figure 4.

Estimates of the basic reproduction number (R₀) across years and seasons. Estimates for R₀ are shown for (A) the dry season and (B) wet season across years. Here we are modeling diarrheal disease as a syndrome caused by multiple pathogens, so R₀ describes the force of transmission for one or more pathogens that may vary through time. Boxplots show variability in estimates across the 10 simulations run each year.

Figure 5.

Improvements in forecast accuracy achieved over predictions made based on historical distributions. Forecast accuracy is shown for three metrics: (A) peak intensity (proportion of forecasts accurate within 25% of observed peak intensity), (B) peak week timing (proportion of forecasts accurate within ±1 week), and (C) attack rate (proportion accurate within 25% of observed attack rate). Dry season accuracies are shown in red and wet season accuracies are shown in blue. Historical accuracy is represented by dashed lines, while SIRS-EAKF forecast accuracy are solid lines. The x-axis represents the timing of the forecast in relation to the predicted peak week; negative values represent forecasts made before the predicted peak. The size of the points represents the number of forecasts produced at each predicted lead week.

Figure 6.

Calibration across seasons and accuracy metrics. Calibration of forecasts generated before the predicted peak are shown by the solid colored lines. The x-axis represents the ensemble prediction interval (PI) percentiles of the forecasts and the y-axis represents the percent of observations that fall within those prediction intervals. The dashed line represents a 1:1 line of an ideally calibrated forecast model. Calibration is shown for (A) peak intensity, (B) peak week timing, and (C) overall attack rate.