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ANALISIS KESTABILAN MODEL MATEMATIKA PADA PENYEBARAN KANKER SERVIKS MENGGUNAKAN KRITERIA ROUTH-HURWITZ Hasnawati Hasnawati; R Ratianingsih; J W Puspita
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 14 No. 1 (2017)
Publisher : Program Studi Matematika, Universitas Tadulako

ANALISIS KESTABILAN MODEL MATEMATIKA PADA PENYEBARAN KANKERSERVIKS MENGGUNAKAN KRITERIA ROUTH-HURWITZ

KESTABILAN MODEL MATEMATIKA PENULARAN PENYAKIT GONORRHOEAE A P Aditya; R Ratianingsih; J W Puspita
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 14 No. 2 (2017)
Publisher : Program Studi Matematika, Universitas Tadulako

KESTABILAN MODEL MATEMATIKA PENULARAN PENYAKIT GONORRHOEAE

PERUBAHAN DISTRIBUSI MERKURI (Hg) TERHADAP WAKTU DI SEDIMEN SUNGAI POBOYA I Febrianti; R Ratianingsih; J W Puspita
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 1 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Poboya is illegal gold mining area at Palu City. The amalgamate process of gold extraction is prepared traditionally using mercury. Tailing of this process which contains mercury is throwed away to the ground. The mercury contain will infiltrate to the soil water and later on pollute Poboya’s river. Related to the mercury that categorized as dangerous material, this research purposes to investigate the mercury distribution changing at Poboya’s river sediment. The mercury distribution changing is investigated by modify the advection-diffusion equation model. The model was completed by the initial conditions and Neumann boundary conditions. To get the numerical solutions, it is used a numerical scheme namely Duffort Frankel finite difference method for the second derivative, and Center Scheme for the first derivative. The solution represents the mercury distribution changing with respect to time at the Poboya’s river sediment. The simulation result explains that 0,0521 ppm mercury is distributed from the upper bound (current source) observation domain following the sediment direction (to estuary) caused by the advection process and decreased due to the diffusion process. For , the mecury was distributed 0,00285 m to the estuary direction with the mercury concentration is 0,005 ppm, until , mercury was distributed 0,00832 m to estuary with mercury concentration is 0,005 ppm. In fact that at the estuary (lower bound), the 0,0244 ppm mercury that was already deposited will be diffused in an opposite direction. The advection process and the low initial mercury concentration, makes the reached distribution distance is no longer far comparing to the opposited mercury distribution. For the mercury was distributed 0,000822 m to the upper direction with mercury concentration is 0,005 ppm, until , the mercury was distributed 0,000873 m with mercury concentration is 0,005 ppm

MODEL PENGENDALIAN ALAMI PENYAKIT EMBUN JELAGA OLEH JAMUR CAPNADIUM SP PADA TANAMAN CENGKEH MENGGUNAKAN KUMBANG HELM CYCLONEDA SPP SEBAGAI PREDATOR KUTU DAUN (COCCOUS VIRIDIS GREEN Sudirman Sudirman; R Ratianingsih; J W Puspita
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 16 No. 1 (2019)
Publisher : Program Studi Matematika, Universitas Tadulako

Soot dew disease is one of the clove plant diseases caused by fungi Capnadium sp. fungus Capnadium sp living on filth of aphids Coccous Viridis Green. The fungus is spread by vectors of black ants that exist on a clove vulnerable. To control the disease naturally, people utilize the helmet beetles Cycloneda spp as a pest predator of aphids Coccous Viridis Green. The mathematical models that represent the natural control of the disease was adapted from the SI model. The model provides 9 exiting critical points which describes the state of the system. The results of the stability analysis of the critical points using the method of Linearization and Routh-Hurwitz shows that there are 4 disease-free critical points such that the solution can be maintained in the neighbourhood of the critical points. All endemic critical points are unstable such that the solution will leave the critical points. Simulation at the endemic critical points indicates the existence of helmet beetles Cycloneda spp population that able to suppress the spread of this disease by preying aphids Coccus Viridis Green.Keywords : Dew Soot, Helmet Beetles, Aphids, Mathematical Models.

Kendali Optimal Model Prognosis Sindrom Metabolik Dengan Faktor Resiko Obesitas Dan Diabetes Melitus Tipe II Menggunakan Minimum Pontryagin Nurannisa; R Ratianingsih; J W Puspita
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 16 No. 2 (2019)
Publisher : Program Studi Matematika, Universitas Tadulako

ABSTRACTMetabolic syndrome (SM) is a compound of risk factors of cordiovascular disease occurancy. Obesity and type IIdiabetes mellitus are the main two of the risk factors. The epidemiological data shous that the prevalence ofmetabolic syndrome in the world is 20-25%. The objective of these research is control to minimize the prognosisof the disease among the SM population that have obesity and type II DM risk factors. The pontryagin minimumprinciple is used to determine the optimal solution of the prognosis model that the optimal control. The solution is derived from the state and co-state state equations that are evaluated of the drug that give to the sufferer in stationary conditions. The performance Index was designed to minimize the number of SM population that suffer obesity and type II diabetes mellitus and the use of sulfonilurea that given as the normoweighted populations and biguanid for obese populations. The simulation of the optional solution shows that the optimal control was derived to control the number SM that have population of the optional solution obesity and type II DM risk with optimal biguanide 500 mg and sulfonilurea 5 mg as much.Keywords : Metabolic Syndrome, Minimum Pontryagin, Obesity, Stability ,Type II Diabetes Mellitus.

Mengkaji Perputaran Uang Bank Melalui Model Kaldor-kalecki: Tinjauan Numerik Untuk Sistem Kartu Kredit A Sehani; R Ratianingsih; J W Puspita
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020)
Publisher : Program Studi Matematika, Universitas Tadulako

Credit Card is a card payment instrument, where the cardholder's payment obligation is firstly fulfilled by the acquirer or publisher which use third party funds in the form of investments to pay the obligation payment of cardholder. These investment funds are managed as the initial fund of credit card customers. Some of the generated profits could be saved as bank deposits, while others are used for joint capital investment funds. The preview description shows the circulation of bank deposit of the credit card system which mathematically corresponds to the concept represented by Kaldor-Kalecki model. The aims of this study is that money circulation process is represented numerically by such model solution using the Runge-Kutta method. The interpretation of the numerical solution of the Kaldor-Kalecki model of the credit card system is simulated for Bank Mega's financial report data in 2017, the results shows that Bank Mega was found a decline of the number of credit card production. It could be said that the numerical solutions well represented the condition of the credit card system issued by Bank Mega. Negative values of numerical solution also reviews as period of the Bank investment

Sistem Pendukung Keputusan Untuk Mendeteksi Penyakit Diabetes Melitus Tipe 2 Menggunakan Metode Learning Vector Quantization (LVQ) N Aliyanti; R Ratianingsih; J W Puspita
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 2 (2020)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2020.v17.i2.15336

ABSTRACT Diabetes is a chronic disease that occurs when the pancreas does not produce enough insulin, or when the body can not effectively use the insulin that is produced. Diabetes mellitus can be divided into two types: Type 1 diabetes mellitus and diabetes mellitus type 2. This study aims to detect diabetes mellitus and may predict the development status (Metabolic Syndrome) using Learning Vector Quantization. The data needed to detect type 2 diabetes are blood sugar levels, genetics, age, physical activity, diet, smoking habits, body mass index, gender and abdominal circumference. In addition, the data also used HbA1C and cholesterol levels to detect the status of the development of type 2 diabetes mellitus (Metabolic Syndrome). The classification process is divided into two stages: stage 1 to determine the type 2 diabetes or Non diabetes mellitus, and phase 2 to predict the prognosis of type 2 diabetes into Metabolic Syndrome or Non Metabolic Syndrome (the patient is still in the category of type 2 diabetes) performed on 200 data respectively divided into 80 training data and 120 testing data. Best detection results at stage 1 that is equal to 96.67% can be obtained using learning rate (α) of 0.7, and the rate of decrement (decα) of 0.75.While the best detection results at stage 2 average accuracy rate of 92.5% using a variety of learning rate (α) and the rate of decrement (decα). Error detection in stage 2 occurs only in the Metabolic Syndrome data detected as Type 2 diabetes mellitus. Keywords : Accuracy, Diabetes Mellitus, Learning Vector Quantization

Dinamika Populasi Pada Ekosistem Mangrove Hajar; J W Puspita; N Nacong; Ridwan
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 18 No. 1 (2021)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2021.v18.i1.15534

Budidaya mangrove merupakan salah satu upaya untuk meminimalisir kerusakan ekosistem laut dan lingkungan sekitarnya saat terjadi tsunami. Eksistensi ekosistem mangrove perlu dijaga dan dilestarikan secara berkelanjutan. Kepiting Uca memiliki peranan penting pada rantai makanan yang berlangsung dalam ekosistem mangrove. Penelitian ini bertujuan mengkaji interaksi antara populasi mangrove dan populasi kepiting Uca dalam ekosistem mangrove melalui pendekatan model matematika. Kami memperoleh empat titik kritis dari model yang telah dibangun. Tiga titik kritis dari model matematika eksis tanpa syarat, namun tidak stabil. Sedangkan titik kritis keempat yang menggambarkan kondisi koeksistensi populasi mangrove dan kepiting Uca dapat dijamin kestabilan lokalnya jika syarat kestabilannya terpenuhi. Hal ini mengindikasikan bahwa kehadiran populasi kepiting Uca dapat menjaga kelestarian ekosistem mangrove. Simulasi numerik diberikan untuk mendukung hasil analitik.

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