3.1. Descriptive and ANOVA
Over the 260 weeks (from 2015 to 2019), 372,498 cases of P. falciparum were recorded in Sussundenga, 177,957 from under 5 years (47.5 %) and 194,541 (52.2 %) from 5 years and older (Figure 3). The average weekly cases for the under 5 age group was 680 (Standard deviation (Sd) = 250.1) and 748 (Sd = 320.1) for the 5 and older age group.
Year 2017 had the weeks with highest peaks in cases with 1,263 cases in the under 5 age group at week 9 and 1,797 cases in the 5 and older age group at week 5. The lowest weekly malaria cases were recorded in 2018 with 30 and 19 cases for the under 5 and five and older age groups respectively, both at week 32. On average, the under 5 age group presented the highest number of cases (1,170 sd 34) at week 2 and the fewest cases at week 35 (354 Sd 17.8). In the five and older age group malaria cases were highest at week 2 (1,295 Sd 245) and the lowest cases (341 Sd 193.5) at week 31.
Year 2019 presented the overall highest number of cases for both age groups with 41,887 and 50,326 cases in the under 5 and 5 and older groups, respectively. Year 2018 presented the least cases 27,611 and 30,777 in the under 5 and 5 and older groups, respectively.
Analysis of Variance (ANOVA) indicated a statistically significant difference in malaria incidence between years and weeks, for both categories, P = 0.0001), DF = 204; and Fcal = 38.863 and Fcal = 16.8374, for 0 to 4 and 5 and more years respectively.
For 0 to 4 years old, there was no difference between years 2017 and 2018 and there was difference between the other years (Table 1A). For more than five years old, there was no difference between years 2015, 2016 and 2017 and there was difference between the other years (Table 1B).
Table 1. Malaria cases mean separation between years. A. 0 to 4 years. B. Five and more years.
3.2. Temporal clusters
Figure 4 presents the weekly malaria temporal clusters for age 0 to 4 and 5 and more years old. For 0 to 4 years old, three malaria clusters were identified: cluster 1 of five weeks, from week 31 to 35, where occurs low cases of malaria, in average 394 sd 168.9 per week. The second cluster, from weeks 20 to 47, with moderate number of cases, in average 570 sd 173.2 cases per week. Cluster 3, from week 48 to week 19, with high malaria cases, in average 855 sd 202.4 weekly.
For five and more years old, two temporal clusters were identified: cluster 1, from week 48 to 24, with high malaria cases, in average 846 sd 272.4 weekly cases and, cluster 2, from week 23 to 47, with moderate cases, in average with 516 sd 171.4 cases.
3.3. Malaria incidence spatial variation for 0 to 4 years old category
Figure 5 presents the choropleth maps of spatial distribution of malaria incidence in the last five years and the average cases in 0 to 4 years. The maps present in average a high concentration of malaria incidence in Sussundenga – Sede RHC and low concentration of malaria incidence in RHCs in Rotanda and Dombe. Moha admirative post presents a moderate concentration of malaria incidence. Overall, children 0 to 4 years in Dombe and Rotanda administrative posts presents 0.5 episodes of malaria per year while, residents of Moha administrative post presents around one-episode case of malaria per year and residents of Sussundenga-Sede presents more than one-episode case of malaria per year.
3.4. Malaria incidence spatial variation for older than five years category
Figure 6 presents the malaria spatial incidence variation from 2015 to 2019 in patients from 5 and more years old. The maps indicate a moderate concentration of malaria incidences in Sussundenga – Sede, Rotanda and Moha admirative posts and low concentration of malaria incidence in admirative posts of Dombe. On average patients in this category will experience 0.27 cases of malaria per year. Overall, one in six residents in Dombe, Rotanda and Moha administrative posts will have an episodes of malaria per year while, one in three residents of Sussundenga-Sede will experience an episode case of malaria per year.
3.5. ARIMA modelling (0 to 4 years old)
Figure 7.A presents the trends for the temporal series plot for age 0 to 4 years. There a decreasing tendency of malaria cases in ages 0 to 4 to years old confirmed by Mann-Kendal test, Sen's slope = -0.521. The series presents several peaks and fluctuations, the weekly peaks are separated by more than few weeks suggesting a seasonal pattern.
The Bartlett test indicated normality for the data, Jack Bera = 4.35, P = 0.114, DF = 2 and no transformation was needed. Dick-Fuller test indicated a non-stationarity of the mean Tau = 4.35, P = 0.114, DF = 2 and first-order differencing was applied and a stationary pattern obtained (Figure 7.B).
Figure 7 C and D presents the features of the data for autocorrelation (ACF) and Partial Autocorrelation (PACF) plot. The ACF indicates an exponential decay and PACF with a single spike at lag 1 suggesting an ARMA (2,1) for non-seasonal and ARMA (1,1) for seasonal components.
In eight experimented, the selected final model for malaria patients 0 to 4 years category was ARIMA (2,2,1) (1,1,1) 52 and the trend equation was:
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All the coefficients were statically significant at 0.05. Table 2A presents the goodness of the fit results.
For diagnostic check, the residual ACF and PACF plot (Figure 5 F and G) both indicate that all the terms are within to the confidence intervals implying that the residuals are “White noise”. The Portmanteau test of the residuals also indicated the model adequacy., Portmanteau = 13.35, P = 0.42, DF = 13.
Using equation 1 the malaria cases for 0 to 4 years patients were forecasted for year 2016 (Table 3). Figure 5 E presents the predicted trends and intervals (90 ad 95 %).
3.6. ARIMA modelling (Five and more years old)
Figure 8.A presents the trends for the temporal series plot for five and older years. There is an increasing tendency of malaria cases in five and more years old patients confirmed by Mann-Kendal test, Sen's slope = 0.100. The series presents several peaks and fluctuations, the weekly peaks are separated by more than few weeks suggesting a cyclical pattern.
The Bartlett test indicated normality for the data, Jack Bera = 17.17, P = 0.1011, DF = 2. Dick-Fuller test indicated a non-stationarity of the mean, Tau = -3.96,, P = 0.118, DF = 2, and first-order differencing was applied and a stationary pattern obtained (Figure 8.B).
Figure 8 C and D presents the features of the data for autocorrelation (ACF) and Partial Autocorrelation (PACF) plot. The ACF indicates an exponential decay and PACF with a single spike at lag 1.
In eight experimented, the selected final model for malaria patients with five and more years was ARIMA (2,2,1) (1,1,1) 52 and the trend equation was:
Xt = (715.3047) + (0.2524547)x (Date)
All the coefficients were statically significant at 0.05. Table 2.B, presents the goodness of the fit results for age category five and more years.
For diagnostic check, the residual ACF and PACF plot (Figure 7 F and G) both indicate that all the terms are interior to the confidence limit implying that the residual are “white noise”. The Portmanteau test of the residuals also indicated the model adequacy to lag 16, Portmanteau = 13.29, P = 0.4253, DF = 13.
Using equation 1 the malaria cases for 0 to 4 years patients were forecasted for year 2016 (Table 3). Figure 5 E presents the predicted trends and intervals (90 ad 95 %).