Table 1

Characteristics of malaria forecasting studies included in review (n=29)

Authors (reference)Population and settingModel specificsMalaria outcomeNumber of data points used for training/testingEvaluation measure
Regression forecasting studies
 Adimi et al3Community health post data from 2004 to 2007 for 23 provinces in Afghanistan; clinical confirmation23 linear regressions (1 for each province); included autoregressive, seasonal and trend parametersMonthly cases31/6 (varied between provinces but last 6 months used only for testing)Root mean squared error and absolute difference
 Chatterjee and Sarkar4Municipal data for 2002–2005 for Chennai (city), India; microscopic confirmationLogistic regression; polynominal and autoregressive parametersMonthly slide positivity rate36/195% CI (for predicted value and compared to observed)
 Gomez-Elipe et al5Health service data from 1997 to 2003 for Karuzi Province, Burundi; clinical confirmationLinear regression; adjusted for population, lagged weather covariates, autoregressive and seasonal parametersMonthly incidence60/24; 1 month ahead forecasts95% CI, correlation, p value trend line of difference (between predicted and observed)
 Haghdoost et al6District health centre data from 1994 to 2001 for Kahnooj District, Iran; microscopic confirmationSeparate Poisson regressions for Plasmodium vivax and Plasmodium falciparum; population offset, lagged weather covariates, seasonality and trend parameters10-day cases213/73Average percent error
 Rahman et al7Hospital data from 1992 to 2001 for all divisions of Bangladesh; clinical confirmationFour linear regressions (1 for each administrative division and one for all of Bangladesh); environmental covariate for weeks of highest correlationYearly cases10, 1 year was removed from series at a timeRoot mean squared error and relative bias (observed-predicted)
 Roy et al8Municipal data for Chennai (city) (2002–2004) and Mangalore (city) (2003–2007), India; microscopic confirmationTwo linear regressions (one for each city); adjusted for population, lagged weather covariates, autoregressive term, interaction terms, polynomial termsMonthly SPR (Chennai), monthly cases (Mangalore)28/8 (Chennai), 48/12 (Mangalore); 1 month ahead95% CI
 Teklehaimanot et al9Health facility data from 1990 to 2000 for all districts in Ethiopia; microscopic confirmation10 Poisson regressions (one for each district); lagged weather covariates, autoregressive term, time trend and indicator covariates for week of the yearWeekly cases572 (varied between districts, training and testing); 52 weeks (year) were removed from series at a time; 1–4 week ahead forecastsCompared performance of alerts from predicted versus observed cases (using potentially prevented cases)
 Xiao et al10Medical and health unit data from 1995 to 2007 for Hainan Province, China; microscopic confirmationPoisson regression; lagged weather covariates, autoregressive termMonthly incidence144/12T-test (predictive value significantly different than actual)
 Yacob and Swaroop11Medical data from 1944 to 1996 for all health districts in Punjab; clinical confirmation19 linear regressions (1 for each district); include coefficients of correlation between rainfall and epidemic figures from 1914 to 1943Seasonal epidemic figure*Coefficient of correlation (between actual and predicted epidemic figure)
 Yan et al12Municipal data from 1951 to 2001 for Chongquin (city), ChinaLinear regression; logarithm curveYearly cases50/1Visual inspection of predicted within range of actual values
ARIMA forecasting studies
 Abeku et al13Health clinics data from 1986 to 1999 for 20 areas in Ethiopia; mixture of microscopic and clinical confirmed20 models (1 for each area) compared approaches: Overall average, seasonal average, seasonal adjustment, ARIMAMonthly cases168/12 (varied between areas but last 12 months only used for testing); 1–12 month ahead forecastsAverage forecast error
 Briët et al14Health facility data from 1972 to 2005 for all districts in Sri Lanka; microscopic confirmation25 models (1 for each district) compared approaches: Holt-Winters, ARIMA (seasonality assessed with fixed effects or harmonics) and SARIMA; lagged weather covariatesMonthly cases of malaria slide positives180/204 (varied between districts but approximately 50% of series reserved for testing); 1–4 month ahead forecastsMean absolute relative error
 Liu et al15Data from 2004 to 2010 for ChinaSARIMAMonthly incidence72/12Visual (plot of predicted vs observed)
 Wangdi et al16Health centre data from 1994 to 2008 for seven districts in Bhutan; microscopic and antigen confirmationSeven models (one for each district): SARIMA and ARIMAX; lagged weather covariatesMonthly cases144/24Mean average percent error
 Wen et al17Data from 1991 to 2002 for Wanning County, ChinaSARIMAMonthly incidence252/1295% CI
 Zhang et al18CDC data from 1959 to 1979 for Jinan (city) China; clinical confirmationSARIMA; lagged weather covariatesMonthly cases84/120 (removed 1967 and 1968 from series)Visual (plot of predicted vs observed)
 Zhou et al19Data from 1996 to 2007 for Huaiyuan County, China; microscopic and clinical confirmationSARIMAMonthly incidence108/12Average error
 Zhu et al20Data from 1998 to 2007 for Huaiyuan and Tongbai counties, ChinaSARIMAMonthly incidence rates84/24; 1–12 month ahead forecasts95% CI and error
Mathematical forecasting studies
 Gaudart et al21Data from cohort of children from 1996 to 2000 in Bancoumana (municipality), Mali from 1996 to 2006; microscopic confirmationVSEIRS modelMonthly incidence rate60 (training and testing); 15 day, 1 month, 2 month, seasonal forecastsMean absolute percentage error and root mean squared error
 Laneri et al22Health centre data (passive and active surveillance) for Kutch (1987–2007) and Balmer (1985–2005) Districts, India; microscopic confirmation2 models (one for each district); compared two types of VSEIRS model to linear and negative binominal regressionsMonthly incidence for parameter estimation; seasonal totals (Sept−Dec) for epidemic forecasting240 (training and testing); 1 to 4 months ahead forecastsWeighted mean square error and prediction likelihood
Neural network forecast studies
 Cunha et al23Ministry of Health data from 2003 to 2009 for Cornwall (City), Brazil; microscopic confirmationCompared neural network to linear regressionMonthly cases72/12; 3, 6 and 12 months forecastsAbsolute error and mean square error
 Gao et al24Data from 1994 to 1999 for Honghe State, ChinaNeural networkMonthly incidence48/12Percent error
 Kiang et al25Hospital and clinic data from 1994 to 2001 for 19 provinces, Thailand; microscopic confirmation19 neural networks (1 for each province); various architectures used (varied by province)Monthly incidence84/12Root mean square error
Other forecasting methods
 Fang et al26Data from 1956 to 1988 for Xuzhou (City), ChinaGrey and Grey Verhulst models (1,1)Yearly incidence30/2Percent error
 Gao et al27Data from 1998 to 2005 for Longgang District, ChinaGrey model (1,1)Yearly incidence6/1Error and percent error
 Guo et al28Data from 1988 to 2010 ChinaGrey model (1,1)Yearly incidence21/2Visual (plot of predicted vs observed)
 Gill29Medical data from 1925 to 1926 for health districts in Punjab; clinical confirmation29 forecasts consisting of visual inspection of rainfall, spleen rates and epidemic potential†Seasonal epidemic (yes/no)Qualitative comparison of prediction (presence of epidemic) to epidemic figure
 Medina et al30Community health centre data from 1996 to 2004 (14 centres) for Niono District, Mali; clinical confirmationMultiplicative Holt-Winters model, age-specific rates (three age groups); compared to seasonal adjustment methodMonthly malaria consultation rates36/72; 2 and 3-month ahead forecasts; one step ahead forecastsMean absolute percentage error and 95% CI
 Xu and Jin31Data from 2000 to 2005 for Jiangsu Province, ChinaGrey modelYearly cases4/1Visual (plot of predicted vs observed number of cases)
  • *Seasonal epidemic figure is the ratio of October incidence to mean spring incidence.

  • †Epidemic potential is the coefficient of variability of fevers during the month of October for the periods of 1868–1921.

  • ARIMA, auto-regressive integrated moving average; ARIMAX, auto-regressive integrated moving average with exogenous input; SARIMA, seasonal auto-regressive integrated moving average; SPR, slide positivity rate; VSEIRS, vector-susceptible-exposed-infected-recovered-susceptible model.