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This study investigated the effects of climatic variables, particularly, rainfall and temperature, on malaria incidence using time series analysis. Our preliminary analysis revealed that malaria incidence in the study area decreased at about 0.35% annually. Also, the month of November recorded approximately 21% more malaria cases than the other months while September had a decreased effect of about 14%. The forecast model developed for this investigation indicated that mean minimum (

Malaria transmission predominantly occurs in tropical and subtropical areas where

Generally, environmental factors have contributed significantly to malaria prevalence and thereby affected its distribution, seasonality, and transmission intensity [

Several studies have attempted to predict epidemics by use of climatic variables that are predictors of malaria transmission potential. In spite of this, little consensus has emerged about the relative importance and predictive value of different factors [

According to Christiansen-Jucht et al. [

Knowledge of the dynamic structure underlying data collected at regular time intervals (i.e., time series data) can be useful in generating forecasts through modeling. This can be achieved either by self-projecting or cause-effect modeling techniques [

The study was carried out at Asankrangwa Catholic Hospital in the Amenfi West District of the Western Region, Ghana (Figure

Map of Ghana showing study area in Amenfi West District.

Monthly data of confirmed malaria cases as well as rainfall and temperature from 2002 to 2015 were obtained from the district hospital and the meteorological office, respectively. Until 2010, detection of malaria parasites in the study area during the period under consideration was done microscopically on stained thick and thin blood smears. However, for the remainder of the period, detection of malaria in the health facility was done using both Rapid Diagnostic Tests (RDT) and microscopy.

A preliminary analysis was first conducted on the dataset to describe and investigate the nature of the trend characterizing the number of malaria cases in the district. In order to determine the trend, linear, quadratic, log-linear, and log-quadratic regression models were fitted and compared. Afterwards, monthly changes in the number of malaria cases were estimated using the selected time trend and a set of seasonal dummy variables (i.e., seasonal categories based on months). The intercept was not included in the model to avoid dummy variable trap. To show differential effects in terms of percentage change, Halvorsen and Palmquist [

In this study, an autoregressive integrated moving average (ARIMA) approach popularly referred to as Box-Jenkins methodology was employed for modeling malaria incidence. The model takes into account past values of the data, prediction errors, and a random term [

Diagnostic tests on the developed models were done using Ljung-Box and ARCH-LM tests. The Ljung-Box test was performed to determine whether model residuals were random and independent over time (i.e., no serial correlation) while the ARCH-LM test was employed to check for homoscedasticity of model residuals (i.e., if variances are constant over time). In order to evaluate the performance of the final model, measures of forecast error such as Mean Percent Error (MPE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percent Error (MAPE), and Mean Absolute Scaled Error (MASE) were computed. For each forecast error estimated lower values are preferred. Mathematical details of the aforementioned statistics and how they are computed are provided elsewhere [

Descriptive statistics of malaria incidence/cases, rainfall, and temperature (minimum, maximum, and average) recorded for the study area are presented in Table

Descriptive statistics of study variables.

Variable | Mean | Minimum | Maximum | CV (%) |
---|---|---|---|---|

Malaria incidence | 809.800 | 192.000 | 2112.000 | 45.730 |

Rainfall | 60.820 | 0.000 | 1022.200 | 181.640 |

Min. temperature | 25.455 | 20.900 | 31.000 | 5.950 |

Max. temperature | 29.549 | 25.500 | 32.900 | 5.660 |

Avg. temperature | 27.507 | 23.500 | 31.000 | 5.090 |

Min. = minimum, max. = maximum, and avg. = average.

Time series plots of data (malaria, rainfall, and temperature) gathered for the research are shown in Figures

Time series plot—malaria cases showing the LLIN intervention in May 2010 (a) and rainfall data (b).

Time series plot of temperature ((a) min.; (b) max.; and (c) avg.).

Figure

Plot of preintervention forecast compared to observed malaria cases.

An investigation of the nature of the trend characterizing malaria incidence was subsequently performed and the results are presented in Table

Trend analysis of malaria incidence.

Model | AIC | AICC | BIC |
---|---|---|---|

Linear | 1967.043 | 2445.953 | 2455.178 |

Quadratic | 1981.416 | 2460.326 | 2469.551 |

Log-linear | −287.694 | 191.215 | 200.441 |

Log-quadratic | −286.082 | 192.827 | 202.053 |

Estimates of log first differenced series with monthly effects.

Variable | Coefficient | Standard error | Percent effect |
---|---|---|---|

January | 0.04697 | 0.10828 | 4.80884 |

February | 0.11713 | 0.10439 | 12.42660 |

March | −0.00834 | 0.10437 | −0.83026 |

April | −0.13063 | 0.10435 | −12.24537 |

May | 0.08189 | 0.10435 | 8.53359 |

June | 0.00370 | 0.10434 | 0.37096 |

July | −0.00751 | 0.10434 | −0.74837 |

August | −0.08839 | 0.10434 | −8.45940 |

September | −0.14806 | 0.10435 | −13.76162 |

October | 0.02261 | 0.10435 | 2.28687 |

November | 0.18997 | 0.10437 | 20.92168 |

December | −0.13216 | 0.10439 | −12.37984 |

Trend | −0.00351 | 0.00754 | −0.35082 |

Following the time series analysis procedure outlined in the previous section, an ARIMA

Parameter estimates of the developed model.

Parameter | Estimate | Std. error | | |
---|---|---|---|---|

ar1 ( | 0.41283 | 0.15768 | 2.61820 | 0.00884 |

ma1 ( | −0.85977 | 0.11499 | −7.47670 | 0.00000 |

Max. temperature | 0.07599 | 0.02579 | 2.94650 | 0.00321 |

Min. temperature | −0.06653 | 0.02843 | −2.34010 | 0.01928 |

Estimated forecast errors for the developed model.

Variable | ME | MSE | MAPE | RMSE | MAE | Theil’s |
---|---|---|---|---|---|---|

Training set | 0.00966 | 0.09953 | 3.48070 | 0.31548 | 0.22677 | 0.90767 |

Test set | −0.08955 | 0.35334 | 8.09080 | 0.59442 | 0.50688 | 0.91227 |

Plot of in-sample forecasts compared to training set data.

Plot of out-of-sample forecasts compared to the test set.

The results indicate that all forecast error values estimated were low and that the model was accurate since MAPE values for both training and test sets were less than 10%. Subsequently, the model was diagnosed using the statistics provided in Table

Diagnostic tests on model residuals.

Method | df | Chi-square | |
---|---|---|---|

Ljung-Box test | 24 | 18.46500 | 0.77990 |

ARCH-LM test | 24 | 34.45800 | 0.07685 |

A forecast plot generated by the model from 2016 to 2020 is shown in Figure

Forecast of malaria Incidence (i.e., based on back-transformed output) with 80% and 95% prediction intervals (PI).

According to Jaffar et al. [

Furthermore, the findings of this study which are consistent with others (e.g., [

Some studies have reported the importance of temperature in malaria transmission or prediction models [

A number of studies have documented some potential predictors of malaria such as population growth [

The findings of this study present a clear association of temperature and malaria incidence and how malaria cases are likely to reduce in the future based on our forecast model. We, however, cannot ignore the fact that other contributory factors may modulate malaria prevalence in the study district. Hence, it is recommended that future works on malaria incidence in the district should incorporate population size, intervention strategies, and vegetation (NDVI) among others to help improve its predictive accuracy. Also, various ongoing interventions such as sleeping in insecticide treated nets (i.e., LLINs), proper drainage systems, and sanitation practices should be continued/encouraged to help curb the disease.

The authors declare that there are no competing interests.

The authors would like to extend their heartiest appreciation to Asankrangwa Catholic Hospital for providing data on malaria infection and to the Western Regional Meteorological Agency of Ghana for giving them data on weather variables for the study.