1 Introduction

Diarrhea diseases represent a major public health challenge worldwide. Despite the efforts made by various countries to combat this pandemic, it remains a problem for many countries, especially those in the developing world. Worldwide, diarrhea disease is the second leading cause of death in children under 5 [1]. Diarrhea-related child deaths are largely preventable. Unfortunately, diarrhea remains a major and poorly understood problem due to the complex interaction between environmental, dietary, water and health factors, combined with poverty and lack of resources (regrettably, the burden of diarrhea remains high and ill-defined due to the interaction). According to UNICEF, some eighty-eight percent of all diarrhea infections worldwide are due to unsafe water supplies, lack of hygienic practices and rudimentary sanitation. Yet, worldwide, 15% of the population still defecates in the open air [2]. Despite the recommendations made by the UN through the Millennium Development Goals (MDGs) and the progress achieved, the targets have not been fully met in urban and rural areas in developing countries. And yet, among the MDG targets, access to drinking water and sanitation is a fundamental right that is decisive for human life, health and dignity[3]. In fact, unsafe water, poor sanitation and poor hygiene habits are the main routes of transmission of faeco-oral diseases, of which diarrhea is considered one of the major public health problems in developing countries. Today, 663 million people have no access to drinking water, and 2.4 billion of the world’s population lack basic sanitation [4]. Drinking water and sanitation are two inter-active factors in the improvement of living conditions and the fight against many communicable diseases. Although easy to prevent, water and sanitation-related diseases remain one of the most serious child health problems worldwide [5]. Indeed, an unsanitary environment is a source of health risks. In sub-Saharan Africa, childhood diarrhoea is a public health problem, due to the proliferation of enteropathogenic germs. The transmission of these germs is favored not only by physical environmental conditions, but also and above all by non-compliance with hygiene measures, the inadequacy or malfunctioning of sanitary infrastructures and community facilities for the evacuation and treatment of wastewater, the insufficient supply of drinking water to households, etc. [6]. Among the main infectious diseases affecting Third World populations, diarrhea diseases occupy an important place. They mainly affect young children, and are one of the main causes of morbidity and mortality [6]. Most studies carried out in sub-Saharan Africa on diarrhea diseases in children have focused on children under five [7]. Every year, 1.8 million people, 90% of them children under five, mostly living in developing countries, die from diarrhea diseases (including cholera), and 88% of this morbidity is attributable to poor water quality, inadequate sanitation and poor hygiene [8] [9]. Diarrhea alone is responsible for 5,000 infant deaths a day worldwide, and children in developing countries suffer five to six episodes of diarrhea a year [9]. In Cameroon, a 2004 study by Banza-Nsungu on the determinants of diarrhea morbidity in children in the city of Yaoundé showed that this morbidity is determined more by parental hygiene behaviour and household standard of living than by elements of the physical environment, whatever the area of residence. Given their vulnerability, children, especially the very young, are highly exposed to the risk of diarrhea contamination. This justifies the interest of our study, which focuses on the explanatory factors of diarrhea morbidity in children under five in selected African countries. In the socio-pathogenic complex of most African countries, the situation of water (its quality) and sanitation, as well as hygiene practices, are, directly or indirectly, the primary cause of diarrhea transmission. To understand the spread of the disease as part of a pathogenic system, it is essential to establish a link between water, sanitation, hygiene practices and public health by analyzing the dynamics of a pathology such as diarrhea in urban and rural areas, taking all these variables into account as a whole [10]. Thus, based on the generally accepted idea that diarrhea morbidity is strongly determined by the quality of environmental hygiene, the question posed is whether the development of this pathology results from failures in drinking water supply and sanitation systems, or from the conjunction (combination) of several factors.

2 Principal Component Analysis

2.1 lines of code and graphs of Principal Component Analysis

2.1.1 Importing data

RTI_Data = read.csv(file = "ACP.csv", header = TRUE, sep = ";", quote = "\"",
                   dec = ",", row.names = 1)
RTI_Data[,1:13]
##                   TEU      TER      TAU      TAR      DEF Rotavirus Pover
## Benin        74.07068 60.77379 74.07068  9.63187 48.50221        76 12.72
## BurkinaFaso  80.85615 34.83605 80.85615 16.61428 33.55375        91 25.28
## Cameroun     81.62940 52.46118 58.18216 21.68085  4.25046        65 22.99
## Centrafrique 48.06423 27.37297 24.54589  7.73507 25.04464        58 65.67
## Cotedivoire  86.15835 58.04740 50.68393 21.69757 21.20376        79  9.73
## Gambie       90.88665 76.39057 61.11410 24.04950  0.06543        96 17.24
## Guinee       92.03279 59.01351 47.03491 21.74426  7.14571        72 13.82
## GuineeBissau 73.07241 52.51840 42.09296 16.16611  8.43078        68 25.96
## Mali         94.70028 74.44696 60.15749 41.92364  4.54229        70 20.84
## Mauritanie   94.58891 55.64086 79.32800 25.01106 26.86689        53  5.35
## Niger        88.25951 40.89417 52.82365  9.00733 64.98919        85 50.61
## Senegal      95.87272 76.97232 70.17145 50.55498  7.70624        84  9.92
## Sierraleone  79.79752 54.05841 34.51521 13.87033 16.42946        75 26.06
## Togo         86.98156 58.46670 32.11767  9.07869 39.47328        80 26.59
##                 ALPHA      HYG   URBA  MORT SOINS      ALIM
## Benin        47.10000 12.13046 49.534  53.6 1.953 10.002389
## BurkinaFaso  34.49000  9.15637 31.877  65.6 1.466 16.289089
## Cameroun     78.23000 36.71183 58.733  35.1 1.347  6.250315
## Centrafrique 37.49000 22.17641 43.120 119.1 0.209 49.476339
## Cotedivoire  89.89342 21.81496 52.661  32.6 1.751 35.247209
## Gambie       58.67000 12.94233 63.852  33.1 1.019  7.642408
## Guinee       45.33000 20.63610 37.668  57.9 0.214  4.873141
## GuineeBissau 53.90000 19.68909 45.041  57.6 2.080 38.821364
## Mali         30.76141 17.30087 45.437  62.9 1.948 13.301896
## Mauritanie   66.96000 41.75241 56.923  25.4 2.361 38.510298
## Niger        38.10000 24.61681 16.894 100.0 0.234 12.782480
## Senegal      57.67000 22.24601 49.086  32.0 1.264 15.932422
## Sierraleone  48.64000 17.83658 43.831  61.1 0.425  5.925322
## Togo         66.53708 17.33833 43.921  58.3 0.825 17.351413

2.1.2 Correlation matrix

MATRICE_COR = cor(RTI_Data)

###Application of Principal Component Analysis

library(FactoMineR)
PCA_G7 = PCA(X = RTI_Data, scale.unit = TRUE, ncp = 13, ind.sup = NULL, 
                 quanti.sup = NULL, quali.sup = NULL, row.w = NULL, 
                 col.w = NULL, graph = TRUE, axes = c(1,2))

Rep_PCA = PCA(RTI_Data[1:13])

summary(Rep_PCA)
## 
## Call:
## PCA(X = RTI_Data[1:13]) 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6   Dim.7
## Variance               5.359   2.626   1.437   1.113   1.035   0.509   0.383
## % of var.             41.224  20.198  11.050   8.561   7.960   3.918   2.945
## Cumulative % of var.  41.224  61.423  72.473  81.034  88.995  92.913  95.859
##                        Dim.8   Dim.9  Dim.10  Dim.11  Dim.12  Dim.13
## Variance               0.259   0.133   0.107   0.026   0.014   0.000
## % of var.              1.993   1.019   0.822   0.199   0.105   0.003
## Cumulative % of var.  97.851  98.870  99.693  99.891  99.997 100.000
## 
## Individuals (the 10 first)
##                  Dist    Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3
## Benin        |  2.878 |  0.138  0.025  0.002 | -0.766  1.597  0.071 |  1.582
## BurkinaFaso  |  3.481 | -1.220  1.985  0.123 | -1.998 10.862  0.330 |  1.805
## Cameroun     |  3.207 |  1.494  2.976  0.217 |  1.802  8.831  0.316 | -0.526
## Centrafrique |  6.299 | -5.482 40.052  0.757 |  2.507 17.093  0.158 | -1.181
## Cotedivoire  |  2.978 |  1.608  3.446  0.292 |  1.302  4.611  0.191 |  0.108
## Gambie       |  3.580 |  2.285  6.958  0.407 | -1.555  6.575  0.189 | -1.524
## Guinee       |  2.382 |  0.052  0.004  0.000 | -1.082  3.187  0.206 | -1.094
## GuineeBissau |  2.397 | -0.453  0.274  0.036 |  1.564  6.656  0.426 | -0.183
## Mali         |  3.227 |  1.533  3.132  0.226 | -0.932  2.360  0.083 | -0.365
## Mauritanie   |  4.629 |  2.528  8.518  0.298 |  3.009 24.631  0.423 |  2.110
##                 ctr   cos2  
## Benin        12.439  0.302 |
## BurkinaFaso  16.196  0.269 |
## Cameroun      1.376  0.027 |
## Centrafrique  6.938  0.035 |
## Cotedivoire   0.058  0.001 |
## Gambie       11.545  0.181 |
## Guinee        5.954  0.211 |
## GuineeBissau  0.166  0.006 |
## Mali          0.663  0.013 |
## Mauritanie   22.133  0.208 |
## 
## Variables (the 10 first)
##                 Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3    ctr
## TEU          |  0.729  9.907  0.531 | -0.403  6.183  0.162 |  0.145  1.454
## TER          |  0.827 12.755  0.684 | -0.277  2.913  0.076 | -0.282  5.538
## TAU          |  0.576  6.191  0.332 | -0.221  1.864  0.049 |  0.666 30.866
## TAR          |  0.721  9.689  0.519 | -0.120  0.552  0.015 | -0.150  1.569
## DEF          | -0.543  5.511  0.295 | -0.185  1.301  0.034 |  0.673 31.507
## Rotavirus    |  0.105  0.204  0.011 | -0.836 26.613  0.699 | -0.035  0.086
## Pover        | -0.918 15.708  0.842 |  0.067  0.170  0.004 | -0.152  1.616
## ALPHA        |  0.522  5.080  0.272 |  0.481  8.824  0.232 | -0.077  0.410
## HYG          |  0.207  0.796  0.043 |  0.698 18.529  0.487 |  0.168  1.955
## URBA         |  0.685  8.752  0.469 |  0.452  7.784  0.204 | -0.308  6.623
##                cos2  
## TEU           0.021 |
## TER           0.080 |
## TAU           0.443 |
## TAR           0.023 |
## DEF           0.453 |
## Rotavirus     0.001 |
## Pover         0.023 |
## ALPHA         0.006 |
## HYG           0.028 |
## URBA          0.095 |
PCA_G7$eig
##           eigenvalue percentage of variance cumulative percentage of variance
## comp 1  5.3591760470           41.224431130                          41.22443
## comp 2  2.6258020751           20.198477501                          61.42291
## comp 3  1.4365631398           11.050485691                          72.47339
## comp 4  1.1129099549            8.560845807                          81.03424
## comp 5  1.0348572328            7.960440252                          88.99468
## comp 6  0.5093944782            3.918419063                          92.91310
## comp 7  0.3829052865            2.945425281                          95.85852
## comp 8  0.2590377103            1.992597772                          97.85112
## comp 9  0.1325013965            1.019241511                          98.87036
## comp 10 0.1068784489            0.822141914                          99.69251
## comp 11 0.0258290245            0.198684804                          99.89119
## comp 12 0.0137002672            0.105386671                          99.99658
## comp 13 0.0004449384            0.003422603                         100.00000
PCA_G7$loadings
## NULL

2.2 Coloring of graphs

summary(PCA_G7)
## 
## Call:
## PCA(X = RTI_Data, scale.unit = TRUE, ncp = 13, ind.sup = NULL,  
##      quanti.sup = NULL, quali.sup = NULL, row.w = NULL, col.w = NULL,  
##      graph = TRUE, axes = c(1, 2)) 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6   Dim.7
## Variance               5.359   2.626   1.437   1.113   1.035   0.509   0.383
## % of var.             41.224  20.198  11.050   8.561   7.960   3.918   2.945
## Cumulative % of var.  41.224  61.423  72.473  81.034  88.995  92.913  95.859
##                        Dim.8   Dim.9  Dim.10  Dim.11  Dim.12  Dim.13
## Variance               0.259   0.133   0.107   0.026   0.014   0.000
## % of var.              1.993   1.019   0.822   0.199   0.105   0.003
## Cumulative % of var.  97.851  98.870  99.693  99.891  99.997 100.000
## 
## Individuals (the 10 first)
##                  Dist    Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3
## Benin        |  2.878 |  0.138  0.025  0.002 | -0.766  1.597  0.071 |  1.582
## BurkinaFaso  |  3.481 | -1.220  1.985  0.123 | -1.998 10.862  0.330 |  1.805
## Cameroun     |  3.207 |  1.494  2.976  0.217 |  1.802  8.831  0.316 | -0.526
## Centrafrique |  6.299 | -5.482 40.052  0.757 |  2.507 17.093  0.158 | -1.181
## Cotedivoire  |  2.978 |  1.608  3.446  0.292 |  1.302  4.611  0.191 |  0.108
## Gambie       |  3.580 |  2.285  6.958  0.407 | -1.555  6.575  0.189 | -1.524
## Guinee       |  2.382 |  0.052  0.004  0.000 | -1.082  3.187  0.206 | -1.094
## GuineeBissau |  2.397 | -0.453  0.274  0.036 |  1.564  6.656  0.426 | -0.183
## Mali         |  3.227 |  1.533  3.132  0.226 | -0.932  2.360  0.083 | -0.365
## Mauritanie   |  4.629 |  2.528  8.518  0.298 |  3.009 24.631  0.423 |  2.110
##                 ctr   cos2  
## Benin        12.439  0.302 |
## BurkinaFaso  16.196  0.269 |
## Cameroun      1.376  0.027 |
## Centrafrique  6.938  0.035 |
## Cotedivoire   0.058  0.001 |
## Gambie       11.545  0.181 |
## Guinee        5.954  0.211 |
## GuineeBissau  0.166  0.006 |
## Mali          0.663  0.013 |
## Mauritanie   22.133  0.208 |
## 
## Variables (the 10 first)
##                 Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3    ctr
## TEU          |  0.729  9.907  0.531 | -0.403  6.183  0.162 |  0.145  1.454
## TER          |  0.827 12.755  0.684 | -0.277  2.913  0.076 | -0.282  5.538
## TAU          |  0.576  6.191  0.332 | -0.221  1.864  0.049 |  0.666 30.866
## TAR          |  0.721  9.689  0.519 | -0.120  0.552  0.015 | -0.150  1.569
## DEF          | -0.543  5.511  0.295 | -0.185  1.301  0.034 |  0.673 31.507
## Rotavirus    |  0.105  0.204  0.011 | -0.836 26.613  0.699 | -0.035  0.086
## Pover        | -0.918 15.708  0.842 |  0.067  0.170  0.004 | -0.152  1.616
## ALPHA        |  0.522  5.080  0.272 |  0.481  8.824  0.232 | -0.077  0.410
## HYG          |  0.207  0.796  0.043 |  0.698 18.529  0.487 |  0.168  1.955
## URBA         |  0.685  8.752  0.469 |  0.452  7.784  0.204 | -0.308  6.623
##                cos2  
## TEU           0.021 |
## TER           0.080 |
## TAU           0.443 |
## TAR           0.023 |
## DEF           0.453 |
## Rotavirus     0.001 |
## Pover         0.023 |
## ALPHA         0.006 |
## HYG           0.028 |
## URBA          0.095 |
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.4.2
library(factoextra)
## Warning: package 'factoextra' was built under R version 4.4.2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
fviz_pca_biplot(PCA_G7, repel = TRUE,col.var = "blue",col.ind = "red")

fviz_eig(Rep_PCA, addlabels = TRUE)

fviz_pca_var(Rep_PCA, col.var = "cos2" , gradient.col = c("blue" , "green" , "red"), repel = TRUE )

fviz_pca_ind(Rep_PCA, col.ind = "cos2", gradient.cols = c("blue" , "green" , "red"), repel = TRUE)

2.3 correlation between variables

library(corrplot)
## Warning: package 'corrplot' was built under R version 4.4.2
## corrplot 0.95 loaded
cor = cor(MATRICE_COR)
corrplot(cor)

library("clusterSim")
## Warning: package 'clusterSim' was built under R version 4.4.2
## Loading required package: cluster
## Loading required package: MASS
Mul1 = data.Normalization(RTI_Data)
library(DataExplorer)
## Warning: package 'DataExplorer' was built under R version 4.4.2
plot_correlation(MATRICE_COR)

2.4 Contribution and Cos2

Rep1 = get_pca_var(Rep_PCA)
corrplot(Rep1$cos2)

corrplot(Rep1$contrib, is.corr =  FALSE)

2.5 Individuals and variables on factorial plan

library(ade4)
## Warning: package 'ade4' was built under R version 4.4.2
## 
## Attaching package: 'ade4'
## The following object is masked from 'package:FactoMineR':
## 
##     reconst
library(ggplot2)
library(factoextra)
fviz_pca_biplot(PCA_G7, repel = TRUE)

fviz_contrib(PCA_G7, choice = "ind", axes = 1)

fviz_contrib(PCA_G7, choice = "ind", axes = 2)

fviz_contrib(PCA_G7, choice = "var", axes = 1)

fviz_contrib(PCA_G7, choice = "var", axes = 2)

2.6 Classification

res.PCA<-PCA(RTI_Data,graph=FALSE)
res.HCPC<-HCPC(res.PCA,nb.clust=6,consol=FALSE,graph=FALSE)
plot.HCPC(res.HCPC,choice='tree',title='Arbre hiérarchique')

plot.HCPC(res.HCPC,choice='map',draw.tree=FALSE,title='Carte des facteurs')

plot.HCPC(res.HCPC,choice='3D.map',ind.names=FALSE,centers.plot=FALSE,angle=60,title='Arbre hiérarchique sur la carte des facteurs')

2.7 Regression multiple avec la fonction lm

library(car)
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.4.2
library(carData)
library(corrplot)
library("clusterSim")
library(DataExplorer)
library(factoextra)
library(ggpubr)
## Warning: package 'ggpubr' was built under R version 4.4.2
print(RTI_Data)
##                   TEU      TER      TAU      TAR      DEF Rotavirus Pover
## Benin        74.07068 60.77379 74.07068  9.63187 48.50221        76 12.72
## BurkinaFaso  80.85615 34.83605 80.85615 16.61428 33.55375        91 25.28
## Cameroun     81.62940 52.46118 58.18216 21.68085  4.25046        65 22.99
## Centrafrique 48.06423 27.37297 24.54589  7.73507 25.04464        58 65.67
## Cotedivoire  86.15835 58.04740 50.68393 21.69757 21.20376        79  9.73
## Gambie       90.88665 76.39057 61.11410 24.04950  0.06543        96 17.24
## Guinee       92.03279 59.01351 47.03491 21.74426  7.14571        72 13.82
## GuineeBissau 73.07241 52.51840 42.09296 16.16611  8.43078        68 25.96
## Mali         94.70028 74.44696 60.15749 41.92364  4.54229        70 20.84
## Mauritanie   94.58891 55.64086 79.32800 25.01106 26.86689        53  5.35
## Niger        88.25951 40.89417 52.82365  9.00733 64.98919        85 50.61
## Senegal      95.87272 76.97232 70.17145 50.55498  7.70624        84  9.92
## Sierraleone  79.79752 54.05841 34.51521 13.87033 16.42946        75 26.06
## Togo         86.98156 58.46670 32.11767  9.07869 39.47328        80 26.59
##                 ALPHA      HYG   URBA  MORT SOINS      ALIM
## Benin        47.10000 12.13046 49.534  53.6 1.953 10.002389
## BurkinaFaso  34.49000  9.15637 31.877  65.6 1.466 16.289089
## Cameroun     78.23000 36.71183 58.733  35.1 1.347  6.250315
## Centrafrique 37.49000 22.17641 43.120 119.1 0.209 49.476339
## Cotedivoire  89.89342 21.81496 52.661  32.6 1.751 35.247209
## Gambie       58.67000 12.94233 63.852  33.1 1.019  7.642408
## Guinee       45.33000 20.63610 37.668  57.9 0.214  4.873141
## GuineeBissau 53.90000 19.68909 45.041  57.6 2.080 38.821364
## Mali         30.76141 17.30087 45.437  62.9 1.948 13.301896
## Mauritanie   66.96000 41.75241 56.923  25.4 2.361 38.510298
## Niger        38.10000 24.61681 16.894 100.0 0.234 12.782480
## Senegal      57.67000 22.24601 49.086  32.0 1.264 15.932422
## Sierraleone  48.64000 17.83658 43.831  61.1 0.425  5.925322
## Togo         66.53708 17.33833 43.921  58.3 0.825 17.351413
attach(RTI_Data)
summary(RTI_Data)
##       TEU             TER             TAU             TAR        
##  Min.   :48.06   Min.   :27.37   Min.   :24.55   Min.   : 7.735  
##  1st Qu.:80.06   1st Qu.:52.48   1st Qu.:43.33   1st Qu.:10.691  
##  Median :86.57   Median :56.84   Median :55.50   Median :19.148  
##  Mean   :83.36   Mean   :55.85   Mean   :54.84   Mean   :20.626  
##  3rd Qu.:91.75   3rd Qu.:60.33   3rd Qu.:67.91   3rd Qu.:23.473  
##  Max.   :95.87   Max.   :76.97   Max.   :80.86   Max.   :50.555  
##       DEF             Rotavirus         Pover           ALPHA      
##  Min.   : 0.06543   Min.   :53.00   Min.   : 5.35   Min.   :30.76  
##  1st Qu.: 7.28584   1st Qu.:68.50   1st Qu.:12.99   1st Qu.:39.91  
##  Median :18.81661   Median :75.50   Median :21.91   Median :51.27  
##  Mean   :22.01458   Mean   :75.14   Mean   :23.77   Mean   :53.84  
##  3rd Qu.:31.88203   3rd Qu.:83.00   3rd Qu.:26.04   3rd Qu.:64.57  
##  Max.   :64.98919   Max.   :96.00   Max.   :65.67   Max.   :89.89  
##       HYG              URBA            MORT            SOINS      
##  Min.   : 9.156   Min.   :16.89   Min.   : 25.40   Min.   :0.209  
##  1st Qu.:17.310   1st Qu.:43.30   1st Qu.: 33.60   1st Qu.:0.525  
##  Median :20.163   Median :45.24   Median : 57.75   Median :1.306  
##  Mean   :21.168   Mean   :45.61   Mean   : 56.74   Mean   :1.221  
##  3rd Qu.:22.229   3rd Qu.:51.88   3rd Qu.: 62.45   3rd Qu.:1.899  
##  Max.   :41.752   Max.   :63.85   Max.   :119.10   Max.   :2.361  
##       ALIM       
##  Min.   : 4.873  
##  1st Qu.: 8.232  
##  Median :14.617  
##  Mean   :19.458  
##  3rd Qu.:30.773  
##  Max.   :49.476
model1 = lm(formula = MORT ~ 
             TEU +TER + TAU + TAR +  DEF + Rotavirus + Pover + ALPHA + 
             + HYG +URBA  + SOINS +ALIM,data=RTI_Data)
summary(model1)
## 
## Call:
## lm(formula = MORT ~ TEU + TER + TAU + TAR + DEF + Rotavirus + 
##     Pover + ALPHA + +HYG + URBA + SOINS + ALIM, data = RTI_Data)
## 
## Residuals:
##        Benin  BurkinaFaso     Cameroun Centrafrique  Cotedivoire       Gambie 
##      0.14703     -0.57963     -0.51995     -0.02540      1.91314      0.29322 
##       Guinee GuineeBissau         Mali   Mauritanie        Niger      Senegal 
##     -0.45867     -0.80044      0.79642      0.02943      0.77636     -0.99013 
##  Sierraleone         Togo 
##      1.72193     -2.30331 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 124.71592   22.69020   5.496    0.115
## TEU           0.31877    0.34591   0.922    0.526
## TER           0.51033    0.36326   1.405    0.394
## TAU           0.68283    0.38151   1.790    0.324
## TAR          -0.28797    0.30794  -0.935    0.521
## DEF          -0.08436    0.18869  -0.447    0.732
## Rotavirus    -1.59104    0.55601  -2.862    0.214
## Pover         1.63142    0.39272   4.154    0.150
## ALPHA         0.40252    0.34994   1.150    0.456
## HYG          -2.01459    0.74747  -2.695    0.226
## URBA         -0.91201    0.39246  -2.324    0.259
## SOINS       -10.54276    4.23720  -2.488    0.243
## ALIM          0.18107    0.14530   1.246    0.431
## 
## Residual standard error: 3.964 on 1 degrees of freedom
## Multiple R-squared:  0.9983, Adjusted R-squared:  0.9776 
## F-statistic: 48.25 on 12 and 1 DF,  p-value: 0.1121
vif(model1)
##       TEU       TER       TAU       TAR       DEF Rotavirus     Pover     ALPHA 
## 15.593449 23.193051 37.532065 12.194087 10.793888 36.901163 34.325134 29.869879 
##       HYG      URBA     SOINS      ALIM 
## 36.145383 17.632950  8.345062  3.757739
confint.default(model1)
##                    2.5 %      97.5 %
## (Intercept)  80.24394410 169.1878892
## TEU          -0.35919393   0.9967337
## TER          -0.20165359   1.2223184
## TAU          -0.06492625   1.4305800
## TAR          -0.89150958   0.3155766
## DEF          -0.45419544   0.2854665
## Rotavirus    -2.68080625  -0.5012814
## Pover         0.86171420   2.4011289
## ALPHA        -0.28334616   1.0883826
## HYG          -3.47959754  -0.5495778
## URBA         -1.68120966  -0.1428063
## SOINS       -18.84752519  -2.2380042
## ALIM         -0.10371075   0.4658517
attributes(model1)
## $names
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "xlevels"       "call"          "terms"         "model"        
## 
## $class
## [1] "lm"
model1$coefficients
##  (Intercept)          TEU          TER          TAU          TAR          DEF 
## 124.71591664   0.31876987   0.51033241   0.68282686  -0.28796648  -0.08436447 
##    Rotavirus        Pover        ALPHA          HYG         URBA        SOINS 
##  -1.59104384   1.63142154   0.40251823  -2.01458766  -0.91200800 -10.54276471 
##         ALIM 
##   0.18107049
model1$residuals
##        Benin  BurkinaFaso     Cameroun Centrafrique  Cotedivoire       Gambie 
##   0.14702765  -0.57962992  -0.51994953  -0.02540386   1.91314319   0.29321729 
##       Guinee GuineeBissau         Mali   Mauritanie        Niger      Senegal 
##  -0.45867307  -0.80044174   0.79641693   0.02942949   0.77636413  -0.99012611 
##  Sierraleone         Togo 
##   1.72193155  -2.30330599

2.8 GRAPHIQUE REGRESSION

library(ggplot2)
donnees = data.frame(RTI_Data)
data_vis= data.frame(valeurs_reelles=donnees$MORT,predictions=predict(model1))
ggplot(data_vis,aes(x=valeurs_reelles,y=predictions))+ geom_point()+ geom_smooth(method="lm",se=FALSE,color="blue")+ labs(x="valeurs_reelles",y="predictions")+ ggtitle(model1)
## `geom_smooth()` using formula = 'y ~ x'

3 Analysis

3.1 Correlation matrix and correlation circle

The correlation matrix shows a strong positive correlation between the variables Urban water access rate, Urban water access rate, Rural sanitation access rate, Urban sanitation access rate, and a strong positive correlation between Diarrhea disease mortality rate, Open defecation share, Share of people living below the poverty line (less than $2.5 per day). - The correlation between the Diarrhea Disease Mortality variable and the share of open defecation shows that open defecation can lead to cases of diarrhea disease that can result in death. - The correlation coefficient between Mortality from diarrhea diseases and Share of people living below the poverty line is also positive. This correlation shows that people living below the poverty line have a high incidence of death from diarrhea disease. - A strong negative correlation between the variable Density of doctors (per 10,000 inhabitants) and mortality from diarrhea diseases means that improving access to healthcare will result in a lower mortality rate from diarrhea diseases. - A strong correlation between the open defecation variable and the proportion of people living in urban areas. This shows that urbanization is a factor in reducing open defecation. ## Inertia graph

This graph demonstrates the diversity of information. The elbow rule allows us to retain the first two axes. The cloud then has a total intensity of 61.42%. As the graph shows, the last eigenvalue is not zero. This observation suggests that only these axes carry real information. Consequently, the description will be limited to these axes. ## Variable contribution graphs

An analysis of these two graphs reveals the following: - The variables rural water access rate, urban water access rate, proportion of people living in urban areas, diarrheal disease mortality rate (per 100,000 population), density of doctors (per 10,000 population), urban sanitation access rate, proportion of population defecating in the open, proportion of population living below the poverty line, rural sanitation access rate contribute most to the creation of axis 1. - The variables proportion of undernourished people, people with basic hand-washing facilities, proportion of children vaccinated against rotavirus contribute most to the creation of axis 2.

3.2 Variable contribution graphs

Analysis of these two graphs reveals the following: - Individuals such as Central Africa, Niger, Senegal and Mauritania contribute enormously to the formation of axis 1. - Individuals such as Central Africa, Niger, Cameroon, Burkina Faso and Mauritania contribute enormously to the formation of axis 2.

3.3 Factorial design and representation quality

The factorial design accounts for 61.42% of the variance. ## Bliplot

According to PCA-BIPLOT, countries such as Cameroon, Cote d’ivoire Gambia and Senegal show high values for variables such as Rural water access rate, Urban water access rate, Share of people living in urban areas, Density of doctors (per 10,000 inhabitants), Urban sanitation access rate, Rural sanitation access rate and Literacy. Unlike these individuals, it is clear that countries such as Burkina Faso, Niger, Togo and Sierra Leone have high values for the variables Diarrhea disease mortality rate (per 100,000 inhabitants), Share of population defecating in the open air, Share of population living below the poverty line. ## Classification plot

The dendrogram shows two major groups. The first group is made up of Côte d’Ivoire, Cameroon, Gambia, Guinea-Bissau, Mauritania, Senegal and Mali, which have a lower mortality rate than the second group, comprising Benin, Burkina Faso, Niger, Togo, Sierra Leone and Guinea. ## Linear regression

The variables used are water access rates, sanitation access rates, open defecation, poverty, literacy, urbanization, physician density as a function of diarrhea mortality. The R2 = 0.9831 is close to 1, so the model is acceptable. #Discussion

While exposure to a given pathology in a given environment is a function of the risk factors and human behaviors present, the level of morbidity or mortality reveals the overall state of health of the population. Basic services such as drinking water and sanitation are considered an essential component of individual and collective hygiene, with an undeniable influence on human health. Thus, the issue of water and the practices associated with it must be considered in the light of the lack of sanitation in the environment, characterized by the absence of improved latrines for all urban households and the poor availability of systems for the safe evacuation of faecal matter, as well as by the practice of open defecation and the discharge of waste water into the environment, which is a source of proliferation of pathogenic germs. The development of diarrhea diseases therefore appears to be the result of a particular ecology arising from the complex relationship between water supply, sanitation and hygiene practices. However, the high prevalence observed in certain countries can be explained by the low level of access to water and the lack of sanitation facilities for better management of faecal matter, as well as poor hygiene practices. While the causes of diarrhea morbidity may be multifactorial, access to water and sanitation is only one factor whose real effect is not easy to identify, especially when correlated with other factors that may totally neutralize the effect of access to these environmental services, such as the socio-economic status of households. It is therefore essential to understand the impact of environmental hygiene on health to ensure sustainable practices that reduce the risk of development of pathogens that cause infectious diseases. In the cities of developing countries, the rate of infant mortality and morbidity attributable to water and sanitation-related diseases remains very high. This is all the more true as improvements in drinking water supply and sanitation systems have been shown to reduce child mortality by over 30% and overall morbidity by almost 37%, particularly in combination with handwashing with soap. Hygiene interventions, including hygiene education and simple handwashing, can reduce the number of cases of diarrhea disease by 45% (UNICEF-WHO, 2009). Water and sanitation have a direct impact on improving hygiene and health, as they break the transmission cycle of many gastrointestinal and other diseases linked to the consumption of contaminated water and food. According to the results obtained, there is a relationship between diarrhea disease and the level of access to water, the level of access to sanitation, the proportion of the population who defecate in the open air, urbanization, educational level, social class and access to health services. In order to reduce cases of diarrhea disease, it would be necessary to increase levels of access to water and sanitation, guarantee adequate health coverage and raise literacy rates. Policies to reduce open defecation and the proportion of people living below the poverty line could also reduce cases. R2 is close to 1, which means the model is acceptable. However, it is clear that the intercept is not zero, which means that to put this model into practice, it would be necessary to set a threshold beyond which the model is no longer valid. # Conclusion

Our study shows that diarrhea disease is a major public health problem in developing countries, where it is one of the main causes of morbidity and mortality in children under five. The results show that there is a significant relationship between diarrhea morbidity and variables such as access to water, sanitation, open defecation, level of education, social class and access to healthcare. These factors underline the need to strengthen public policies to improve access to drinking water, promote better hygiene practices and develop infrastructure.