Jurnal Matematika, Statistika dan Komputasi
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Stability Analysis of Mathematical Model on HIV Infection with the Effects of Antiretroviral therapy
Get PDFHIV is a retrovirus, a virus which has enzymes and can convert genetic material from RNA to DNA. Antiretroviral therapies are the treatment to make the activity of the virus slow. The purpose of this article is to develop a mathematical model of HIV infection by reviewing antiretroviral therapy, analyze the equilibrium point, and determine the effectiveness of antiretroviral therapy. There are two equilibrium points in this HIV infection model, namely infection-free equilibrium and infected equilibrium. Numerical simulations are carried out based on selected parameters showed that infection free equilibrium is reached when the effectiveness of antiretroviral therapy is 0,4 for RT inhibitor and 0,3 for Protease Inhibitor. This means that antiretroviral therapy may change infected conditions to infection free conditions
Target prediction of compounds on jamu formula using nearest profile method
Get PDFJamu is one of Indonesia\u27s cultural heritage, which consists of several plants that have been practiced for centuries in Indonesian society to maintain health and treat diseases. One of the scientification efforts of Jamu to reveal its mechanism is to predict the target-protein of the active ingredients of the Jamu. In this study, the prediction of the target compound for Jamu was carried out using a supervised learning approach involving conventional medicinal compounds as training data. The method used in this study is the closest profile method adopted from the nearest neighbor algorithm. This method is implemented in drug compound data to construct a learning model. The AUC value for measuring performance of the three implemented models is 0.62 for the fixed compound model, 0.78 for the fixed target model, and 0.83 for the mixed model. The fixed compound model is then used to construct a prediction model on the herbal medicine data with an optimal threshold value of 0.91. The model produced 10 potential compounds in the herbal formula and its 44 unique protein targets. Even though it has many limitations in obtaining a good performance, the closest profile method can be used to predict the target of the herbal compound whose target is not yet known
Forecasting Bank Indonesia Currency Inflow and Outflow Using ARIMA, Time Series Regression (TSR), ARIMAX, and NN Approaches in Lampung
Get PDFThere are various types of data, one of which is the time-series data. This data type is capable of predicting future data with a similar speed as the forecasting method of analysis. This method is applied by Bank Indonesia (BI) in determining currency inflows and outflows in society. Moreover, Inflows and outflows of currency are monthly time-series data which are assumed to be influenced by time. In this study, several forecasting methods were used to predict this flow of currency including ARIMA, Time Series Regression (TSR), ARIMAX, and NN. Furthermore, RMSE accuracy was used in selecting the best method for predicting the currency flow. The results showed that the ARIMAX method was the best for forecasting because this method had the smallest RMSE.Dalam Ilmu statistika terdapat berbagai macam tipe data, salah satunya adalah data deret waktu. Data deret waktu merupakan serangkaian data pengamatan yang disusun berdasarkan urutan waktu. Data deret waktu dapat digunakan untuk meramalkan data yang akan datang sesuai dengan rentang waktu yang sama dengan sebelumnya dimana analisis tersebut adalah metode peramalan. Metode peramalan diterapkan pada pengambilan kebijakan dalam menentukan peredaran uang kartal di masyarakat yang dilakukan oleh Bank Indonesia (BI) adalah Inflow dan Outflow uang kartal. Inflow dan Outflow uang kartal merupakan data time series bulanan yang diduga dipengaruhi oleh waktu (time). Ada beberapa metode time series yang bisa digunakan untuk meramalkan Inflow dan Outflow uang kartal diantaranya: ARIMA, Time Series Regression (TSR), ARIMAX dan FFNN. Pemilihan metode terbaik menggunakan akurasi RMSE
Stability Analysis of Divorce Dynamics Models
Get PDFThis article examines the mathematical model of divorce. This model consists of four population classes, namely the Married class (M), the population class who experiences separation of separated beds (S), the population class who is divorced by Divorce (D), and the population class who experiences depression or stress due to divorce Hardship (H). This study focuses on the stability analysis of divorce-free and endemic equilibrium points. Local stability was analyzed using linearization and eigenvalues methods. In addition, the basic reproduction number is provided via the next generation matrix method. The existence and stability of the equilibrium point are determined from . The results showed that the rate of interaction between population M and populations other than H is very influential on efforts to minimize divorce. Divorce can be minimized when the transmission rate is reduced to . Reducing the transmission rate and increasing the rate of transfer from split bed class to married class can turn divorce endemic cases into non-endemic cases. A numerical simulation is given to confirm the analysis results
Bayesian inference for Pareto distribution with prior conjugate and prior non conjugate
Get PDFThe purpose of this study is to determine the best estimator for estimating the shape parameters of the Pareto distribution with the known scale parameter. Estimation of these parameters is done by using the Gamma distribution as the prior distribution of the conjugate and the Uniform distribution as the non-conjugate prior distribution. A comparison of the two prior distributions is done through simulation studies with various sample sizes. The best estimator net is a method that produces the smallest posterior variance, absolute bias, and Bayes confidence interval. This study proves that the Bayes estimator by using the prior conjugate distribution produces all indicators of the goodness of the model with a smaller value than the non-conjugate prior distribution. Thus it can be concluded that the estimator with prior conjugate will produce a better predictive value than prior non-conjugate
Modeling Claim Frequency in Indonesia Auto Insurance Using Generalized Poisson-Lindley Linear Model
Get PDFThis paper will discuss the modeling of claim frequency from Indonesian auto insurance using the generalized Poisson-Lindley linear model. This modeling method assumes that the data of claim frequency are from populations that follow generalized Poisson-Lindley distribution. Generalized Poisson-Lindley linear model is an alternative to modeling count data that contains overdispersion. The parameters in the generalized Poisson-Lindley linear model can be estimated using the maximum likelihood estimation method through Newton Raphson\u27s iteration numerical method. The data are the secondary data took from XYZ Company for the 2013 policy which is overdispersed. The data contains policyholder partial loss claims for comprehensive motor vehicle insurance products. From the research conducted it was concluded that the data is suitable to be modeled with generalized Poisson-Lindley linear models and produce better models than ordinary Poisson linear modeling because of produced the smaller AIC value. Of the 3 predictor variables that are modeled on the frequency of claims, 2 variables influenced they are the use variable and vehicle brand variable
Penentuan Cadangan Premi Asuransi Jiwa Seumur Hidup Menggunakan Metode Zillmer
Get PDFCadangan premi adalah kewajiban perusahaan asuransi untuk membayar sejumlah dana yang harus disiapkan oleh perusahaan asuransi di kemudian hari. Cadangan premi dapat ditentukan menggunakan dua metode, yaitu cadangan retrospektif dan cadangan prospektif. Dalam penelitian ini menggunakan data simulasi asuransi jiwa seumur hidup pada nasabah berusia 25-35 tahun berdasarkan jenis kelamin dan biaya yang telah ditentukan oleh PT. X Samarinda. Cadangan premi akan dihitung menggunakan metode Zillmer pada cadangan prospektif. Perhitungan cadangan premi dibantu dengan Tabel Mortalitas Indonesia 1999 dan Tabel Mortalitas Indonesia 2011. Berdasarkan hasil analisis diperoleh karakteristik cadangan premi Zillmer nasabah laki-laki lebih besar dibandingkan dengan cadangan premi Zillmer nasabah perempuan. Cadangan premi Zillmer menggunakan Tabel Mortalitas Indonesia 1999 lebih tinggi dibandingkan dengan Tabel Mortalitas Indonesia 2011. Dengan demikian, penggunaan Tabel Mortalitas Indonesia 1999 lebih menguntungkan perusahaan asuransi dibandingkan dengan Tabel Mortalitas Indonesia 2011. Kata Kunci : Cadangan Premi, Cadangan Prospektif, Metode Zillmer, Tabel Mortalitas Indonesia. Cadangan premi adalah kewajiban perusahaan asuransi untuk membayar sejumlah dana yang harus disiapkan oleh perusahaan asuransi di kemudian hari. Cadangan premi dapat ditentukan menggunakan dua metode, yaitu cadangan retrospektif dan cadangan prospektif. Dalam penelitian ini menggunakan data simulasi asuransi jiwa seumur hidup pada nasabah berusia 25-35 tahun berdasarkan jenis kelamin dan biaya yang telah ditentukan oleh PT. X Samarinda. Cadangan premi akan dihitung menggunakan metode Zillmer pada cadangan prospektif. Perhitungan cadangan premi dibantu dengan Tabel Mortalitas Indonesia 1999 dan Tabel Mortalitas Indonesia 2011. Berdasarkan hasil analisis diperoleh karakteristik cadangan premi Zillmer nasabah laki-laki lebih besar dibandingkan dengan cadangan premi Zillmer nasabah perempuan. Cadangan premi Zillmer menggunakan Tabel Mortalitas Indonesia 1999 lebih tinggi dibandingkan dengan Tabel Mortalitas Indonesia 2011. Dengan demikian, penggunaan Tabel Mortalitas Indonesia 1999 lebih menguntungkan perusahaan asuransi dibandingkan dengan Tabel Mortalitas Indonesia 2011. Kata Kunci : Cadangan Premi, Cadangan Prospektif, Metode Zillmer, Tabel Mortalitas Indonesia.
Analisis Kestabilan Model Mangsa Pemangsa dengan Pemanenan Ambang Batas pada Populasi Pemangsa
Get PDF Abstrak Penelitian ini mengkaji model satu mangsa dan satu pemangsa yang saling berkompetisi. Fungsi predasi dari pemangsa diasumsikan menggunakan fungs1 respon Holling tipe II. Dengan asumsi bahwa adanya kompetisi intraspesifik pada popuasi pemangsa serta dilakukan pemanenan ambang batas pada popuasi pemangsa. Pada model tersebut dilakukan analisis tentang syarat kewujudan dan kestabilan titik keseimbangan interior. Analisis kestabilan titik keseimbangan interior dilakukan dengan metode linearisasi dan dengan memperhatikan nilai eigen dari matriks Jacobi yang diperoleh. Terdapat sepuluh titik kesetimbangan yang diperoleh pada model, satu diantaranya dapat dinterpretasikan. Titik tersebut dinyatakan stabil asimtotik. Berdasarkan hasil anasis menggunakan beberapa parameter, diketahui bahwa ada suatu waktu pemanenan ambang batas harus dihentikan karna sudah tidak memenuhi syarat kriteria ambang batas yang telah ditentukan.Kata kunci : Model mangsa pemangsa, Pemanenan ambang batas, Titik kesetimbanganAbstract This study examines the model of one prey and one predator who mutates each other. The predation function of predators is assumed to use the Holling type II response function. Assuming that the existence of intraspecific competition in predatory population and theshold harvesting for predatory population is carried out. In this model, an analysis of the actual conditions and stability of the interior balance point is carried out. Analysis of the interior stability balance points was carried out by linearization method and by taking into account the eigenvalues of the Jacobian matrix obtained. There are ten equilibrium points of engagement obtained on the model, one of which can be interpreted. This point is stated as asymptotically stable. Based on the results of analysis using several parameters, it is known that there is a time when harvesting the threshold must be stopped because it has not fulfill the specified criteria for threshold.Keyword : Prey-predator model threshold harvesting, equibrium poin
Transformasi Fourier Fraksional dari Fungsi Gaussian
Get PDFThe fractional Fourier transform is one of the generalizations of ordinary Fourier transform that depend on a particular angle . In this paper we will derive the fractional Fourier transforms of a function that is well known in the field of analysis, namely Gaussian function
Perbandingan Metode Regresi Logistik dan Random Forest untuk Klasifikasi Data Imbalanced (Studi Kasus: Klasifikasi Rumah Tangga Miskin di Kabupaten Karangasem, Bali Tahun 2017)
Get PDFPenelitian ini bertujuan untuk mendapatkan model terbaik untuk klasifikasi data imbalanced, yaitu rumah tangga sampel Susenas Maret 2017 di Kabupaten Karangasem, ke dalam kategori miskin atau tidak. Metode yang digunakan adalah Regresi Logistik dan Random Forest dimana masing-masing diterapkan skema cross validation (CV), yaitu stratified 5-fold CV, skema under sampling, oversampling dan combine sampling untuk mengatasi masalah data imbalanced serta proses feature selection. Hasil penelitian menunjukkan bahwa penerapan skema under sampling, oversampling dan combine sampling pada model Regresi Logistik memberikan efek meningkatnya rata-rata nilai sensitivity dan turunnya rata-rata nilai akurasi dan specificity. Sedangkan pada model Random Forest, efek tersebut hanya terlihat dari hasil skema under sampling saja. Proses feature selection dapat menurunkan varian nilai akurasi, specificity, sensitivity dan AUC pada model Regresi Logistik dan Random Forest hanya pada skema tertentu. Model terbaik secara keseluruhan adalah model model Regresi Logistik dengan skema combine sampling dan tanpa proses feature selection dengan rata-rata nilai akurasi, specificity, sensitivity dan AUC masing-masing sebesar 78,13%, 79,16%, 64,44% dan 77,77%