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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI MAJAMATH: Jurnal Matematika dan Pendidikan Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Journal of Fundamental Mathematics and Applications (JFMA) AMMA : Jurnal Pengabdian Masyarakat
Renny Renny
Jurusan Matematika, Universitas Jenderal Soedirman
Humanities Chemistry Decision Sciences, Operations Research & Management Education Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Nursing

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Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor Susi Agustianingsih; Rina Reorita; Renny Renny
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 3 (2020): JMSK, MAY, 2020
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (787.721 KB) | DOI: 10.20956/jmsk.v16i3.6942

Abstract

The SIR model is one of the mathematical model which describes the characteristic of the spread of infectious disease in differential equation form by dividing the human populations into three groups. There are individual susceptible group, individual infective group, and individual recovered group. This model involves vaccination, quarantine, and immigration factors. Vaccination and quarantine must be given as much as it needs, so a control is required to minimize infection of disease and the number of individual infective with a minimum costs. In this research, optimal control of SIR model with vaccination, quarantine, and immigration factor is solved by using Pontryagin maximum principle and numerically simulated by using Runge-Kutta method. Numerical simulation results show optimal control of treatment, citizen of vaccination, immigrant of vaccination, and quarantine will accelerate the decline of infected number with the minimum cost, compared with the optimal control of SIR model without quarantine factor.
Model Dinamik Kontrol Optimal Predator-Prey dengan Respon Fungsional Beddington-De Angelis pada Tanaman Padi Renny Renny; Rina Reorita
MAJAMATH: Jurnal Matematika dan Pendidikan Matematika Vol. 4 No. 1 (2021): Vol. 4 No.1 Maret 2021
Publisher : Prodi Pendidikan matematika Universitas Islam Majapahit (UNIM), Mojokerto, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36815/majamath.v4i1.869

Abstract

Pada penelitian ini akan digunakan model predator-prey dengan respon fungsional Beddington-De Angelis yang dikembangkan oleh Prasad , namun dengan memberikan suatu kontrol optimal pada model sehingga diharapkan pengendalian terhadap OPT (predator) tidak akan memberikan dampak negatif bagi lingkungan. Kontrol optimal yang digunakan adalah dengan menggunakan teori bang-bang control dan singular control. Hasil simulasi model menunjukkan bahwa dengan menggunakan bang-bang control dan singular control, diperoleh bahwa model dinamik kontrol optimal predator-prey dengan respon fungsional Beddington de-Angelis dengan pemberian kontrol berupa pemberian pestisida kepada hama tanaman di lahan persawahan akan mempercepat penurunan proporsi jumlah hama yang ada dan juga berpengaruh terhadap proporsi tanaman padi yang ada.
ANALISIS KESTABILAN MODEL LESLIE-GOWER DENGAN PENGARUH WAKTU TUNDA DAN PEMANENAN PROPORSIONAL Azhari Kemalasari; Rina Reorita; Renny Renny
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 14 No 1 (2022): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2022.14.1.5898

Abstract

The main purpose of this research is to study the Leslie-Gower model and the response of the Holling type II with time delay and proportional harvesting. The method used in the completion of the model is qualitative, namely by analyzing the stability of the model's equilibrium point. The Leslie-Gower model and Holling type II response with delay time and proportional harvesting have four equilibrium points. There is one point of unstable equilibrium and one point of equilibrium that is stable. Meanwhile, for the other two equilibrium points, it depends on the value of the parameters taken. The delay time resulted in oscillations in the model. The greater the delay time value used, the greater the inequality in oscillations that occur in the system. This means the model will take longer to stabilize.
PENYELESAIAN NUMERIK MODEL PREDATOR-PREY DENGAN SKEMA BEDA HINGGA TAK-STANDAR Rina Reorita; Renny Renny
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 1 (2019)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (281.769 KB) | DOI: 10.14710/jfma.v2i1.24

Abstract

Interaction between predator and prey can be represented as a system of non-linear differential equation which is difficult to be solved analytically. In this research, a predator-prey model with an addition of harvesting factor is discretized into a system of difference equation using non-standard finite difference scheme. The analysis result shows that the developed scheme has qualitative property which is consistent to the continuous system.
GeoGebra Sebagai Aplikasi Visual untuk Topik Turunan dan Integral di MGMP Matematika SMA Kabupaten Purbalingga Sri Maryani; Nunung Nurhayati; Siti Rahmah Nurshiami; Renny Renny; Rina Reorita
AMMA : Jurnal Pengabdian Masyarakat Vol. 1 No. 12 (2023): AMMA : Jurnal Pengabdian Masyarakat
Publisher : CV. Multi Kreasi Media

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

GeoGebra is an interactive geometry software that supports the implementation of mathematics learning. With this software, it is hoped that students' interest in getting to know mathematics more closely will increase through mathematical experiments. GeoGebra can be used not only by students but can also be used by teachers as educators. At present teachers are required to be able to keep up with technological advances, this is in line with RI Law no. 14 of 2005 in terms of increasing the professional competence of teachers. The Covid-19 pandemic has brought changes in terms of interacting with technology. This has a positive impact on teachers as educators. GeoGebra for math teachers is a technological innovation that strongly supports mathematics learning. The GeoGebra application can provide mathematical visualization so that teachers as educators and students as students will find it easier to understand deeper mathematical material. Several math topics exist in senior secondary schools and require visualization to make them easier to understand, including derivative and integral material. Mathematics which is introduced at the high school level (SMA) requires reasoning, visualization and imagination in understanding the concepts of limits and derivatives. This community service (PKM) provides GeoGebra training to high school Mathematics MGMP teachers in Purbalingga Regency for derivative and integral topics. First, high school mathematics MGMP teachers in Purbalingga district were given a pre-test and post-test regarding initial knowledge of derivatives and integrals from 24 representatives of mathematics teachers in Purbalingga district. The results of the pre-test showed that 60.83% of mathematics teachers could answer each point correctly, while the results of the post-test showed an increase in teachers' understanding of derivative and integral topics, namely 80.78% of mathematics teachers were able to answer each point correctly. questions asked. Based on these data, it can be seen that the GeoGebra training provided during this PKM increased the ability of mathematics teachers to understand GeoGebra for derivative and integral topics by 19.95%.
Co-Authors Azhari Kemalasari Nunung Nurhayati Rina Reorita Siti Rahmah Nurshiami, Siti Rahmah Sri Maryani Susi Agustianingsih