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All Journal Natural Science: Journal of Science and Technology Jurnal Vektor Penyakit JURNAL ILMIAH MATEMATIKA DAN TERAPAN Communication in Biomathematical Sciences Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Transcendent Journal of Mathematics and Applications

Rina Ratianingsih

Department Of Mathematics, Faculty Of Mathematics And Natural Sciences , Tadulako University, Palu, Indonesia

Author-ID : 358254

Computer Science & IT Economics, Econometrics & Finance Environmental Science Health Professions Immunology & microbiology Mathematics Physics Public Health Social Sciences Veterinary

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ANALISIS KESTABILAN MODEL MATEMATIKA PENYEBARAN PENYAKIT SIFILIS PADA MANUSIA Muliyani, N; Ratianingsih, R; Nacong, N
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 1 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Syphilis is a sexually transmitted infection caused by the bacterium Treponema pallidum spiroset subspecies pallidum. Transmitted through sexual contact, the infection can also be transfered from mother to fetus during pregnancy or at birth, that causes congenital syphilis. The mathematical model that represents the spread of the disease was adapted from a mathematical model SEI. The model classifiles human population into vulnerable suscepted Â women and men, Exposed , and Infected , sub-populations of women vulnerable , sub-populations women incubation period , sub-populations of women infected Â and a sub-population of men vulnerable , sub-populations incubation period male , sub-populations laki- infected men Â considered in the model. The derived models gives two critical point that is free disease and endemic critical point. The existence of a critical point Â must satisfye Â and . The model was Â analyzed by the linierized method and Routh-Hurwitz criteria to determine the system stability. The simulation shows that, in case of free-disease Â syphilis spread condition, the population of women and men has increased. The growth of women population is higher than the men population. it means that the spread of syphilis occurs faster in the men sub-population. In endemic condition of syphilis disease spread, the women population will growth rapidly than the men population.

MEMBANGUN MODEL PENYEBARAN PENYAKIT AKIBAT ASAP KEBAKARAN HUTAN Kurniawan, B; Ratianingsih, R; Hajar, Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 1 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Forest fires impact a very serious problem because it could cause health problem, especially respiratory disease such as (ISPA), Asthma and Bronchitis. The study of the health disorders is conducted by consider mathematicaly the spread of disease due to forest fires smoke. The model is constructed by devide the human population into six subpopulations, that is vulnerable S(t), exposed E(t), Asthma infected A(t), Bronchitis infected B(t) and recovered R(t).The governed model is analyted at every critical points using Routh-Hurwitz method. The results gives two critical points that describe a free disease conditions ( ) and an endemic conditions ( ). A stabil ( ) is occured if Â and Â where the threshold point of the stability is expressed as Â and Â . Endemic conditions Â will be asymptotically stable when Â and Â with Â . The condition of free disease of forest fires is occured in a long time period, while the endemic conditions is occurred in a short time period. It could be interpreted that the disease spread due to the forest fires smoke is not easy to overcome.

MENGKAJI PERILAKU HARGA KOMODITI PANGAN DI KOTA PALU MENGGUNAKAN METODE BACKPROPAGATION Peole, I N; Ratianingsih, R; Lusiyanti, D
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 1 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Artificial neural network is an information processing paradigm that is inspired by biological neural cell systems, like the brain, that processes information. The purpose of this research is to develop neural networks to predict the price of food commodities using backpropagation method. The research was conducted by using the rate of monthly price of food commodities in Palu from January 2011 - December 2015. The data is used to predict food commodity prices forduring 2016. The backpropagation networks consists of three layers. The first layer of input is constructedin the form of monthly prices of IR 64, ciherang, membramo, cimandi, superwin, sintanur, cisantana, sticky black, sticky white, yellow corn dry, white corn, soybeans, peanuts, green beans, cassava, sweet potato, onion, garlic, red pepper large, red pepper curls, cayenne pepper, cabbage round, potatoes, tomatoes, carrots, cauliflower, beans, onion, avocado, red apples, green apples, oranges, jackfruit, mango, pineapple, papaya, banana, banana horns, rambutan, bark, olive, durian, watermelon, and mangosteen from January â€“ December that consist of 12 variables. One hidden layer consistof five neurons and the other one is the output, that isÂ the food commodity prices. The training process shows that on a maximum iterations on 500, constant learning rate 0,3 and 0,6 momentum, the predictions have 97.92% of level accuracy. The identification resultof food commodity prices behavior in Palu is predicted as follow: IR 64 Rp7.387, ciherang Rp8.182, membramo Rp8.150, cimandi Rp8.131, superwin Rp8.228, sintanur Rp8.660, cisantana Rp8.122, black sticky rice Rp21.383, white sticky rice Rp16.558, dry yellow corn Rp5.983, white corn Rp9.283, soybeans Rp14.600, peanuts Rp20.008, green beans Rp16.375, cassava Rp8.225, sweet potato Rp8. 542, red onion Rp28.550, garlic Rp21.208, red chili Rp27.308, curly red chili Rp23.650, cayenne Rp36.450, round cabbage Rp6.833, Rp12.067 potatoes, tomatoes Rp6.108, carrots 11.000, cauliflower Rp8.625, beans Rp10.333, scallion Rp25.242, avocado 11.000, red apple Rp29.023, green apple Rp31.067, orange Rp6.083, jackfruit Rp23.483, mango Rp11.187, pineapple Rp8.183, papaya Rp10.600, bananas Rp8.481, horn banana Rp2.683, rambutan Rp8.450, barking Rp5.625, tan Rp8.366, durian Rp19.208, watermelon Rp14.528 and mangosteen Rp18.067. It is predicted that the food commodity prices increased monthly.

PERUBAHAN DISTRIBUSI MERKURI (Hg) TERHADAP WAKTU DI SEDIMEN SUNGAI POBOYA Febrianti, I; Ratianingsih, R; Puspita, J W
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 Poboyaâ€™s river. Related to the mercury that categorized as dangerous material, this researchÂ purposes to investigate the mercury distribution changing at Poboyaâ€™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 Poboyaâ€™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 distributedÂ 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. ForÂ Â 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 DINAMIK FASE PERTUMBUHAN BUAH KELAPA Yulinda, Yulinda; Jaya, A I; Ratianingsih, R
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 2 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

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 ð‘‘ð‘€ ð‘‘ð‘¡ = ð‘… âˆ’ ð›¼ð‘€ âˆ’ ðœ‡1ð‘€, ð‘‘ð‘ƒ ð‘‘ð‘¡ = ð›¼ð‘€ âˆ’ ðœ‡2ð‘ƒ âˆ’ ð›½ð‘ƒ, ð‘‘ð¶ ð‘‘ð‘¡ = ð›½ð‘ƒ âˆ’ ðœ‡3ð¶ âˆ’ Ïµð¶, ð‘‘ð‘€ð‘Ž ð‘‘ð‘¡ = ðœ–ð¶ âˆ’ ðœ‡4ð‘€ð‘Ž âˆ’ Î³ð‘€ð‘Ž, ð‘‘ð‘€ð‘ ð‘‘ð‘¡ = ð›¾ð‘€ð‘Ž âˆ’ ðœ‡5ð‘€ð‘ âˆ’ ðœŽð‘€ð‘ , ð‘‘ð‘€ð‘ ð‘‘ð‘¡ = ðœŽð‘€ð‘ âˆ’ ðœ‡6ð‘€ð‘ . 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

MEMBANGUN MODEL DINAMIS PENANGKARAN POPULASI MALEO (Macrochepalon Maleo) YANG MEMPERTAHANKAN EKSISTENSINYA DARI PREDATOR Gusmawan, T; Ratianingsih, R; Nacong, N
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 2 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Maleo (Macrocephalon maleo) is one of the endangered endemic species of Sulawesi due to diminishing spawning habitat, community exploitation and predators. The dynamic model of maleo population captivity to conserve its existence from predators is a mathematical model that describes the dynamics of maleo population growth cycle (M) with the threat of predators (P). In this study, the population of eggs maleo divided into two groups that are eggs in the free zone (Tb) and eggs in breeding (Tp). The eggs are in the captive breeding will be transfered to the exposure group (E). The model represents the interaction between the predators and populations reflecting maleo in each growth phase. The model has two critical points, namely the critical point ð‘‡1 = ( 0,0,0,0, ðœ‘ Âµ2 ) describing maleo extinction condition and critical point ð‘‡2 = (ð‘€âˆ— , ð‘‡ð‘âˆ— ,ð¸ âˆ— , ð‘‡ð‘âˆ— , ð‘ƒ âˆ— ) which describes the endemic conditions of maleo growth dynamics. The stability analysis shows that the system is unstable at both critical points. It is because the values of the first column in the Routh Hurwitz table changes in sign. Simulations of the endemic conditions showed that the maleo and egg populations in the free zone are decreasing with respect to time even though the exposed maleo still exist. The unstable endemic indicates that the existence of maleo breeding program in conservation areas still need another efforts support.

PENANGANAN PRODUKSI BUAH PISANG PASCA PANEN MELALUI MODEL PENGENDALIAN GAS ETILEN Dafri, M; Ratianingsih, R; Hajar, Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 2 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Bananas is a kind of fruit that has many benefits and economic value. However, because it is perishable, an unappropriate post-harvest handling will decreasing the economic value. Many factors affect the ripening of bananas, one of it is ethylene gas. The ethylene gas that contained in the banana flows from the higher concentration to the lower one. The flow should be controlled in order to make it decaying properly. Temperature is a parameter that affects the flow of ethylene. This research offers storage temperature regulation such that the life time of banana could be extended. A mathematical model that represents the ethylene flow among the subpopulations is discussed. The population are devided into sub-population of unripe bananas, normal ripe bananas, ripe bananas wounds, and rotten bananas. The Stability of the model is evaluated in the critical point by Jacobian matrix and the Routh Hurwitz Criteria. The control is design by minimizing the temperature parameters using the Pontryagin Minimum Principle. Simulation is ilustrated in four cases, the firts case is no bananas wound initially, second case is no bananas rot initially, third case is no ripened normal bananas initially, and the fourth case is the bananas ripe initially exiting. The simulations shows that before controling the temperature, in the amount of 120 bananas of firts case, the proces is condcuted in sixteen days, ten days for the second case, nine days for the third case, and eight days for the fourth case. After controling the temperature, for some amount of bananas of firts case, the proces is conduted in seventeen days, eleven days for the second case, ten days for the third case, and nine days for the fourth case.

PENGATURAN PERSEDIAAN BERAS DI PERUM BULOG DIVRE SULTENG DENGAN METODE ECONOMIC ORDER QUANTITY (EOQ) Nildawati, Nildawati; Ratianingsih, R; Sahari, A
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 2 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

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.

KAJIAN MATEMATIS FITOREMEDIASI: PENENTUAN DISTRIBUSI KONSENTRASI MERKURI (Hg) PADA AKAR BAKAU (Rhizophora mucronata) MENGGUNAKAN METODE BEDA HINGGA Nurhidayah, Nurhidayah; Jaya, A I; Ratianingsih, R
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 16 No. 1 (2019)
Publisher : Program Studi Matematika, Universitas Tadulako

The existence of mercury as a pollutant in the water environment caused by industrial activities and natural process can gives directly and indirectly impact to the marine life. As an example, it makes the reduction of water quality. Considering the mercury as the most dangerous pollutant, it would require a proper handling program to reduce the amount of mercury in the water environment. such as planting of hyperakumulator plant. Rhizophora mucronata is one of hyperakumulator plants that can absorb mercury effectively. This study discusses the distribution of mercury (Hg) concentrations in Rhizophora mucronata roots, that is investigated mathematically using diffusion model. The modification of the model is ð‘¢ð‘¡ = ð‘˜ð‘¢ð‘¥ð‘¥ + ð‘“(ð‘¥), where ð‘“(ð‘¥) states absorption roots function in absorbing mercury. A numerical scheme is derived by apply the finite difference method explicit scheme to get the numerical solutions. The simulation shows that the mercury concentrations is reduced from the root bark of the roots towards the central part. The difference of concentration distribution of mercury (Hg) in each layer, from the root bark of the roots towards the central part, will also decreases from the first week to the fifth week of time interval.Keywords : Diffusion Equations, Explicit Finite Difference Schemes, Mangrove, Mercury

KENDALI OPTIMAL MODEL PENYEBARAN PENYAKIT BLOOD DESEASE BACTERIUM (BDB) PADA TANAMAN PISANG KEPOK DENGAN INOKULASI BAKTERI ENDOFIT Islami, N; Ratianingsih, R; Nacong, N
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 16 No. 1 (2019)
Publisher : Program Studi Matematika, Universitas Tadulako

Banana plants are the most widely grown plants in Indonesia. In its growth period, banana plants can experience an attack of the disease Blood Desease Bacterium (BDB) caused by Ralstonia solanacearum Phylotipe IV which is the main cause of the loss of banana yield in Indonesia. BDB can cause plant death and crop failure. To represent this phenomenon a mathematical model was developed to reperents the spread BDB of Kepok banana plants by inoculating endophytic bacteria. Adapted 2 SEI epidemic models for banana and SI plant populations for the insect population trigona spp. The SEI model of banana population is divided into 3 subclasses, namely the BDB susceptible population class (ð‘†â„Ž), exposed population class (ð¸â„Ž), and population class infected with BDB disease (ð¼â„Ž). It was also observed the class of banana population that received treatment (ð‘†ð‘¡ ). This group was a class of banana population that was given endophytic bacteria. The SI model was adapted for the insect population trigona spp. which are grouped into 2 subclasses, namely the vulnerable population class to infect BDB (ð‘†ð‘£ ), and the population class is ready to infect BDB (ð¼ð‘£ ). Analysis of the stability of the model is carried out at a critical point then an optimal control of the spread of BDB disease through inoculation of endophytic bacteria is carried out. Controlling the rate of suppression of BDB transmission in bananas is done by keep the Î² parameters (isolates of endophytic bacteria inoculated into banana plants) for the purpose of reducing the incidence of BDB in banana plants. The simulation are carried out for optimal control design, using the principle of minimum Pontryagin, optimal solutions are obtained which show that controlling BDB disease with endophytic bacterial inoculation is said to be successful because it can reduce the number of infected banana plant populations.Keywords : BDB Disease, Endophytic bacteri, Inoculation, Ralstonia Solanacearum Phylotipe IV , Trigona spp., The Minimum Principle of Pontryagin.

Co-Authors Abdul Mahatir Najar Abu, M Aditya, A P Agus Indra Jaya Agusman Sahari Ahmad, M T Aldri Frinaldi Aliyanti, N Asran, Erni Azim Chijra Dafri, M Desy Lusiyanti Endang Susilawati Fadilah, R Fauji, M Febrianti, I Febrianti, Ratih Govan, Govan Gusmawan, T Gusni, Gusni Hajar Hajar Hardiyanti Hasbi Hasnawati Hasnawati Hayani Anastasia Husnah, Siti I Wati I Wayan Sudarsana Ica Murwanti Indra Wati Islami, N Ismail, M S Ismawati, Nurul J. W. Puspitaa Jaya, A I Juni Wijayanti Puspita Kamisi, N Karini, I Khairiah, J Kurniawan, B Landita, A Lasongke, Fahri Alam Maasawet, R R Marwan Marwan Megawati Muliyani, N Mustakim, J R Mutmainnah, M Nasria Nacong Nildawati, Nildawati Nirmalasari, Ririn Nuranisa, Nuranisa Nurannisa Nurhidayah Nurhidayah Nurul Ismawati Nyamun, Suwito S Peole, I N Prahasti, Syafira Pratiwi, G A Puragombo, Rista Puspita, J W Rivaldi, Rivaldi Rosida Rosida Rusmi, Rusmi Sahari, A Salman Salman samarang samarang Sato, M Sehani, A Setiawaty, R Sibi, Rika Sudirman Sudirman Tadjuka, M A Triwidodo, G Utami, Vicya Wahyudin, A Wahyuni, Ni Luh Sri windy rusma astuti Yahya, R A Yulinda yulinda

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