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Model Matematika Penyebaran Penyakit Bakteri Pumbuluh Kayu Cengkeh (BPKC) Chijra; Ratianingsih, R; Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 16 No. 2 (2019)
Publisher : Program Studi Matematika, Universitas Tadulako

ABSTRACTClove wood vessels is one of the most damaging diseases of clove plants. This disease is caused by the bacterial Ralstonia Syzygii. the bacterial Rasltonia Syzygii lives in clove wood vessels. The bacterial Ralstonia Syzygii ispread through the Hindola Spp vector. The matemathical model that represents the spread of the disease isdeveloped from the SEI model (Suspectible, Exposed, Infected). The model gives 4 critical points ð‘‡1, ð‘‡2, ð‘‡3 and ð‘‡4 exist interaction between bacterial population Ralstonia Syzygii and Hindola Spp vector is less than the level of vulnerable clove recruitman divided by carrying capacity of Ralstonia Syzygii bacterial multiplied by Hindola Spp carrying capacity. The results of system stability analysis at the critical point using linearization give unstable three critical points ð‘‡1, ð‘‡2, ð‘‡3which describes equilibrium conditions and a stable ð‘‡4 critical point which describes endemic conditions. Numerical simulations are carried out to describe temporary disease-free conditions, and stable endemic conditionsKeywords : Clove Wood vessel Disease, Linierization Method, SEI Model

Analisis Kestabilan Penyebaran Penyakit Antraks Pada Populasi Hewan Dengan Pemberian Vaksinasi: Studi Kasus Untuk Infeksi Pada Populasi Manusia Megawati; Ratianingsih, R; Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 16 No. 2 (2019)
Publisher : Program Studi Matematika, Universitas Tadulako

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 â€“ 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

Kestabilan Model Matematika Infeksi Primer Penyakit Varicella Dan Infeksi Rekuren Penyakit Herpes Zoster Oleh Virus Varicella Zoster Hardiyanti; Ratianingsih, R; Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020)
Publisher : Program Studi Matematika, Universitas Tadulako

Varicella and herpes zoster are two infectious skin diseases of human that caused by varicella zoster virus, where varicella disease is a primary infection that often infected younger people while herpes zoster disease is a recurrent disease that often infected older people because of reactivation of latent varicella-zoster virus. If the pain caused by herpes zoster after recurrent phase is a appeared then the condition is known as postherpetic neuralgia. This study builds a mathematical model of primary infection (varicella disease) and recurrent infection (herpes zoster disease) developed from the SIR model (Susceptible, Infected, Recovered). The human population is divided into seven subpopulations, namely susceptible, infection, recovered of varicella, herpes zoster and postherpetic neuralgia subpopulation. Stability analysis at the critical point by linearization method gives a critical point ð‘‡1 that guaranted to exist and unstable if ð›¼ ðœ‡(ð›½1+ðœ‡) ð´ , while the critical point ð‘‡1 does not have any reqruitment. Stability analysis at the endemic disease-free critical point is represented ð‘‡1 that will be unstable if ð‘‡2 exist and stable ð‘‡1 if ð‘‡2 exist. Numerical simulations by simulated to describe such temporary disease-free conditions and an endemic stable conditions.

Optimalisasi Biaya Transportasi Pendistribusian Pupuk Bersubsidi Menggunakan Model Transportasi Metode Modified Distribusition (MODI) Pertiwi, N; Jaya, A I; Hajar
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.i2.15337

ABSTRACT This study was conducted to obtain the optimal transport costs in the distribution of subsidized fertilizer in PT. GCS and PT.PPI. This research was done in two steps is to create a transport model of the data obtained and determine its solution initially with Least Cost method, and determine the optimal solution with ModifiedDistribution (MODI) method. Based on research that obtained the initial solution is Rp. 65.040.000 and optimal solution is Rp. 64.950.000. While the cost of transportation from the company is RP. 70.500.000. This shows that both distributors can optimize the total cost of transport for the distribution of subsidized fertilizer in January 2017 with the distribution cost savings of Rp. 5.550.000. Keywords : Least Cost Method, Modified Method of Distribution, Optimization, Transportation

Membangun Model Matematika Penyebaran Penyakit Difteri Oleh Corynebacterium Diphtheriae Pada Populasi Manusia: Membangun Model Matematika Penyebaran Penyakit Difteri Oleh Corynebacterium Diphtheriae Pada Populasi Manusia Sato, M; Ratianingsih, R; Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 18 No. 2 (2021)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2021.v18.i2.15705

Penyakit difteri pada manusia disebabkan oleh Corynecbacterium diphtheriae. Difteri menular melalui kontak langsung dan tidak langsung, menyerang semua kelompok usia, dan menyebabkan komplikasi bahkan kematian pada manusia. Penelitian ini bertujuan untuk membangun model matematika penyebaran penyakit difteri pada populasi manusia dengan menggunakan model SEIR (Susceptible-Exposed-Infected-Recovered) berdasarkan kondisi Corynebacterium diphtheriae. Model tersebut melibatkan subpopulasi manusia yang rentan terhadap penyakit (ð‘†), subpopulasi manusia pada masa inkubasi (ð¸), subpopulasi manusia yang terinfeksi (ð¼), subpopulasi manusia yang telah sembuh dari penyakit (ð‘…), subpopulasi manusia yang dikarantina (ð‘ˆ), subpopulasi bakteri sehat (ð»), populasi virus yang menginfeksi bakteri (ð‘‰), dan subpopulasi bakteri mampu menghasilkan toksin (ð‘€). Model matematika ini dianalisis kestabilannya dengan menggunakan metode linearisasi dan kriteria Routh-Hurwitz. Hasil penelitian menunjukkan bahwa titik kritis menggambarkan kondisi endemik yang stabil tanpa syarat. Hal inimenunjukkan bahwa penyakit difteri akan tetap ada dalam populasi manusia.

Mathematical Model of The Spread of Foot and Mouth Diseases (FMD) Hajar; Nacong, Nasria
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 21 No. 1 (2024)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2024.v21.i1.16853

Foot and Mouth Disease (FMD) is a contagious animal disease and can cause death. FMD is caused by an RNA virus belonging to the genus Apthovirus, family Picornaviridae. FMD can be transmitted through direct contact with exposed animals, indirect contact and through the air. In this research, a mathematical model of the spread of FMD in animal populations will be constructed by adapting the SIR (Susceptible, Infected, Recovered) model. From this model two critical points are obtained. The first critical point is the disease-free critical point and the second critical point is the endemic critical point for FMD. The existence of can be guaranteed, because all parameters are positive. And it is stable jika .. Furthermore exists and is stable if ..

Dynamic Model of The Spread of Vascular Streak Dieback Disease (VSD) by Oncobasidium Theobromae on Cocoa Trees with Trichoderma Sp Control Sibi, Rika; Ratianingsih, Rina; Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 21 No. 1 (2024)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2024.v21.i1.17110

Disease Vascular Streak Dieback (VSD) is caused by the fungus Oncobasidium theobromae which produces basidiospores and grow on infected cacao branches. Biological control of VSD disease used Trichoderma sp. The mathematical model that represented the spread of this disease is adapted from the SIS and provided two existing critical points, namely the disease-free critical point and the endemic critical point . Analysis of system stability at the critical points using the Linearization method and the Routh-Hurwitz indicated that the is stable and appearing a threshold for the growth rate of Oncobasidium theobromae that must be less than 0.767. The is exist and stable with a threshold for spore growth rate of Oncobasidium theobromae is greater than 0.767. Simulations at the both critical points showed that the spore growth rate of Oncobasidium theobromae is very fluently in the spread of the disease. In this case, suppressing the growth rate of Oncobasidium theobromae could be used as a good treatment to control the disease.

ANALISIS KESTABILAN MODEL MATEMTIKA PENYEBARAN PENYAKIT BUSUK BUAH TANAMAN KAKAO AKIBAT JAMUR PHYTOPHTHORA PALMIVORA PADA KONDISI BEBAS PENYAKIT DAN ENDEMIK Yahya, R A; Ratianingsih, R; Hajar, Hajar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 14 No. 2 (2017)
Publisher : Program Studi Matematika, Universitas Tadulako

ANALISIS KESTABILAN MODEL MATEMTIKA PENYEBARAN PENYAKIT BUSUK BUAH TANAMAN KAKAO AKIBAT JAMURÂ Â PHYTOPHTHORA PALMIVORA PADA KONDISIÂ BEBAS PENYAKIT DAN ENDEMIK

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.

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.

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