JK discloses partial ownership of SK Analytics. The remaining authors declare no competing financial interests.
Ecological and laboratory studies have demonstrated that temperature modulates West Nile virus (WNV) transmission dynamics and spillover infection to humans. Here we explore whether inclusion of temperature forcing in a model depicting WNV transmission improves WNV forecast accuracy relative to a baseline model depicting WNV transmission without temperature forcing. Both models are optimized using a data assimilation method and two observed data streams: mosquito infection rates and reported human WNV cases. Each coupled model-inference framework is then used to generate retrospective ensemble forecasts of WNV for 110 outbreak years from among 12 geographically diverse United States counties. The temperature-forced model improves forecast accuracy for much of the outbreak season. From the end of July until the beginning of October, a timespan during which 70% of human cases are reported, the temperature-forced model generated forecasts of the total number of human cases over the next 3 weeks, total number of human cases over the season, the week with the highest percentage of infectious mosquitoes, and the peak percentage of infectious mosquitoes that on average increased absolute forecast accuracy 5%, 10%, 12%, and 6%, respectively, over the non-temperature forced baseline model. These results indicate that use of temperature forcing improves WNV forecast accuracy and provide further evidence that temperature influences rates of WNV transmission. The findings provide a foundation for implementation of a statistically rigorous system for real-time forecast of seasonal WNV outbreaks and their use as a quantitative decision support tool for public health officials and mosquito control programs.
West Nile virus (WNV) is the leading cause of domestically acquired arthropod-borne viral disease in the United States. Here we show that accurate retrospective forecasts of mosquito infection rates and human WNV cases can be generated for a variety of locations in the U.S. Incorporation of temperature forcing into a baseline dynamic model improves our ability to accurately forecast WNV outbreaks and provides further evidence that temperature modulates rates of WNV transmission. These findings provide a foundation for implementation of a statistically rigorous system for real-time short-term and seasonal forecast of WNV. Such a decision support tool would help public health officials and mosquito control programs target control of infectious mosquito populations, alert the public to future periods of elevated WNV spillover transmission risk, and identify when to intensify blood donor screening.
West Nile virus (family
Vector control agencies monitor mosquito and viral activity and use this information to guide mosquito and WNV control measures [
In a recent study, we showed that accurate and reliable predictions of seasonal WNV outbreaks can be made using a parsimonious mathematical model representing the transmission dynamics of WNV among mosquitoes and birds, as well as spillover to humans [
Ecological and laboratory studies have demonstrated that physical environmental factors (e.g., temperature, precipitation, hydrology, and humidity [
Here, we explore whether the addition of a biological parameter depicting the relationship between temperature and the extrinsic incubation period will improve our ability to forecast WNV. The challenge is that the inclusion of too many processes results in a high-dimensional model structure, which, given the limited observational data streams available, may be difficult to optimize. We use the relationship between temperature and the extrinsic incubation period to expand our previously developed parsimonious model to include an environmental factor, a temperature-forcing parameter, that modulates the zoonotic transmission of WNV between mosquito vectors and avian hosts. We couple this mechanistic model with the ensemble adjustment Kalman filter (EAKF) [
Grey represents daily temperature, and red is the temperature climatology, i.e. the average of daily weather observations.
Retrospective WNV predictions were generated for 12 different counties representing a total of 110 outbreak years (
Blue represents the baseline model and red represents the temperature-forced model. The dotted lines are the ensemble mean forecasts and solid lines are the ensemble mean posterior distribution, orange
Forecast accuracy was evaluated for both the short-term, 1–4 weeks in the future, and the season. Short-term forecast were deemed accurate if the ensemble mean trajectory was within ±25% or ±1 case, whichever was larger, of the number of human cases reported for each of the next 4 weeks. Seasonal forecast accuracy was assessed using 4 metrics: total human WNV cases, total infectious mosquitoes, peak infectious mosquitoes and peak timing. Forecasts were deemed accurate if the ensemble mean trajectory was within ±25% or ±1 case, whichever was larger, of the first metric, within ±25% of the next two metrics, and within ±1 week of the fourth metric. Forecast accuracy across all outbreaks, regions and seasons, was assessed for both the baseline model and temperature-forced model as a function of calendar week. Forecasts were further grouped by prediction lead-time, here defined as the week of forecast generation minus the week of predicted peak mosquito infection.
Both the baseline model and temperature-forced model produced accurate short-term forecasts (see
For the seasonal forecasts, the baseline model generated more accurate forecasts as a function of calendar week for total number of human cases, peak timing, and peak magnitude early in the season but by the middle of the season (the end of July), weeks 31, 30, and 31, for these 3 metrics, respectively, the temperature-forced model forecasts were more accurate (
A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger.
Prior to the predicted peak, the baseline system forecast the number of human cases, the peak mosquito infection rate, and the seasonal mosquito infection rate more accurately than the temperature-forced system (
A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead.
Seasonal forecast accuracy was also compared to local historical average outbreak conditions to determine if the system could simply forecast accurately whether an outbreak was earlier or later than normal, or larger or smaller than normal. The average outbreak for each county was defined as the mean value for the 4 metrics (total human WNV cases, total infectious mosquitoes, peak infectious mosquitoes and peak timing) for all years excluding the forecast year. Both forecasting approaches were greater than 65% accurate predicting all 4 metrics 3 weeks prior to the predicted week of peak mosquito infection, see
Absolute error was calculated and compared for each prediction of observed peak of infectious mosquitoes, maximum mosquito infection rate, and the total number of human cases over the entire season, while the root mean squared error (RMSE) was calculated for predictions of the total number of mosquitoes observed over the season.
The short-term forecast accuracy for human cases was also evaluated using the Wilcoxon signed-rank test (see
We further evaluated differences in forecast accuracy based on geographic location (northern v. southern) and precipitation levels (wetter v. drier) (see
We additionally simulated and compared 6 different temperature-forcing structures in order to better understand the impact of temperature on WNV disease dynamics (see
Red represents climatology and yellow represents observed local temperature—daily climatology (red line), observed local daily temperature (yellow line), observed seasonal average temperature (yellow dashed), permuted observed local daily temperature (yellow dot) and permuted climatology (red dot). A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger.
Our findings demonstrate that a simple WNV model, iteratively optimized with data assimilation methods and weekly observations of mosquito infection rates and human WNV cases, can produce accurate forecasts of mosquito infection rates, infectious mosquito biting pressure and human cases in a variety of locations around the U.S. (
Specifically, the temperature-forced forecast model improves prediction accuracy for 4 of the 5 metrics evaluated: short-term (1–4 week) human cases, the total number of human cases, peak timing of infectious mosquitoes, and peak magnitude of infectious mosquitoes. These improvements manifest prior to when the majority of human cases are reported and prior to the peak week of mosquito infectiousness. Also, the results were not sensitive to the tolerance (e.g. ±25%) used to define accuracy (see
The forecasts of the total number of infectious mosquitoes on average were more accurately predicted using the baseline model. When broken down by calendar week it is apparent the baseline model is more accurate forecasting total infectious mosquitoes early in the season, but around week 30, when mosquito infection rates have risen, the temperature-forced model is more accurate (see
Estimated mosquito-bird contact rates differed between the baseline model and the temperature-forced model (
In expanding the WNV forecast system, we had to choose which physical environmental effects to incorporate. While precipitation, hydrology, humidity and temperature all influence WNV dynamics [
In addition to affecting viral development, temperature forcing may also impact host seeking behavior, gonotrophic period, and vector survival. For instance, estimates of mosquito-bird contact rates and mosquito birth/mortality rates differ between the two model forms (see
Although the number of counties included in this study is not geographically exhaustive, the findings provide evidence that the methods presented can be flexibly applied to a diversity of regions to produce accurate forecasts. The 12 counties included here represent a diverse set of locations with differences in population density, ecosystems (e.g.. wet/dry, warm/cold), primary vectors, and mosquito monitoring practices. In spite of these differences the EAKF was still able optimize the forecast model for simulation and skillful forecast. We believe that the method is applicable to regions (e.g. the Northern Plains) not represented in this sample, provided appropriate mosquito monitoring and disease surveillance systems are in place. We also expect the temperature-forced model to function better than the baseline model given the improvements in forecast accuracy apparent across latitude and precipitation levels (see
The greater forecast accuracy for wet versus dry counties may be indicative of a need to represent hydrologic effects. Precipitation in dry counties may have a larger impact on vector abundance than in wet counties, where breeding habitats are more plentiful and thus not as dependent on rainfall [
Mosquito population dynamics vary with local conditions [
Among the different temperature-forcing approaches compared, we found evidence that observed seasonal temperature variability is important but inter annual differences are not. Both the climatological and daily-observed temperature-forced forecasts were more accurate than the baseline model for peak timing, peak magnitude and total human WNV cases during the majority of the outbreak season. In contrast, forcing with a seasonal average temperature or permuted weather performed worse than the baseline model. These findings indicate that a local seasonal temperature cycle improves forecast accuracy by giving the model additional biologically relevant structure.
It is interesting that forecasts with climatological temperature forcing were more accurate than those generated using observed temperature conditions. This finding indicates that short-term fluctuations of temperature due to synoptic variability may actually degrade forecast accuracy. Whether this effect is due to the transience of these signals, which corrupts filter optimization, or the simplicity of the model, which may not appropriately represent the effects of these fluctuations on transmission dynamics, is not clear.
Overall, inclusion of temperature forcing improves the forecast skill of our parsimonious WNV model and provides further evidence that temperature modulates rates of WNV transmission. Though these forecast models do not represent the full complexity of WNV transmission dynamics, including effects such as ongoing mosquito control efforts, within county spatial heterogeneity [
The present forecasts, if operationalized, could provide public health officials, mosquito control programs, and parks departments a quantified estimate of WNV spillover transmission risk. Such enumeration is important because decision makers often rely on a limited number of heuristic principles instead of assessing probabilities when making operational decisions. In general, these heuristic principals are useful, but sometimes lead to severe and systematic errors [
As real-time forecast of WNV is operationalized, potential challenges will arise due to the need for robust timely data sets of both mosquito monitoring and human cases. In response to the emergence of WNV, an electronic surveillance system for arboviral disease, ArboNET, was developed by the Centers for Disease Control and Prevention (CDC) in 2000, and the CDC classified human cases of WNV as a nationally notifiable disease. ArboNET requires state and local health departments to report weekly human WNV case counts, along with infection of mosquitoes, birds and other animals, in order to monitor WNV activity across the country; however, this passive system has long lag times between when the data are generated and reported. In a retrospective study of Colorado hospital discharge data between 2003 and 2005 only 77% of hospital WNV cases were ever reported, and of those cases only 51% were reported within 7 days [
In addition to accelerated human case reporting, some areas of the US might benefit from more active mosquito monitoring. Mosquito monitoring practices vary around the country and are influenced by local socioeconomic factors, the tax base, and the public/political will to budget for mosquito surveillance [
In addition to a more active monitoring program, operational forecasting would benefit from shorter lags between when mosquitoes are trapped and test results are received. The lag associated with tests results varies by abatement district. Large districts such as the city of Chicago or Maricopa County run in-house laboratories that provide same day or one-to-two day testing lags, whereas others ship samples to state laboratories, which subsidize testing, but have substantially longer lags: 7 to 10 days [
The general under reporting of human WNV infections [
Should resources be provided to generate timely data streams, real-time WNV forecasts could be operationalized. These real-time forecasts could be used as a decision support tool by public health officials, mosquito control programs, and parks departments to help target control of infectious mosquito populations, alert the public when WNV spillover transmission risk is elevated, and identify when to intensify blood donor screening.
In order to forecast WNV, abundant mosquito infection rate data are needed. We contacted 68 agencies that either collect or store mosquito-monitoring data. These agencies were contacted because historical WNV outbreaks had occurred in these regions, providing incentive for in-depth mosquito monitoring. Twenty-six agencies agreed to provide data, of which 12 different US counties (
Weekly human cases of WNV were obtained from ArboNET, the national arboviral surveillance system and local county health departments [
Local temperature data for each of the 12 counties included in this study were assembled for 1981–2000 and each outbreak year. Temperature (T) data were compiled from the National Land Data Assimilation System (NLDAS) project-2 dataset at an hourly time step on a 0.125° regular grid from 1979 through the present [
Forecasts of WNV were generated using compartmental models that describe the transmission dynamics of WNV among mosquitoes and birds, as well as spillover transmission to humans. Two different compartmental models were tested: one with temperature forcing and the other without. Both models employed a standard susceptible-infected-recovered (SIR) epidemiological construct. The model with temperature forcing is represented by the following equations:
The contact rate,
Temperature may also influence transmission efficiency. Here we model the extrinsic incubation period as a function of temperature using published rates for
For each annual outbreak, a 300-member ensemble of the compartmental model was initiated (see
We also explored how knowledge of observed temperature, in theory, would improve our ability to forecast. The use of observed temperature is not realistic for real-time forecast, as future temperature conditions are not known; however, as applied here, it can be used to forecast WNV outbreaks retrospectively and determine if such information would, in theory, improve forecast accuracy.
We compared 6 different scenarios in which temperature was applied differently into the model. The 6 scenarios are: 1) the baseline model without temperature forcing, 2) our principal temperature forcing: daily climatology temperature forcing, 3) observed daily temperature forcing (i.e., real weather, which is not feasible for use in real time forecasting as such data would not be available), 4) observed seasonal average temperature forcing, 5) permuted observed temperature values for a given year and location; and 6) permuted temperature values from the historical 1981–2000 record.
In addition to evaluating forecast ensemble mean trajectory accuracy for the 6 different scenarios in which temperature forcing was applied differently, we also assessed whether forecast error differed significantly for climatology temperature forcing versus observed daily temperature forcing and observed daily temperature forcing versus the baseline model using a Wilcoxon signed-rank test.
The code that support the findings of this study are available from the corresponding author upon request.
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The blue dotted lines are the ensemble mean forecasts from the baseline model, the grey area is the spread of the ensemble forecast (light grey represents area between the 10th and 90th percentile and the darker grey area represents the spread between the 25th and 75th percentile), blue lines are the ensemble mean posterior distribution, orange
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The red dotted lines are the ensemble mean forecasts from the temperature forced model, the grey area is the spread of the ensemble forecast (light grey represents area between the 10th and 90th percentile and the darker grey area represents the spread between the 25th and 75th percentile), red lines are the ensemble mean posterior distribution, orange
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A forecast was deemed accurate if the forecast number of human WNV cases were within ±25% or ±1 case of the number of reported cases from point of forecast to the number of weeks in the future, whichever was larger.
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A forecast was deemed accurate if the forecast number of human WNV cases were within ±25% or ±1 case of the number of reported cases from point of forecast to the number of weeks in the future, whichever was larger. Note that lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead.
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A forecast was deemed accurate if: 1) peak timing was earlier or later than average; 2) peak infection rate was higher or lower than average; 3) total infectious mosquitoes were higher or lower than average; and 4) human WNV cases were higher or lower than average. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead.
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead. Counties south of 40° N were used in this analysis (Maricopa County AZ, Orange County CA, Sacramento County CA, Yolo County CA, Iberia Parish LA, St Tammany Parish LA, and Clark County NV).
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead. Counties north of 40° N were used in this analysis (Boulder County CO, Weld County CO, Cook County IL, and Allen County IN, and Suffolk County NY).
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead. Counties that receive less than 10 mm/day of precipitation annually were used in this analysis (Maricopa County AZ, Orange County CA, Boulder County CO, Weld County CO, and Clark County NV).
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead. Counties that receive more than 10 mm/day of precipitation annually were used in this analysis (Sacramento County CA, Yolo County CA, Cook County IL, Allen County IN, Iberia Parish LA, St Tammany Parish LA, and Suffolk County NY).
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead. Counties that receive more than 10 mm/day of precipitation annually were considered wet (green), Sacramento County CA, Yolo County CA, Cook County IL, Allen County IN, Iberia Parish LA, St Tammany Parish LA, and Suffolk County NY and dry counties received less than 10 mm/day of precipitation annually (yellow), Maricopa County AZ, Orange County CA, Boulder County CO, Weld County CO, and Clark County NV.
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead. Northern counties are north of 40° N latitude (Boulder County CO, Weld County CO, Cook County IL, and Allen County IN, and Suffolk County NY) and southern county are south of 40° N (Maricopa County AZ, Orange County CA, Sacramento County CA, Yolo County CA, Iberia Parish LA, St Tammany Parish LA, and Clark County NV).
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5 different temperature data streams were used in the model: 1) daily climatology from 1981 to 2000 as described in the main manuscript (red line); 2) observed local daily temperature (yellow line); 3) observed seasonal average temperature, calculated for each outbreak year and location as the mean daily temperature for all weeks the forecast was generated (one temperature value is used for the whole season and fluctuates from season to season, yellow dashed line); 4) permuted observed temperature values: randomly select temperature values from all days in a season (yellow o); and 5) permuted temperature values from the climatology: randomly select temperature values from the day of year which were forecasted in that season (red o).
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Red represents climatology and yellow represents observed local temperature—daily climatology (red line), observed local daily temperature (yellow line), observed seasonal average temperature (yellow dashed), permuted observed local daily temperature (yellow dot) and permuted climatology (red dot). A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead.
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A forecast was deemed accurate if: 1) peak timing was within ±2, ±3, or ±4 weeks of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±20%, ±30% or ±50% of the observed peak infection rate; 3) total infectious mosquitoes were within ±20%, ±30% or ±50% of the observed; and 4) human WNV cases were within ±20%, ±30% or ±50% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection.
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A forecast was deemed accurate if total weekly infectious mosquitoes over a season were within ±25% of the observed.
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger.
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A forecast was deemed accurate if: 1) peak timing was within ±1 week of the observed peak of infectious mosquitoes; 2) peak infection rate was within ±25% of the observed peak infection rate; 3) total infectious mosquitoes were within ±25% of the observed; and 4) human WNV cases were within ±25% or ±1 case of the total number of reported cases, whichever was larger. Note that for all metrics lead week is shown with respect to the week of peak mosquito infection. The size of the dot at each lead week represents the number of forecast generated for that lead week; larger dots indicate more forecasts were generated with a particular predicted lead.
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The boxes and whiskers show the median (red horizontal line), 25th and 75th percentiles (box boundaries), the whiskers mark the highest and lowest values within a multiple of 1.5 of the interquartile range of the box boundaries, and outliers are shown as red (+).
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These data are the daily input for the temperature-forced model. The red dotted line is 14.3°C, which represents the minimum threshold for virus development [
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The uncertainty associated with the proportion of mosquitoes infected becomes sensible when 300 or more mosquitoes are sampled.
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Absolute error was calculated and compared for each prediction of observed peak of infectious mosquitoes, maximum mosquito infection rate, and the total number of human cases over the entire season, whereas root mean squared error (RMSE) was used to calculate future forecasts of the total number of mosquitoes observed over the season. 1 indicates the temperature-forced model forecasts had statistically significantly less error than the baseline model and -1 indicates the baseline model forecasts had statistically significant less error.
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Absolute error was calculated and compared for each prediction of total number of human cases over the next week, 2 weeks, 3 weeks and 4 weeks. 1 indicates the temperature-forced model forecasts had statistically significantly less error than the baseline model and -1 indicates the baseline model forecasts had statistically significant less error.
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Absolute error was calculated and compared for each prediction of observed peak of infectious mosquitoes, maximum mosquito infection rate, and the total number of human cases over the entire season, whereas root mean squared error (RMSE) was used to calculate future forecasts of the total number of mosquitoes observed over the season. 1 indicates the reported daily observed temperature-forced model forecasts had statistically significantly less error than the baseline model and -1 indicates the baseline model forecasts had statistically significant less error.
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Absolute error was calculated and compared for each prediction of observed peak of infectious mosquitoes, maximum mosquito infection rate, and the total number of human cases over the entire season, whereas root mean squared error (RMSE) was used to calculate future forecasts of the total number of mosquitoes observed over the season. 1 indicates the daily observed temperature-forced model forecasts had statistically significantly less error than the daily climatology temperature-forced forecasts and -1 indicates the daily climatology temperature-forced forecasts had statistically significant less error.
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We are grateful to the staff of the Suffolk County Arthropod-Borne Disease Laboratory, the Division of Vector Control, and the New York State Department of Health Arbovirus Laboratory for assistance in mosquito and arboviral surveillance efforts and viral analysis of the mosquito samples; Paul Geery and the staff of the Des Plaines Valley Mosquito Abatement District, the staff of the Northwest Mosquito Abatement District, Shamika Smith and the rest of the staff of the city of Chicago’s arboviral surveillance efforts, Kelly Bemis and the Cook County health department; the staff of the Southern Nevada Health District, especially Heather Anderson-Fintak and Vivek Raman, and Christopher T. Bramley and staff at the Clark County Department of Public Works; the staff of Iberia Parish Mosquito Abatement District; the staff of St. Tammany Parish Mosquito Abatement District; David Fiess, Joshua Blauvelt, and the staff of Vector Control & Environmental Services Fort Wayne-Allen County Department of Health and Taryn Stevens of the Vector-Borne Epidemiology Resource Center Indiana State Department of Health; the staff of Maricopa County Environmental Services Department and assistance from Irene Ruberto and Hayley D. Belisle-Yaglom at the Arizona Department of Health Services; Michael “Doc” Weissmann and the staff at the Colorado Mosquito Control, and Leah Colton at the Colorado Department of Public Health and Environment; and Dr. Jacklyn Wong and Ervic Aquino at the Vector-Borne Disease Section, California Department of Public Health. We are also thankful for the help Jennifer Lehman, Dr. Erin Staples, and the CDC Division of Vector-Borne Infectious Diseases who provided us with weekly human WNV case data. Sasikiran Kandula for discussions on statistical tests. Carla Martin, Dr. Nathaniel DeFelice, and Dr. Richard DeFelice for discussions on WNV case diagnostics and reporting protocols. Dr. Jacqueline MacDonald Gibson for discussions about risk perception.