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All Journal Jurnal Ilmu Dasar JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI CAUCHY: Jurnal Matematika Murni dan Aplikasi Kubik Jurnal Fourier NUMERICAL (Jurnal Matematika dan Pendidikan Matematika) BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND Majalah Ilmiah Matematika dan Statistika (MIMS) KUBIK: Jurnal Publikasi Ilmiah Matematika EBAMUKAI; JURNAL PENGABDIAN ILMU PENGETAHUAN DAN TEKNOLOGI
Joko Harianto
Program Studi Matematika, Fakultas MIPA, Universitas Cendrawasih
Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation

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Analisis Sensitivitas Model SEIV pada Kasus Penularan Penyakit Polio Angelika, Venthy; Harianto, Joko
Jurnal Fourier Vol. 12 No. 2 (2023)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2023.122.60-68

Abstract

The trend of polio transmission cases until 2023 is still fluctuating and does not tend to decrease monotonically. This incident is important to discuss, especially about the factors that influence cases of polio transmission. One of the studies used to describe the incidence of polio transmission is through mathematical model analysis. One of the mathematical models used to represent the incidence of polio transmission is a dynamic model with the Susceptible-Exposed-Infected-Vaccinated (SEIV) compartment. The SEIV model analyzed in this study involves seven parameters. If the value of each parameter fluctuates, it will affect cases of polio transmission. Therefore, this research aims to analyze the influence of each parameter in the SEIV model on cases of polio transmission. The method used in this research is the literature study method. Secondary data in this study was used to create a SEIV model simulation. The findings of this research are that two parameters have the greatest influence on cases of polio transmission. The infection transmission rate parameter is the most influential parameter in terms of increasing cases of polio transmission because the sensitivity index value is the highest among the other six parameters. Meanwhile, the natural death rate parameter is the parameter that has the most influence on reducing cases of polio transmission. This is because based on the sensitivity index value, the death rate parameter has the lowest sensitivity index value among the other six parameters.
Analisis Sensitivitas Model Penularan Koinfeksi COVID-19 dan HIV/AIDS Harianto, Joko; Abraham; Kawuwung, Westy B.
Jurnal Fourier Vol. 13 No. 1 (2024)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2024.131.52-64

Abstract

Penularan koinfeksi COVID-19 dan HIV/AIDS merupakan masalah kesehatan masyarakat yang menjadi pusat perhatian terutama di negara-negara berkembang di dunia. Artikel ini merupakan salah satu kajian untuk mempelajari kejadian penularan koinfeksi COVID-19 dan HIV/AIDS. Model yang digunakan terdiri dari delapan kompartemen antara lain: rentan, vaksinasi, COVID-19, infeksi COVID-19, infeksi HIV, AIDS, koinfeksi COVID-19 dan HIV, koinfeksi COVID-19 dan AIDS. Analisis kestabilan titik ekuilibrium model dan kontrol optimalnya telah dibahas sebelumnya. Hasil dari analisis tersebut digunakan sebagai landasan teori untuk melakukan analisis sensitivitas parameter modelnya. Oleh karena itu, tujuan penelitian ini adalah menentukan parameter model yang paling sensitif terhadap kasus penularan koinfeksi COVID-19 dan HIV/AIDS. Metode studi literatur digunakan untuk mendukung analisis sensitivitas parameter model. Simulasi modelnya menggunakan software Maple dengan data sekunder. Parameter laju kontak COVID-19, laju kontak HIV, laju kesembuhan infeksi COVID-19 dan angka kematian akibat AIDS merupakan parameter yang paling sensitif terhadap kasus penularan koinfeksi COVID-19 dan HIV/AIDS. Parameter laju kontak COVID-19 dan laju kontak HIV adalah parameter yang paling sensitif terhadap peningkatan kasus penularan koinfeksi COVID-19 dan HIV/AIDS karena nilai indeks sensitivitasnya tertinggi dibandingkan parameter lainnya. Sedangkan, parameter laju kesembuhan infeksi COVID-19 dan angka kematian akibat AIDS memiliki nilai indeks sensitivitas terendah dibandingkan parameter lainnya. Parameter laju kesembuhan infeksi COVID-19 dan angka kematian akibat AIDS adalah parameter yang paling sensitif terhadap penurunan kasus penularan koinfeksi COVID-19 dan HIV/AIDS.
Local Stability Dynamics of Equilibrium Points in Predator-Prey Models with Anti-Predator Behavior Harianto, Joko; Suparwati, Titik; Dewi, Alfonsina Lisda Puspa
Jurnal ILMU DASAR Vol 22 No 2 (2021)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/jid.v22i2.23991

Abstract

This article describes the dynamics of local stability equilibrium point models of interaction between prey populations and their predators. The model involves response functions in the form of Holling type III and anti-predator behavior. The existence and stability of the equilibrium point of the model can be obtained by reviewing several cases. One of the factors that affect the existence and local stability of the model equilibrium point is the carrying capacity (k) parameter. If x3∗, y3∗ > 0 is a constant solution of the model and ∈ (0,x3∗), then there is a unique boundary equilibrium point Ek (k , 0). Whereas, if k ∈ (x4∗, y4∗], then Ek (k, 0) is unstable and E3 (x3∗, y3∗) is stable. Furthermore, if k ∈ ( x4∗, ∞), then Ek ( k, 0) remains stable and E4 (x4∗, y4∗) is unstable, but the stability of the equilibrium point E3 (x3∗, y3∗) is branching. The equilibrium point E3 (x3∗, y3∗) can be stable or unstable depending on all parameters involved in the model. Variations of k parameter values are given in numerical simulation to verify the results of the analysis. Numerical simulation indicates that if k = 0,92 then nontrivial equilibrium point Ek (0,92 ; 0) stable. If k = 0,93 then Ek (0,93 ; 0) unstable and E3∗(0,929; 0,00003) stable. If k = 23,94, then Ek (23,94 ; 0) and E3∗(0,929; 0,143) stable, but E4∗(23,93 ; 0,0005) unstable. If k = 38 then Ek(38,0) stable, but E3∗(0,929; 0,145) and E4∗(23,93 ; 0,739) unstable.Keywords: anti-predator behavior, carrying capacity, and holling type III.
PELATIHAN PENERAPAN PEMBELAJARAN BERHITUNG CEPAT BAGI ANAK-ANAK SEKOLAH SABATH GMHK JEMAAT NENDALI DAN ANAK-ANAK SEKOLAH MINGGU GKI I. S. KIJNE, ABEPURA Bowaire, Anike; Zakaria V. Kareth; Novana V. J. Kareth; Joko Harianto; Wani Tabuni; Mesakh Wandikbo; Krista M. Ansanay; Magrice S. Maran
EBAMUKAI PAPUA JURNAL PENGABDIAN ILMU PENGETAHUAN DAN TEKNOLOGI
Publisher : Universitas Cenderawasih

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31957/ejpipt.v2i1.169

Abstract

Aktivitas belajar berhitung menggunakan permainan yang menyenangkan, khususnya abacus, terbukti dapat meningkatkan kemampuan berhitung anak sebesar 40% . Selain itu, kemampuan matematika yang baik membekali anak untuk memiliki minat pada bidang sains dan teknologi. Kampung Nendali terletak di pinggir Jalan Raya Sentani - Waena yang juga berada di pesisir Danau Sentani dan berjarak sekitar 14,6 km dari Universitas Cenderawasih Kampus Waena, dan GKI I. S. Kijne berada di Abepura yang berjarak sekitar 1 km dari Universitas Cenderawasih Kampus Abepura dan sekitar 5.9 km dari Universitas Cenderawasih Kampus Waena. Tujuan dari pelatihan penerapan pembelajaran berhitung cepat menggunakan metode abacus adalah memperkenalkan, melatih dan meningkatkan kemampuan berhitung anak-anak Sekolah Sabath GMHK Jemaat Nendali dan Sekolah Minggu GKI I. S. Kijne, Abepura. Kegiatan pengabdian dilakukan melalui pelatihan secara metode edukasi-persuasif yakni pendekatan yang dilakukan kepada anak-anak berupa sosialisasi, pelatihan, serta dilanjutkan dengan pendampingan dalam rangka transfer pengetahuan berupa ceramah/ seminar, simulasi perhitungan, dan praktek bersama.
DINAMIKA LOKAL MODEL EPIDEMI SVIR DENGAN IMIGRASI PADA KOMPARTEMEN VAKSINASI Harianto, Joko; Suparwati, Titik; Sari, Inda Puspita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 2 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (645.635 KB) | DOI: 10.30598/barekengvol14iss2pp293-300

Abstract

This article is included in the scope of mathematical epidemiology. The purpose of this article is to describe the dynamics of the spread of disease with some assumptions given. In this paper, we present an epidemic SVIR model with the presence of immigration in the vaccine compartment. The analysis of equilibrium point stability discussed only local stability. First, we formulate the SVIR model, then the equilibrium point is determined, furthermore, the basic reproduction number is determined. In the end, the stability of the equilibrium point is determined depending on the number of basic reproduction. The result is that if the basic reproduction number is less than one then there is a unique equilibrium point and the equilibrium point is locally asymptotically stable. This means that in those conditions the disease will tend to disappear in the population. Conversely, if the basic reproduction number is more than one, then there are two equilibrium points. The endemic equilibrium point is locally asymptotically stable and the disease-free equilibrium point is unstable. This means that in those conditions the disease will remain in the population
KESTABILAN LOKAL TITIK EKUILIBRIUM MODEL PENYEBARAN PENYAKIT POLIO Harianto, Joko; Angelika, Venthy; Seru, Feby
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.153-167.2023

Abstract

The fact shows that polio is very dangerous to humanity, it is necessary to study the dynamics of the spread of polio. One way, namely a mathematical approach in the form of a mathematical model for the spread of polio. The mathematical model used in this study is the SEIV model. This study aims to provide a description of the dynamics of the spread of polio. The results of this study are expected to be used as a reference to study the dynamics of the spread of polio in an area. The method used in the implementation of this research is literature study. The first stage starts with the model formulation. The second stage analyzes the model that has been formed and the last one makes a model simulation. The formed SEIV model is a system of nonlinear differential equations. The basic reproduction number  parameter is obtained from the analysis of the system. If the basic reproduction number less than one, then there is a single point of  free disease equilibrium that is locally stable asymptotically. Conversely, if the basic reproduction number more than one, then there are two points of equilibrium, namely the point of free equilibrium of disease  and the endemic equilibrium point . When the basic reproduction number more than one endemic equilibrium point  is stable asymptotically locally. Based on the simulation, if  the basic reproduction number less than one for t → ∞ and value (S, E, I, V) are close enough to E*, the system solution will move to E*. This means that if the basic reproduction number less than one, the disease will not be endemic and tends to disappear in an infinite amount of time. Conversely, if the basic reproduction number more than one for t → ∞ and the value (S, E, I, V) are close enough to E^, then the system solution will move towards E^. This means that if the basic reproduction number more than one, then the disease will remain in the population but not reach extinction in an infinite amount of time
Mathematical Modeling of Foot and Mouth Disease Spread on Livestock using Saturated Incidence Rate Fahcruddin, Imam; Harianto, Joko; Fitrial, Denny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.10264

Abstract

Foot and Mouth Disease (FMD) is an acute infectious disease that attacks livestock, thus threatening the availability of food and the husbandry industry. This paper discusses the formulation of a mathematical model for the spread of FMD in livestock with a saturated incidence rate. The research method used is quantitative mathematical modeling with simulation, with stages including problem identification, determining assumptions, model formulation, analysis and model simulation. The discussion results obtained two equilibrium points, namely the non-endemic equilibrium point and the endemic equilibrium point, and then analyzed for stability. Numerical simulation is presented using Runge-Kutta approximation with MATLAB. Furthermore, after a sensitivity analysis, the parameters that greatly influenced the spread of FMD were direct or indirect contact (which led to the entry of the FMD virus) and the supporting capacity of livestock. Then the most influential parameter in reducing the spread of FMD is the application of culling on exposed animals and infected animals. The FMD modeling is a form of mathematical application to simulate the spread of disease on livestock.
Co-Authors Abraham Angelika, Venthy Bowaire, Anike Dewi, Alfonsina Lisda Puspa FEBY SERU fitrial, denny Imam Fahcruddin Jonner Nainggolan Katarina Lodia Tuturop Katarina Lodia Tuturop Katarina Lodia Tuturop Kawuwung, Westy B. Krista M. Ansanay Magrice S. Maran Mesakh Wandikbo Mira Aprilia Marcus Novana V. J. Kareth Sari, Inda Puspita Titik Suparwati Venthy Angelika Venthy Angelika Wani Tabuni Zakaria V. Kareth