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Model Matematika Penyebaran Penyakit Bakteri Pumbuluh Kayu Cengkeh (BPKC) Chijra; 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 (669.691 KB) | DOI: 10.22487/2540766X.2019.v16.i2.14985

Abstract

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 ????1, ????2, ????3 and ????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 ????1, ????2, ????3which describes equilibrium conditions and a stable ????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; 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

Abstract

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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (725.899 KB) | DOI: 10.22487/2540766X.2020.v17.i1.15180

Abstract

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 ????1 that guaranted to exist and unstable if ???? ????(????1+????) ???? , while the critical point ????1 does not have any reqruitment. Stability analysis at the endemic disease-free critical point is represented ????1 that will be unstable if ????2 exist and stable ????1 if ????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) N Pertiwi; A I Jaya; 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

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
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

Abstract

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.
Membangun Model Matematika Penyebaran Penyakit Difteri Oleh Corynebacterium Diphtheriae Pada Populasi Manusia: Membangun Model Matematika Penyebaran Penyakit Difteri Oleh Corynebacterium Diphtheriae Pada Populasi Manusia M Sato; R Ratianingsih; 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

Abstract

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 (????), subpopulasi manusia pada masa inkubasi (????), subpopulasi manusia yang terinfeksi (????), subpopulasi manusia yang telah sembuh dari penyakit (????), subpopulasi manusia yang dikarantina (????), subpopulasi bakteri sehat (????), populasi virus yang menginfeksi bakteri (????), dan subpopulasi bakteri mampu menghasilkan toksin (????). 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.