Analysis of the Impact of Population Growth in DKI Jakarta Using Logistic Model

The rapid population growth in the DKI Jakarta area has an impact on its population and creates an unfriendly environment. The author is motivated to analyse the effect of the population growth rate in DKI Jakarta over the next 10 years. The process of estimating population growth is calculated by a mathematical model called the logistic model. The logistic model is the model that developed by differential equation like the following 𝑑𝑁 𝑑𝑡 = 𝑁 (𝑎 − 𝑏𝑁) . This model illustrates that population growth is determined by the difference between the number of births and deaths of the population. In addition, an analysis of the resulting environmental impact and the impact of its handling will also be discussed. Based on estimation, the population in DKI Jakarta Province in 2022 is predicted around 10,636.685 people and it will reach 10,938.900 in 2030. It means there will be a 3% increase in population from 2019 to 2030 in DKI Jakarta Province. These values increase annually and they are predicted to have an impact on increasing the traffic congestion by 3%, from 70% to 72.1%. Another result has also occurred in air pollution. The average of air pollution increasing by 3%, from 39.6 𝜇𝑔/𝑚 3 to 40.79 𝜇𝑔/𝑚 3 . These two factors show that the increase of population growth will have an impact on increasing the average traffic congestion and the percentage of air pollution in DKI Jakarta. 10,674,126; 10,711,663; 10,749,297; 10,787,026; 10,824,850; 10,862,771; 10,900,788; and 10,938,900. These values increase annually and they are predicted to have an impact on increasing the traffic congestion by 3%, from 70% to 72.1%. The another result has also occurred in air pollution. The average of air pollution increasing by 3%, from 39.6 𝜇𝑔/𝑚 3 to 40.79 𝜇𝑔/𝑚 3 . This study provides an overview of the increasing population in the province of DKI Jakarta over the next ten years and provides caution of the social impacts. This paper suggests alternative solutions such as the use of nine alternative sources of electrical energy: electricity sources include solar-photovoltaics (PV), concentrated solar power (CSP), wind, geothermal, hydroelectric, wave, tidal, nuclear, and coal with carbon capture and storage (CCS) technology and the use of


Introduction
DKI (Special Capital Region) Jakarta Province is the capital city of the country which is the center of the economy and government (Zhu & Simarmata, 2015;Syalianda & Kusumastuti, 2021;Shatkin, 2022).As a result, many people are competing to come into Jakarta and look for work.Based on data from the Central Agency of Statistics, in 2021 the total population in DKI Jakarta reached 20 million people.The data is spread over five districts and cities such as: Kepulauan Seribu, Jakarta Selatan, Jakarta Timur, Jakarta Pusat, Jakarta Barat, dan Jakarta Utara (Yoo, Kim, & Hadi, 2014;Kamh, Khalifa, & El-Bahrawy, 2016;Heidrich, Jayathunga, Bock, & Götz, 2021;Rukmana, & Ramadhani, 2021).If the data is compared to area which have 662.33  2 , the result is a very high population density.For five districts and cities in DKI Jakarta, the population density data for each city in 2021 are as follows: 2774, 14475, 16729, 20360, 19608, 12749, and 15978 per  2 ("BPS Provinsi DKI Jakarta," n.d.).
Furthermore, mathematical modeling is carried out to help solve this problem.The logistic model is used to estimate population growth in DKI Jakarta over the next 10 years.This model was chosen because of its algorithm to model growth rates as in the following research such as Grey Prediction Model of Population Growth (Tong, Yan, & Chao, 2020), Fractional Numerical Dynamics For Logistic Population (Qureshi, Yusuf, & Aziz, 2021), A Closed-Form Solution to The Ramsey Model with Logistic Population Growth (Guerrini, 2010), and Logistic Population in The World's Largest Cities (Mulligan, 2006;Chen, 2014;Hsieh, 2014;Vieira, Hiar, & Cardoso, 2022).In this paper, we used a logistic model to model population growth in DKI Jakarta province and analyzed the impact on the social sector.
The social sectors have been discussed in this paper are traffic problems and air pollution levels.We compared the results of the estimated population in DKI Jakarta with these two variables.The results of the analysis are presented in graphical form and the recommendations are given to each of the following problems with graphical analysis to obtain the solutions of the problems.
In the next section, we will discuss the method and the results.the method used is mathematical modeling related to the field of biology.The logistic model can explain the growth of an object by using the differential equation.The idea is to consider the difference between the birth rate and the death rate of the object.the result is obtained by estimating the rate of population growth and calculating the analytical solution from the logistic model.

Method
The method used in this study is mathematical modeling using a logistic model as described in (Pagalay, 2009).
By taking the logarithmic property we get For each 1 t elements times T and ( ) Nt respect to the population growth at times t, 0 N respect to the initial condition, a and b respect to the bird and death rate.We assume K is the maximum growth, then a will decrease as () Nt approaches K and will be negative if () Nt exceeds K .As this result we can modify Equation (2) become Equation (3) as follows: The population described in equation 3 is DKI Jakarta residents.

Results
Population data for the last three years is used to determine the rate of growth and is attached to The birt rate a will be derived from Equation 1 as follows.

Discussion
The traffic index stated the average congestion of DKI Jakarta in 2019 is 70% ("Jakarta Traffic Report | TomTom Traffic Index," n.d.).Based on Table 1 the population in 2019 is 10,557.810.On the other hand, the estimated population in 2030 is 10,938.900.there will be a 3 percent increase in population from 2019 to 2030.This means the traffic congestion in 2030 may increase to reach 72.1%.
In Figure 2 we can see the average of air pollution in DKI Jakarta.The data are taken from ("Kota Paling Berpolusi Di Dunia 2021 -Rangking PM2.5 | IQAir," n.d.).In Figure 2 the air pollution index is given.From January to December 2020 the values are 30.9; 27; 32.9; 40.3; 39.8; 57.9; 54.4; 52.4; 45.3; 39; 41.3; and 13.7.So, the average air population index is 39.6 / 3 .Based on Table 1 the population in 2020 is 10,562,090.On the other hand, the estimated population in 2030 is 10,938,900.There will be a 3 percent increase in population from 2019 to 2030.This means that the average air pollution index may increase to 40.79 / 3 .
This study provides an overview of the increasing population in the province of DKI Jakarta over the next ten years and provides caution of the social impacts.This paper tries to provide alternative solutions to prevent these undesirable impacts.As discussed by (Jacobson, 2009) regarding the use of nine alternative sources of electrical energy such as electricity sources include solar-photovoltaics (PV), concentrated solar power (CSP), wind, geothermal, hydroelectric, wave, tidal, nuclear, and coal with carbon capture and storage (CCS) technology and the use of two alternative liquid fuel sources such as include corn-ethanol (E85) and cellulosic-E85.In addition, the considerable efforts to reduce carbon dioxide levels are necessary.As the study conducted by (Rachim & Firdaus, 2021), CO2 levels can increase the temperature.Some possible solutions for traffic jams such as considering the presence of trucks crossing the main road as discussed by (Rachim, Salmah, & Solekhudin, 2017) and applying control signals in the form of variable speed limit and ramp metering to regulate vehicle entry and exit flows as reviewed by (Hajiahmadi et al., 2016).

Conclusion
The logistic model has been formulated in Equations ( 1), (2), and (3).We estimated the population growth of DKI Jakarta from 2022 to 2030 using equation (3).The result are 10,636,685; 10,674,126; 10,711,663; 10,749,297; 10,787,026; 10,824,850; 10,862,771; 10,900,788; and 10,938,900.These values increase annually and they are predicted to have an impact on increasing the traffic congestion by 3%, from 70% to 72.1%.The another result has also occurred in air pollution.The average of air pollution increasing by 3%, from 39.6 / 3 to 40.79 / 3 .This study provides an overview of the increasing population in the province of DKI Jakarta over the next ten years and provides caution of the social impacts.This paper suggests alternative solutions such as the use of nine alternative sources of electrical energy: electricity sources include solar-photovoltaics (PV), concentrated solar power (CSP), wind, geothermal, hydroelectric, wave, tidal, nuclear, and coal with carbon capture and storage (CCS) technology and the use of two alternative liquid fuel sources: corn-ethanol (E85) and cellulosic-E85 to prevent these undesirable impacts.This paper also give suggestion to solve traffic congestion, such as considering the presence of trucks crossing the main road and applying control signals in the form of variable speed limit and ramp metering to regulate vehicle entry and exit flows Further research can be developed by further observing the existing data and can also be applied to all regions in Indonesia.

Figure 1 .
Figure 1.Estimated Population Growth in DKI Jakarta

Table 1 .
The Population of DKI Jakarta from 2019 to 2021

Table 2 .
Estimated Population of DKI Jakarta (Data in Thousand Units).