R Ratianingsih
Program Studi Matematika, Jurusan Matematika FMIPA, Universitas Tadulako, Jalan Soekarno-Hatta Km.09 Tondo, Palu 94118, Indonesia

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STUDI PENYEBARAN PENYAKIT FLU BURUNG MELALUI KAJIAN DINAMIS REVISI MODEL ENDEMIK SIRS DENGAN PEMBERIAN VAKSINASI UNGGAS Murwanti, Ica; Ratianingsih, Rina; Jaya, Agus Indra
Natural Science: Journal of Science and Technology Vol 2, No 1 (2013): Volume 2 Number 1 (March 2013)
Publisher : Univ. Tadulako

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Abstract

Program vaksinasi unggas yang dilakukan untuk menghambat penyebaran penyakit flu burung dapat dikaji melalui model matematika. Dalam penelitian ini penyebaran penyakit tersebut di amati melalui revisi model endemik SIRS dengan memperhatikan pemberian vaksinasi pada unggas. Hal ini dilakukan dengan merevisi kompartemen penyebaran penyakit tersebut yang selanjutnya digunakan untuk menentukan persamaan pembangun model yang  direpresentasikan dalam sistem persamaan diferensial. Sistem tersebut menggambarkan  interaksi antara kelompok manusia dan kelompok unggas. Analisa kestabilan sistem di kedua titik  kritisnya dilakukan dengan menentukan nilai eigen sistem yang diperoleh dari determinan matriks jacobi  linearisasi sistem di masing-masing titik kritis. Kestabilan sistem selanjutnya diamati dibidang (  yang dibagi oleh kurva parameter   . Kedua parameter tersebut secara berturut-turut menyatakan tingkat vaksinasi unggas dan tingkat kematian alami populasi unggas. Kestabilan di titik kritis kedua membutuhkan syarat  bahwa  tingkat kematian manusia karena flu burung ( ) harus lebih kecil dari  tingkat kelompok manusia yang telah sembuh dari flu burung terjangkit penyakit kembali ( . Hasil simulasi memperlihatkan bahwa penyebaran penyakit flu burung dapat diturunkan dengan program vaksinasi bila tingkat vaksinasi unggas lebih besar dari tingkat kematian alami unggas
MENGKAJI PENYEBARAN PENYAKIT FILARIASIS MELALUI IDENTIFIKASI DAERAH KESTABILAN DARI REVISI MODEL SAK Susilawati, Endang; Ratianingsih, Rina; Jaya, Agus Indra
Natural Science: Journal of Science and Technology Vol 2, No 2 (2013): Volume 2 Number 2 (August 2013)
Publisher : Univ. Tadulako

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Abstract

Model SARK merupakan model matematika yang dapat digunakan untuk menggambarkan penyebaran penyakit Filariasis. Kajian penyebaran penyakit tersebut dilakukan melalui pengamatan terhadap dinamika model SARK. Penyebaran penyakit ini dapat dicegah melalui program pengobatan. Pengkajian dilakukan dengan merevisi model SAK menjadi model SARK untuk selanjutnya dianalisa dengan menentukan titik kesetimbangan dan analisis kestabilan dengan metode linearisasi, mengkaji kestabilan sis­tem berdasarkan kriteria nilai eigen dari matriks Jacobian. Hasil penelitian ini adalah model SARK sebagai berikut :           yang memiliki satu titik kritis . Model SARK memberikan nilai eigen  dan  bernilai negatif dan  dan  bernilai positif. Kondisi awal rasio jumlah penduduk pada kelas infectives, recovered dan kronis masing-masing diambil secara berturt-turut 1, 0 dan 0. Hasil identifikasi terhadap peran parameter  dan  adalah semakin besar nilai laju kesembuhan , maka akan mengakibatkan waktu yang dibutuhkan oleh populasi infectives untuk memasuki populasi recovered semakin singkat. Hal ini disebabkan peran pengobatan pada populasi infektives sehingga populasi tersebut sembuh dari penyakit.
Deteksi Penyakit Schistosomiasis Melalui Identifikasi Telur Cacing Pada Feses Manusia Menggunakan Probabilistic Neural Network (PNN) windy rusma astuti; Hayani Anastasia; R Ratianingsih; J. W. Puspitaa; samarang samarang
Jurnal Vektor Penyakit Vol 14 No 1 (2020): Edisi Juni
Publisher : Balai Penelitian dan Pengembangan Kesehatan Donggala, Badan Penelitian dan Pengembangan Kesehatan, Kementerian Kesehatan RI

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (302.53 KB) | DOI: 10.22435/vektorp.v14i1.2013

Abstract

Abstract Schistosomiasis is a zoonotic disease caused by a blood worm in the Trematode class of the genus Schistosoma that lives in a vein. This disease is one of the oldest and most important diseases in the world. In Indonesia, Schistosomiasis is caused by Schistosoma Japonicum Sp. This study focused on the detection of Schistosomiasis disease through identification of worm eggs found in human feces. Based on the result of the observations of the Schistosomiasis Laboratory in Kaduwaa and Dodolo Villages in North Lore Subdistrict, Poso Regency it was found the worm eggs of other species in feces of resident in Kaduwaa and Dodolo villages, namely Ascaris Lumbricoides worm eggs and Ancylostoma Duodenale worm eggs. Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) methods are used to extract the egg image for the identification process, while Probabilistic Neural Network (PNN) methods were used to classify the species of the egg. The identification results are influenced by image capture techniques, image cutting techniques, the pixel size in the image, smoothing parameter values, and the number of sample images that used to train and test the data. The average accuracy of worm egg images identification using PNN is 98% with using the value of smoothing parameters 0,2. This result also shows that the Probabilistic Neural Network (PNN) method could be applied to identify the image of worm eggs found in human feces. Abstrak Schistosomiasis merupakan penyakit zoonosis yang disebabkan oleh cacing darah kelas Trematoda dari genus Schistosoma yang tinggal dalam pembuluh darah vena. Penyakit ini merupakan salah satu penyakit tertua dan paling penting di dunia. Di Indonesia, Schistosomiasis disebabkan oleh cacing Schistosoma Japonicum Sp. Penelitian ini berfokus pada deteksi penyakit Schistosomiasis melalui identifikasi telur cacing yang terdapat pada feses manusia. Hasil observasi di Laboratorium Schistosomiasis desa Kaduwaa dan Desa Dodolo Kecamatan Lore Utara Kabupaten Poso memperlihatkan ditemukannya pula telur cacing dari spesies lain pada feses masyarakat desa Kaduwaa dan Desa Dodolo, yaitu telur cacing Ascaris Lumbricoides dan Ancylostoma Duodenale. Metode Principal Component Analysis (PCA) dan Linear Discriminant Analysis (LDA) digunakan untuk ekstraksi citra telur dalam proses identifikasi, sementara metode Probabilistic Neural Network (PNN) digunakan untuk klasifikasi spesies telur. Hasil identifikasi dipengaruhi oleh teknik pengambilann citra, teknik pemotongan citra, besarnya piksel pada citra, nilai smoothing parameter, serta jumlah citra sampel yang digunakan untuk data pelatihan dan pengujian. Akurasi rata-rata identifikasi citra telur cacing menggunakan PNN tertinggi yaitu dengan menggunakan nilai smoothing parameter . Hal ini menunjukkan bahwa metode Probabilistic Neural Network (PNN) dapat diterapkan untuk identifikasi citra telur cacing yang terdapat pada feses manusia.
RANCANG BANGUN SISTEM INFORMASI TERPADU FMIPA UNIVERSITAS TADULAKO M S Ismail; I Wayan Sudarsana; Rina Ratianingsih
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 13 No. 1 (2016)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1344.429 KB) | DOI: 10.22487/2540766X.2016.v13.i1.7493

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RANCANG BANGUN SISTEM INFORMASI TERPADU FMIPA UNIVERSITAS TADULAKO
The role of top-predator in the preservation of coral reefs ecosystem Jaya, Agus Indra; Puspita, Juni Wijayanti; Ismawati, Nurul; Ratianingsih, Rina
Communication in Biomathematical Sciences Vol 1, No 1 (2017)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (265.337 KB) | DOI: 10.5614/cbms.2017.1.1.5

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The coral reef ecosystem in Indonesian as part of Coral Triangle Region has been significantly decreasing in the last decades. This damage has been known widely due to coastal development, pollution, and uncontrolled fishing and harvesting. Among other many living species in the environment, the existence of coral reefs is directly related to the existence of Drupella sp. and Acanthaster planci as the coral predators, while the existence of the predators also related to the Napoleon wrasse and Giant triton/ Trumpet shell as the top predator. This study discusses the interaction among the coral reefs, the predators and the top predators, which is represented in a dynamical model of predator-prey-top predator. In the absence of top predators, the system is reduced as a two-predator-prey model with only one surviving predator, Acanthaster planci, which has more effective predation behavior. The role of Napoleon wrasse as a top predator of both Acanthaster planci and Drupella sp. is significantly important to protect the coral reef from the excessive predation from Acanthaster planci and Drupella sp. A stable co-existence is shown between coral reef, Acanthaster planci and Napoleon wrasse. With the appearance of Giant tritons which predate only Acanthaster planci, a co-existence between five species may occur with abundant species of Giant triton.
PENGATURAN PERSEDIAAN BERAS DI PERUM BULOG DIVRE SULTENG DENGAN METODE ECONOMIC ORDER QUANTITY (EOQ) Nildawati Nildawati; R Ratianingsih; A Sahari
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 2 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (681.258 KB) | DOI: 10.22487/2540766X.2018.v15.i2.11355

Abstract

Perum BULOG of Central Sulawesi Division is a national rice logistic company that its responsibility is to guarantee the sufficiency to meet the rice needs. Perum BULOG also responsible to keep rice price stability. One of the rice price component is the inventory costs that need to be managed. In this research the management is refered to the rice scheme demand of four storages, that are Olaya, Lawanga, Jaya Kencana Toili and Galang. This study uses EOQ (Economic Order Quantity) that consist of five priorities, that are determining the of economical order, determining the amount of safety stock, determining the maximum inventory quantities, determining the reorder point and determining total inventory cost. The results showed that the number of economical order storage of Olaya is 1.817.120,57 kg/message, Lawanga is 1.893.400,78 kg/message, Jaya Kencana Toili is 1.575.543,38 kg/messages and Galang is 1.578.742,75 kg/message. The total Inventory Security for Olaya is 32.371,28 kg, Lawanga is 41.020,07 kg, Jaya Kencana Toili is 30.630,61 kg, and Galang is 57.307,99kg. The maximum inventory for Olaya is 1.849.491,85 kg, Lawanga is 1.934.420,85 kg, Jaya Kencana Toili is 1.606.173,99 kg, and Galang is 1.636.050,74 kg. The reorder point is proposed when rice stock of Olaya reaches 323.664,52 kg, Lawanga reaches 357.282,87 kg, Jaya Kencana Toili reaches 249.620,29 kg and Galang reaches 277.188 kg. The total inventory cost that use Economic Order Quantity is Rp. 2.507.626,39 for Olaya, Rp. 2.612.893,07 for Lawanga, Rp.2.174.249 ,87 for Jaya Kencana Toili, and Rp 2.178.665,00 for Galang. The Efficiency cost of rice supplies BULOG Division is Rp.40.405,29 for Olaya, Rp. 719.256,02 for Lawanga, Rp. 51187.63 for Jaya Kencana Toili, and Rp. 153.528,73 for Galang. These result gives greatest efficiency at the cost of supplies of Perum BULOG Division Central Sulawesi for Lawanga 22% as much.
Analisis Kestabilan Penyebaran Penyakit Antraks Pada Populasi Hewan Dengan Pemberian Vaksinasi: Studi Kasus Untuk Infeksi Pada Populasi Manusia Megawati; R Ratianingsih; Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 16 No. 2 (2019)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (949.536 KB) | DOI: 10.22487/2540766X.2019.v16.i2.14989

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ABSTRACTAnthrax is an infectious disease that caused by the Bacillus anthracis bacteria. The disease attacks animals such as cows in acute and preacute stage. Anthrax is a zoonotic disease that can be transmitted to humans through three types of media that are skin, digestive and respiratory tracts. To overcome the high death risk, treatment and vaccination of the period 6 – 12 months are conducted. The aims of this study is developing a mathematical model of anthrax spread in animal populations with vaccination treatment. The model is also consider human populations, such that the SIRSV model (susceptible, Infected, Recovered, susceptible and Vaccine) is used for animal population and SI model (susceptible, Infected) is used for human population. The stability of model is analyzed at the critical points by linearization method. The free-disease unstable critical point and the stable endemic critical point are derived. The simulation shous that the number of infected animal and infected human population is not significantly different and indicates that the vaccination treatment could overcome the spread of anthrax succesfully.Keywords : Anthrax, Critical Point Endemic, Critical Point Non Disease, linearization method, Mathematical Models
MODEL DINAMIK FASE PERTUMBUHAN BUAH KELAPA Yulinda Yulinda; A I Jaya; R Ratianingsih
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 2 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (585.558 KB) | DOI: 10.22487/2540766X.2018.v15.i2.11348

Abstract

Coconut (Cocos nucifera L.) is one of the Indonesian potential natural plant resources. Its fruit is a main part of the tree that plays an important role in raw materials industry. It is because the material could be processed to be a benefical various products. The diversity of the coconut fruit products leads to the importance of the study on coconut growth phase development. The model is expressed in a system of differential equation ???????? ???????? = ???? − ???????? − ????1????, ???????? ???????? = ???????? − ????2???? − ????????, ???????? ???????? = ???????? − ????3???? − ϵ????, ???????????? ???????? = ???????? − ????4???????? − γ????????, ???????????? ???????? = ???????????? − ????5???????? − ????????????, ???????????? ???????? = ???????????? − ????6???????? . The dinamic of coconut growth phase is studied by consider its stability at the critical point. The stability is determined using linearization method. The solution is analyzed both analitically and numerically. Simulated a stable endemic critical point indicates that the coconut production could be well prevent in each phase of growth
MENGKAJI MODEL PENGENDALIAN POPULASI AEDES AEGYPTI DENGAN STERILE INSECT TEHNIQUE (SIT) DAN KOMBINASINYA DENGAN INSEKTISIDA Wati, I; Ratianingsih, R; Jaya, Agus Indra
Natural Science: Journal of Science and Technology Vol 3, No 1 (2014): Volume 3 Number 1 (March 2014)
Publisher : Univ. Tadulako

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Abstract

Dengue fever is one of disease which can be transmited by Aedes aegypti. However the prevention on this disease is become global concern. One approche that can be done is by controlling of mosquito population. Related to that issue, this study was done by an application of potryagyn maximum principle in optimal control theory, based on Sterile Insect Technique (SIT). It can be done biologically by introduction of male sterile mosquito (mutan which can be produce by mutagen such as gamma radiation) into the population. It expected that the number of sterile mosquitos will increase by the time. Our result showed that the population of juvenile, immature male and female mosquitos,  fertile male and female, and also sterile male mosquito on the population will grow and reach the stagnan condition after 50 days. Those data indicate that the number of sterile male will increase without any reduction of the population itself. If this method be combained with insecticide chemical method, the population of mosquitos can be reduced/eliminated efectively.
MENGKAJI MODEL PENGENDALIAN POPULASI AEDES AEGYPTI DENGAN SIT DAN KOMBINASI SIT DAN INSEKTISIDA Wati, Indra; Ratianingsih, Rina; Jaya, Agus Indra
Natural Science: Journal of Science and Technology Vol 2, No 3 (2013): Volume 2 Number 3 (December 2013)
Publisher : Univ. Tadulako

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Abstract

Salah satu penyakit yang diakibatkan oleh gigitan Aedes aegypti adalah Demam Berdarah Dengue (DBD). Pencegahan penyakit ini menjadi prioritas global karena dapat berakibat kematian pada penderita. Untuk menekan jumlah penderita Demam Berdarah Dengue (DBD) maka dilakukan suatu program yang dapat mengendalikan populasi Aedes aegypti. Teori optimal kontrol diterapkan pada model populasi Aedes aegypti sebagai metode pengendalian secara matematika dengan menerapkan Prinsip Maksimum Pontryagin.Secara biologi, metode pengendalian yang digunakan adalah Sterile Insect Technique (SIT), yang  merupakan teknik pengendalian dengan memberikan mutagen atau radiasi gamma pada nyamuk jantan sehingga menjadi steril. Nyamuk steril inilah yang nantinya akan dilepaskan ke lingkungan untuk kawin dengan nyamuk normal sehingga nyamuk normal akan menjadi steril. Hasil penelitian menunjukkan bahwa program Sterile Insect Technique (SIT) hanya bersifat mensterilkan dan tidak menekan jumlah populasi nyamuk. Untuk itu penelitian ini membahas kombinasi program Sterile Insect Technique (SIT) dan Insektisida yang merupakan teknik pengendalian secara kimia. Hasil penelitian menunjukkan bahwa kombinasi programSIT dan Insektisida dapat membasmi populasi nyamuk dengan baik.