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Malaria is considered endemic in over hundred countries across the globe. Many cases of malaria and deaths due to malaria occur in Sub-Saharan Africa. The disease is of great public health concern since it affects people of all age groups more especially pregnant women and children because of their vulnerability. This study sought to use vector autoregression (VAR) models to model the impact of climatic variability on malaria. Monthly climatic data (rainfall, maximum temperature, and relative humidity) from 2010 to 2015 were obtained from the Ghana Meteorological Agency while data on malaria for the same period were obtained from the Ghana Health Service. Results of the Granger and instantaneous causality tests led to a conclusion that malaria is influenced by all three climatic variables. The impulse response analyses indicated that the highest positive effect of maximum temperature, relative humidity, and rainfall on malaria is observed in the months of September, March, and October, respectively. The decomposition of forecast variance indicates varying degree of malaria dependence on the climatic variables, with as high as 12.65% of the variability in the trend of malaria which has been explained by past innovations in maximum temperature alone. This is quite significant and therefore, policy-makers should not ignore temperature when formulating policies to address malaria.

Malaria is considered endemic in over hundred countries across the globe and many cases of malaria and deaths due to malaria occur in Sub-Saharan Africa. The disease is of great public health concern since it affects people of all age groups more especially pregnant women and children because of their vulnerability [

Malaria is not only the burden of the health sector in various countries, but it also permeates every aspect of the social as well as economic lives of their people [

Adu-Prah and Tetteh [

Studies have been carried out that link climatic variability and incidence of malaria. For instance, Sena et al. [

Meanwhile, the results from a study by Asare and Amekudzi [

Within Ghana, there are variations in climatic conditions during any one season or period since the northern part is mostly savannah, the middle belt tropical forest, and the coastal area savannah. These differences will have direct links to mosquito habitats and therefore the transmission of malaria. Therefore, a knowledge of climatic variability and its influence on the incidence of malaria can be used to predict malaria occurrences and hence provide early warning system information to health administrators and decision- and policy-makers for the control of the disease. In relation to modelling malaria and climatic variability, the use of multivariate models, especially, vector autoregression models, is however limited. Little has been done in the area of developing multivariate models that combines climatic variability to predict the seasonal prevalence of malaria cases in the country and inform the development of warning systems. Most studies used univariate methods in predicting malaria incidence. This study will develop a multivariate model in the form:

The objective of this study is to model the trends of climatic variability and malaria in Ghana using vector autoregression.

The study area used in this study is Kumasi Metropolitan Area in Ashanti Region in Ghana. The Kumasi Metropolitan Area (Figure

Map of Kumasi Metropolitan Area.

The study area falls within tropical forest zone in Ghana and is dominated by the maritime air from the south and this results in two rainy seasons throughout the year. The first begins in April and ends in July whereas the second begins in September and ends in November. These two rainy seasons are both followed by the dry season.

The quantitative data consisted basically of secondary data from the Ghana Meteorological Agency and Health Service. The meteorological variables (2010-2015) include rainfall, maximum temperature, and relative humidity and were on mean monthly basis. The malaria data were also obtained based on monthly cases for the years 2010-2015 in the Kumasi Metropolitan Area.

Vector autoregression (VAR) model developed by Sims [

The basic form of the VAR model of order p suggested by Sims [

For this study,

The parameters in the model are estimated by generalised least squares.

The Augmented Dickey Fuller (ADF) test is a unit root test for stationarity. The null hypothesis for the ADF test is that there is a unit root while the alternative hypothesis differs slightly according to the equation used. The simplest alternative hypothesis is that the time series is stationary. Unit roots can cause unpredictable results in time series analysis.

For a range of lag orders

Despite the fact that VAR coefficients capture the anticipated impact of a variable, there are often a lot of coefficients to interpret. It is usually more common to examine the model’s residuals which represent unforeseen contemporaneous events. The next subsections provide relatively nontechnical explanations of some of the common techniques used for structural analysis of VAR models.

Both the Granger-causality and instantaneous causality were investigated. For both tests, the vector of endogenous variables is divided into two subvectors,

Instantaneous causality is characterized by nonzero correlation of

In impulse response analysis, the exogenous and deterministic variables are treated as fixed and may therefore be dropped from the system. The adjusted endogenous variables are now denoted by

Denoting the

The accuracy of forecasts generated by the fitted model was evaluated using mean absolute percentage error (MAPE) values.

The data for this study comprises time series of monthly cases of malaria for the study area and some climatic variables including rainfall (Rain), maximum temperature (Tmax), and relative humidity (RH). The climatic data were obtained from the Ghana Meteorological Agency for January 2010 to December 2015 while the malaria data were obtained from the Ghana Health Service, also for January 2010 to December 2015. Table

Descriptive statistics.

Minimum | 1st quartile | Median | Mean | 3rd quartile | Maximum | |
---|---|---|---|---|---|---|

Malaria | 36047 | 55284 | 66803 | 65318 | 73325 | 87765 |

Tmax | 27.40 | 30.07 | 31.85 | 31.62 | 33.23 | 36.00 |

RH | 53.00 | 73.00 | 78.50 | 76.62 | 83.00 | 98.00 |

Rain | 0.00 | 60.27 | 103.75 | 115.26 | 166.38 | 379.80 |

Time series plot of malaria and the climatic variables.

Time series plot of the first difference of malaria and climatic variables.

Each variable in the differenced data was tested for the presence of a unit root using a test suggested by Dickey and Fuller [

Augmented Dickey Fuller (ADF) unit root test for malaria and maximum temperature

Malaria | Tmax | |||||
---|---|---|---|---|---|---|

tau3 | phi2 | phi3 | tau3 | phi2 | phi3 | |

Test-statistic | -3.5848 | 4.4182 | 6.5665 | -3.7926 | 5.0994 | 7.3618 |

1pct | -4.04 | 6.50 | 8.73 | -4.04 | 6.50 | 8.73 |

5pct | -3.45 | 4.88 | 6.49 | -3.45 | 4.88 | 6.49 |

10pct | -3.15 | 4.16 | 5.47 | -3.15 | 4.16 | 5.47 |

Augmented Dickey Fuller (ADF) unit root test for relative humidity and rainfall

RH | Rain | |||||
---|---|---|---|---|---|---|

tau3 | phi2 | phi3 | tau3 | phi2 | phi3 | |

Test-statistic | -3.6268 | 4.5966 | 6.8736 | -4.341 | 6.2939 | 9.4236 |

1pct | -4.04 | 6.50 | 8.73 | -4.04 | 6.50 | 8.73 |

5pct | -3.45 | 4.88 | 6.49 | -3.45 | 4.88 | 6.49 |

10pct | -3.15 | 4.16 | 5.47 | -3.15 | 4.16 | 5.47 |

A VAR model of the monthly malaria and climatic variables was estimated with 12 lags for each variable in each equation. Each equation has 4x12 unrestricted coefficients plus one coefficient for a constant and one for a trend. The number of lags was chosen based on four tests: the Final Prediction Error (FPE) test [

Optimal lag length selection.

Lag | AIC | HQ | SC | FPE |
---|---|---|---|---|

1 | 3.222141e+01 | 3.255130e+01 | 3.306651e+01 | 9.881112e+13 |

2 | 3.172640e+01 | 3.227623e+01 | 3.313490e+01 | 6.086123e+13 |

3 | 3.162184e+01 | 3.239159e+01 | 3.359374e+01 | 5.613160e+13 |

4 | 3.092405e+01 | 3.191372e+01 | 3.345935e+01 | 2.917406e+13 |

5 | 3.052771e+01 | 3.173732e+01 | 3.362641e+01 | 2.106825e+13 |

6 | 3.008062e+01 | 3.151015e+01 | 3.374272e+01 | 1.501048e+13 |

7 | 2.988180e+01 | 3.153126e+01 | 3.410730e+01 | 1.441608e+13 |

8 | 2.973971e+01 | 3.160911e+01 | 3.452861e+01 | 1.569618e+13 |

9 | 2.981110e+01 | 3.190042e+01 | 3.516340e+01 | 2.329626e+13 |

10 | 2.893095e+01 | 3.124020e+01 | 3.484665e+01 | 1.537346e+13 |

11 | 2.725518e+01 | 2.978436e+01 | 3.373428e+01 | 5.713970e+12 |

12 | 2.544600e+01 | 2.819510e+01 | 3.248850e+01 | 2.750571e+12 |

The instantaneous and Granger-causality tests [

Granger causality tests.

Cause variable | Null hypothesis | F-value | p-value | Decision |
---|---|---|---|---|

RH | RH does not Granger-cause Malaria | 2.2201 | 0.009492 | Reject the null hypothesis |

Rain | Rain does not Granger-cause Malaria | 2.1121 | 0.01381 | Reject the null hypothesis |

Tmax | Tmax does not Granger-cause Malaria | 4.9524 | 2.747e-06 | Reject the null hypothesis |

Instantaneous causality tests.

Cause variable | Null hypothesis | Chi-squared-value | p-value | Decision |
---|---|---|---|---|

RH | No instantaneous causality between RH and Malaria | 20.872 | 0.0001119 | Reject the null hypothesis |

Rain | No instantaneous causality between Rain and Malaria | 20.374 | 0.000142 | Reject the null hypothesis |

Tmax | No instantaneous causality between Tmax and Malaria | 21.795 | 7.198e-05 | Reject the null hypothesis |

Both tests indicate that malaria is influenced by all three climatic variables (relative humidity, rainfall, and maximum temperature). An important caveat about the above F-Tests must be noted. Although they indicate whether other variables Granger-cause malaria, it is still possible that other variables can influence malaria through other equations in the system. For this reason, we turn to the decomposition of the variances of forecast errors.

Forecast error variance decomposition (FEVD) is popular in interpreting VAR models. Results for the FEVD for both malaria and the climatic variables are presented in Figure

Forecast error variance decomposition.

Impulse response analysis was utilized to analyze the dynamic interactions between malaria and the climatic variables of the VAR (12) process. The orthogonal impulse response of malaria to the climatic variables is presented in Figure

Impulse response analysis.

The VAR (12) model developed can be used as a predictive model for making forecasts of future malaria cases. The forecasts for the differenced malaria cases for the first half of 2016 are presented in Figure

Malaria forecast for the first half of 2016.

Month | Forecast | Lower | Upper | CI |
---|---|---|---|---|

Jan | 55450.59 | 36772.56 | 74128.62 | 18678.03 |

Feb | 58612.25 | 37218.14 | 80006.35 | 21394.10 |

Mar | 60632.76 | 38454.46 | 82811.05 | 22178.30 |

Apr | 61812.94 | 39302.72 | 84323.15 | 22510.21 |

May | 62505.33 | 39750.81 | 85259.85 | 22754.52 |

Jun | 62937.90 | 39946.85 | 85928.94 | 22991.05 |

Forecast series of malaria.

The mean absolute percentage error (MAPE) provides an indication of the average size of forecasting error expressed as a percentage of the relevant observed value irrespective of whether that forecasting error is positive or negative [

In this study, it was discovered that all three climatic variables influence malaria in the Kumasi Metropolitan Area. The highest positive effect of maximum temperature on malaria is in September, whereas the lowest negative effect is in March. Also, the highest positive effect of relative humidity on malaria is observed in March while the highest positive effect of rainfall on malaria is observed in October.

Further results indicate that on the average, while a greater percentage of the variability in the trend of malaria has been explained by past innovations in malaria cases, a significant proportion (about 12.65%) of the variability in the trend of malaria has been explained by past innovations in maximum temperature. Also, about 11.10% of the variability in the trend of malaria has been explained by past innovations in rainfall figures and only 2.58% of the variability in the trend of malaria has been explained by past innovations in relative humidity. This further indicates that the three climatic variables have varying effect on malaria with maximum temperature having a greater effect, followed by rainfall and then relative humidity. Therefore, modelling malaria and the climatic variables together will improve the forecast of malaria. These results are in line with studies conducted by Darkoh et al. [

One limitation of this study is the nonavailability of data over a longer period of time. For time series models, the rule of thumb is that one should have at least fifty (50) to sixty (60) data points but preferably more than hundred (100) observations [

This paper develops and estimates a vector autoregression (VAR) model of the monthly malaria cases and some important climatic variables including rainfall, maximum temperature, and relative humidity in the Kumasi Metropolitan Area. The model is used to investigate the dynamic linkages between malaria and climatic variability. The model is also used to simulate the responses of malaria to innovations in climatic variability.

Results of the Granger and instantaneous causality tests lead to a conclusion that malaria is influenced by all three climatic variables. The impulse response analyses indicate that the highest positive effect of maximum temperature, relative humidity, and rainfall on malaria is observed in the ninth, third, and tenth months, respectively. The decomposition of forecast variance indicates varying degree of malaria dependence on the climatic variables, with as high as 12.65% of the variability in the trend of malaria being explained by past innovations in maximum temperature alone. Results obtained from this study are useful for policy-makers as this will help come up with policies knowing the effects of climatic variability on malaria incidence in the Kumasi Metropolitan Area.

The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; and in the decision to publish the results.

The authors declare no conflicts of interest.

Sylvia Ankamah conducted the work as part of her postmasters’ research under the CIRCLE programme. Kaku S. Nokoe was her mentor for the postmaster’s research and Wahab A. Iddrisu helped in the analysis stage of the research work.

This work is supported by funding from the Department for International Development (DfID) under the Climate Impact Research Capacity and Leadership Enhancement (CIRCLE) programme. Additionally, the authors are thankful to the Ghana Meteorological Agency and Health Directorate for providing the data.