Projection of Climate Change on the Probability of Dengue Hemorrhagic Fever in North Sumatra Province

Climate change is a major threat to global prosperity. The industrial revolution has occurred since 1750 to 2010 where the increase in global air temperature has reached 0.7°C. Rising temperatures and fluctuating rainfall is the identification of climate change, one of the impacts of climate change is changing the distribution of some types of mosquitoes (Aedes Aegypti).Based on the results of the analysis of the main components, a good model uses an accuracy rate of about 85% and passes the test individually and as a whole. Indonesia has a tropical climate where warm temperatures and high rainfall variability are a comfortable habitat for Aedes Aegypti mosquitoes. The breeding and life cycle of the Aedes Aegypti mosquito is directly influenced by climatic conditions. The purpose of this study is to determine the normal rainfall map, an overview of climate projection patterns, identification of characteristics of climate change in the short term (2011 – 2040), medium term (2041 – 2070) and long term (2071-2100) based on rainfall and temperature projections in North Sumatra province. Statistical methods used to determine the effect of climate on health (dengue) include statistical downscaling, delta bias correction, Principal Component Analysis, and ordinal logistic regression. The results of the ordinal logistic regression analysis show that rainfall that is suitable for dengue fever ranges from 100 - 300 mm. For North Sumatra rainfall ranges from 50 - 600 mm. In March and November is the strongest threat because of the peak with high rainfall intensity where the danger of flooding and dengue. The air temperature ranges from 24.5 - 28.5 o C, this condition is still optimal for the development of the Aedes Aegypti mosquito. The climate change projection index for the short term (2011 - 2040), medium term (2041 - 2070) and long term (2071 - 2100) shows a consistent increase with a range of 0.40C, this value will affect the acceleration of the reproduction of the Aedes aegypti mosquito as the cause of DHF. The projection probability of dengue hemorrhagic fever shows that North Sumatra Province still has a high chance of being categorized as a high risk area for dengue fever with a probability value of 0.82 - 0.99.


INTRODUCTION
Climate change is a major threat to global prosperity.Solidarity, partnership, cooperation, and collaboration are key in addressing climate change issues globally.Indonesia with its huge natural potential contributes to the handling of climate change.The seventh President of the Republic of Indonesia conveyed Indonesia's commitment to address climate change issues at the Climate Change Conference of the Parties (COP26) at the Projection of Climate Change ……….. Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram, April. 2023. Vol. 11, No.2 | 394 Scottish Event Campus, Glasgow, Scotland in 2021.North Sumatra Province was chosen as the location of the Global Covenant of Mayors for Climate and Energy (GCoM) Asia Project program on climate change mitigation and adaptation.
Several areas in North Sumatra Province are industrial areas with high consumption of greenhouse gas (GHG) emissions.The increase of GHG in the atmosphere is the main cause of climate change produced by industrial activities.GHGs have the effect of accelerating the global warming process and increasing the frequency of extreme weather and climate events (Pabalik et al., 2015).The increase in temperature and fluctuating rainfall is an identification of climate change (Putra et al., 2020).According to the United States Environmental Protection Agency (US EPA), several sectors of life that are potentially affected by climate change include health, agriculture, forestry, water resources, infrastructure, coastal areas, fisheries, and other natural environments (Githeko et al., 2003).
Disease transmission is strongly influenced by climatic factors (Brisbois & Ali, 2010).The Intergovernmental Panel on Climate Change (IPCC) states that one of the impacts of climate change is changing the distribution of several mosquito species (Malaria and Aedes Aegypti) and other diseases (IPCC, 2007).Indonesia has a tropical climate where warm temperatures and high rainfall variability provide a comfortable home for the Aedes Aegypti mosquito.The peak incidence of dengue fever occurs at a temperature interval of 27 -29 oC (Tarmana, 2017).Flooding is very common in North Sumatra due to reduced forest conservation, erosion, and siltation of rivers.Flooding is very supportive of the development of the Aedes Aegypti mosquito.For this reason, this research will discuss climate change that occurs, the need for adaptation and mitigation of dengue hemorrhagic fever by projecting scenarios estimating the amount of greenhouse gas (GHG) emissions in the future.
Future climate change is described through the Radiative Concentration Pathways (RCP) scenario.RCP has 4 scenarios, namely RCP2.6,RCP4.5, RCP6.0 and RCP8.5.The RCP4.5 scenario assumes that all countries in the world take part in mitigation efforts (GHG reduction) simultaneously and effectively (Thomson et al., 2011).This research will project future extreme climate conditions for the short-term (2021 -2050), medium-term (2051 -2080), and long-term (2081 -2100) periods in North Sumatra, so that based on the resulting future extreme climate change projections, adaptation and mitigation actions can be taken by stakeholders in Indonesia, especially North Sumatra for planning in the program to deal with dengue cases.
Climate change has several elements as a reference, the main elements are rainfall and temperature.This research focuses on rainfall and temperature, where if the normal conditions of climate compatibility (rainfall and temperature) with the mosquito's living environment, the normal cycle occurs in the Aedes Aegipty mosquito so that dengue fever cases do not experience significant changes.The existence of climate change issues (changes in rainfall and temperature increase) and according to several studies have an impact on the health sector, especially on dengue fever cases, making changes to the normal cycle of the Aedes Aegipty mosquito.Based on these climate projections, what about the probability of dengue hemorrhagic fever cases in North Sumatra Province.
This study was conducted with the aim of obtaining the characteristics of future extreme climate change in the North Sumatra region and the probability of Dengue Fever occurrence based on climate change projections in the short term (2011 -2040), medium term (2041 -2070) and long term (2071 -2100) based on the scenario.

METHOD
Statistical methods were used to determine the effect of climate on health (dengue), including statistical downscaling, delta bias correction, Principal Component Analysis, and ordinal logistic regression.The grouping of data modes is Observation Data and Climate Model Data.  1 shows the description of the rcp scenario.Data in the study includes: 1) Rainfall projection data in units of measurement millimeters (mm) monthly time series from 2011 -2100 with North Sumatra grid stored in the form of a matrix grid in Netcdf format was converted to Excel; 2) Air temperature projection data in units of degrees Celsius (oC) monthly time series from 2011 -2100 with North Sumatra grid stored in the form of a matrix grid in Netcdf format converted to Excel; and 3) The model data is then divided into three periods: short-term (2011 -2040), medium-term (2041 -2070), and long-term (2071 -2100).Global model data used ensemble data from CORDEX SEA.RCP4.5 was developed by the GCAM modeling team at the Pacific Northwest National Laboratory JGCRI (Joint Global Change Research Institute), USA.It is a stabilization scenario with stable radiative forcing after 2100, without exceeding the longterm radiative forcing target limit.The research area is shown in Figure 1 and the metadata in Table 2.This research uses several calculations, namely downscaling statistics, delta bias correction, principal component analysis, weighted distance inverse interpolation and ordinal logistic regression.Statistical downscaling is a technique that uses statistical downscaling to see the relationship between global-scale data and local-scale data.Climate variables in the global model are stored in the form of grid data with a horizontal resolution ranging from 50 -500 km and then downscaled to a resolution of 25 km as shown in Figure 3. Bias correction with the delta method is used to arrange the correction factor of the model data before testing the accuracy of the model data, illustration of bias correction is shown in Figure 4.The Delta method is a simple downscaling method commonly used to prepare climate change scenarios at the local scale (Faqih, 2017).The formula of the Delta Method calculation is: X_(cor,i) is corrected value; μ_p is average in the projection period; X_(o,i) is observation value; μ_b is average in the baseline period.Principal Component Analysis (PCA) can be used to reduce the dimension of data without significantly reducing the characteristics of the data (Cahyadi, 2007).PCA is a form of linear transformation projection of variable data.The formula of PCA calculation is: If the origin variable group {X1, X2, …, Xp} has a variance matrix  then the variance of the principal component is : Vector a1 is matrix feature vector  which corresponds to the root of the largest feature.Linear combination of {X1, X2, …, Xp} form KU1 = a1x = a11x1 + … + a1pXp known as first KU and has a variance of 1 = largest characteristic root.Form KU2 = a2x = a21x1 + … + a2pXp.Searching for vectors a2 so the variety maximum of KU2, and KU2 not correlated with KU1.a2 is none other than the feature vector that corresponds to the second largest feature root of the matrix .Example 1  2  …  p > 0 is the feature vector that corresponds to the feature vector a1, a2, …, ap by matrix , and the length of each of the vectors is 1, or ai'ai = 1 for i = 1, 2, …, p. So, KU1 = a1'x, KU2 = a2'x, …, KUp = ap'x onsecutive is first main component, second, …, by-p to x.More var (KU1) = 1, var(KU2) = 2, …, var (KUp) = p, or the characteristic root of the variance matrix  is variety of major components.
Dengue hemorrhagic fever is It is an infectious disease caused by the dengue virus of the flavivirus genus that is transmitted through the bite of the Aedes Aegypti mosquito.There are several climatic parameters that can affect the incidence of Dengue hemorrhagic fever.(Wirayoga, 2013) through his research discusses the relationship between climate parameters (temperature, rainfall, humidity and wind speed) and the incidence of DHF in Semarang City.
The weighted distance inverse interpolation method is an interpolation method by making the distance between the predicted point and the measured point a weighting factor.The formula for this method is: The formula for calculating self-weight is: (Eq. 6) ∑    =1 = 1 (Eq. 7) dio = Distance between the point whose value is predicted and the neighboring points, p = inverse power of weighted distance Categorical data on response variables can be nominal or ordinal, for the case of ordinal response variables, the regression model that can be used is the ordinal logistic regression model.In this logistic model (logit link), the ordinal nature of the response variable Y is expressed in cumulative odds so that the cumulative logit model is a model obtained by comparing the cumulative odds, namely the odds of being less than or equal to-j response category on the p predictor variables expressed in the X vector (P[Y≤j|X]), with a probability greater than the response category to-j (P[Y≥j|X]) (Hosmer dan Lemeshow, 2000).Cumulative probability P(Y≤j|X) is defined as follows: with j = 1,2,…,J is response category (Agresti, 1990) In terms of classification, the cumulative logit model is a classification function.The classification function formed when there are J response categories is a number of J -1.If (X) = P(Y = j I X ) π j = states the probability of response category to-j at p the predictor variable expressed in vector X and P (Y≤j|X) states the cumulative probability at p predictor variables expressed in vector X then the value of (X) π j obtained by the following equation : with j = 1,2, …, J.For five response categories where j = 1, 2, 3, 4, 5 then the value of the response category probability toj is : ) (Eq. 9) By utilizing the two cumulative opportunities above, the opportunities for each response category will be obtained as follows: 1 () = ( ≤ 1I) = ) (Eq. 12) For value classification  1 () at equation 1 to 3 will be used as a guideline for classification.An observation will fall into the response category j based on the largest   () (Wibowo, 2002).

RESULTS AND DISCUSSION
The air temperature for North Sumatra Province at BMKG stations ranges from 24.5 -28.5 0 C, with the highest temperature occurring in May and the lowest occurring in November.The overall temperature allows for the growth of Aedes Aegypti mosquitoes can be seen in Figure 5.The rainfall pattern at BMKG stations is a climate element that is discussed in this study.The normal monthly rainfall (1991 -2020) for North Sumatra Province generally ranges from 50 mm -600 mm can be seen in Figure 7.In general, the seasonal period in the North Sumatra region can be categorized into periods of December -January -February (DJF), March -April -May (MAM), June -July -August (JJA) and September -October -November (SON).DJF and JJA are dry periods, while MAM and SON are wet periods.Based on the monthly normal distribution of rainfall, the North Sumatra region is included in the Equatorial rainfall type, which means that it has each of the two peaks and two valleys rainfall patterns.The first rain peak is generally in March, while the second rain peak is generally in November.The second rainy peak has a higher rainfall accumulation than the first rainy peak.The first dry peak is generally in February, while the second dry peak is generally in July as shown in Figure 6.When viewed from climatological factors, namely rainfall and air temperature are theoretically the optimum factors for the development of the aedes aegypti mosquito, plus supporting rainfall puddles as a breeding ground, so North Sumatra has a vulnerability in the health sector as a result of climate change.The results of descriptive analysis of data on the number of DHF cases in North Sumatra Province shown in Figure 8 show that it varies greatly.The number of monthly cases with the period 2019 -2022 shows that October is the highest total number of dengue cases at 8694 cases and the lowest in April at 5201 cases.In Table 3 based on the Ministry of Health which divides 3 (three) levels of risk, from the dengue hemorrhagic fever data in general, North Sumatra is in the medium to high risk category.Principal component analysis can produce more optimal values to represent all variations.Problems that commonly occur in a large variety of data include a large number of variables that make analysis difficult and multicollinearity that invalidates conclusions.In Figure 9, the rainfall outlier plot aims to identify outliers.Any point that is above the reference line is an outlier.Outliers can significantly affect the results of the analysis.Therefore, if an outlier is identified in the data, one should examine the observations to understand why they are unusual.Correct any measurement or data entry errors.Consider removing data related to special causes and repeating the analysis.In these results, there are several outliers.The rainfall biplot in Figure 10 aims to assess the structure of the data and the load of the first two components on one graph.Minitab plots the value of the second principal component versus the value of the first principal component, as well as the loadings for both components.This biplot shows the following: The overall data has a large positive loading on component 1, the point in the bottom right corner may be an outlier.In figure 11 Loading plots of rainfall aim to identify which variables have the greatest effect on each component.Loadings can range from -1 to 1. Loadings close to -1 or 1 indicate that the variable strongly influences the component.Loadings close to 0 indicate that the variable has a weak influence on the component.Loading plots can also help characterize each component in terms of variables.This plot has a large positive loading on component 1, so this component primarily measures stability.Stamet Aek Godang, Stamet FL Tobing, Stageof Gunung Sitoli and Stamet Binaka have large negative weights on component 2. In Figure 12 the Score plot of rainfall aims to assess the structure of the data and detect clusters, outliers and trends.Data grouping on the plot can indicate two or more separate distributions in the data.If the data follows a normal distribution and there are no outliers, the points will be randomly distributed around zero.In this scree plot, the point in the bottom corner may be an outlier.In figure 13 this Scree plot of rainfall shows that the eigenvalues start to form a straight line after the second principal component.Therefore, the remaining principal components account for a very small proportion of the variability (close to zero) and may not be important.
In Principal Component Analysis (principal component analysis) can be seen in table 4, eigenvalues (also called characteristic values or latent roots) are variants of the principal components.Measure the eigenvalues to determine the number of principal components.Keep the principal component with the largest eigenvalue.For example, using the Kaiser criterion, only use principal components with eigenvalues greater than 1.Proportion is the proportion of variability in the data explained by each principal component, determining which principal component explains most of the variability in the data.The higher the proportion, the more variability is explained by the principal component.The proportion measure can help decide whether the principal component is important enough to retain.The principal component with a proportion of 0.452 explains 45.2% of the variability in the data.Therefore, this component is important to include.Another component has a proportion of 0.034, and thus explains only 3.4% of the variability in the data.These components may not be important enough to include.Cumulative is the cumulative proportion of the sample variability explained by the successive principal components.Use the cumulative proportion to assess the total amount of variance explained by the successive principal components.The cumulative proportion can help determine the number of principal components to use.Keep the principal components that explain an acceptable level of variance.The acceptable level depends on the application.70% of the variance explained by the principal components is required if only using them for descriptive purposes.However, if you want to perform other analyses on the data, perhaps at least 85% of the variance explained by the principal components.In Figure 14, the air temperature outlier plot aims to identify outliers.Any point that is above the reference line is an outlier.Outliers can significantly affect the results of the analysis.Therefore, if you identify an outlier in the data, you should examine the observation to understand why it is unusual.Correct any measurement or data entry errors.Consider removing data related to special causes and repeating the analysis.In these results, there are several outliers.In figure 15 this Biplot shows the following: The overall data has a large positive load on component 1, the point in the bottom right corner may be an outlier.In figure 16 Loading plots of air temperature aim to identify which variables have the greatest effect on each component.Loadings can range from -1 to 1. Loadings close to -1 or 1 indicate that the variable strongly influences the component.Loadings close to 0 indicate that the variable has a weak influence on the component.Loading plots can also help characterize each component in terms of variables.This plot has a large positive loading on component 1, so this component primarily measures stability.BBMKG Wil I, Stamet Aek Godang, Stamar Belawan and Stamet Kualanamu have a large negative weight on component 2 of around (-0.25) to (-0.5).In Figure 17, the Score plot of air temperature aims to assess the structure of the data and detect clusters, outliers, and trends.The clustering of data on the plot may indicate two or more separate distributions in the data.If the data follows a normal distribution and there are no outliers, the points will be randomly distributed around zero.In this score plot, the point in the bottom corner may be an outlier.In Figure 18 this Scree plot of air temperature shows that the eigenvalues start to form a straight line after the second principal component.Therefore, the remaining principal components account for a very small proportion of the variability (close to zero) and may not be important.

Figure 11 .
Figure 11.Loading Plot of Precipitation Figure 12.Score Plot of Precipitation

403 Figure 16 .
Figure 16.Loading Plot of Air Temperature Figure 17.Score Plot of Air Temperature

Figure 18 .
Figure 18.Scree Plot of Air Temperature Observation Data 1) Observed rainfall data in millimeters (mm) monthly time series from 2006 -2022 from a network of BMKG stations spread throughout North Sumatra Province in Ms. Excel format; 2) Observed air temperature data in degrees Celsius (oC) monthly time series from 2006 -2022 from a network of BMKG stations spread throughout North Sumatra Province in Ms.

Table 1 .
RCP Scenario Description

Table 2 .
Metadata of BMKG observation stations used in the research(BMKGSoft, 2021)

Table 3
Classification into 3 (three) risk levels November Med High High Med Med High High High Med High Med Low Med High December Med High Med Med Med High Med Med Med High Med Low Med Med Description: Low = Low Risk, Med = Medium Risk, High = High Risk June Med High Med Med Med Med Med High Med Med Med Med Low High July Med High Med Med Med Med Med Med Med Med High Med Low High August Med High Med Med Med Med Med High Med Med High Low Low High September Med High Med Med Med High Med High Med Med High Low Low High October Med High Med Med Med High Med High Med High High Low Med High Simbolon et al.Projection of Climate Change ……….. Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram, April.2023.Vol.11, No.2

Table 4 .
Principal Component Analysis of Rainfall Principal

Table 5 .
Principal Component Analysis Air Temperature Principal