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All Journal Medicina Jurnal Penelitian Pendidikan Matematika dan Sains SITEKIN: Jurnal Sains, Teknologi dan Industri E-Dimas: Jurnal Pengabdian kepada Masyarakat Didacticofrancia: Journal Didactique du FLE English and Literature Journal Jurnal EMT KITA BAREKENG: Jurnal Ilmu Matematika dan Terapan Communication in Biomathematical Sciences WAKTU: Jurnal Teknik UNIPA Jurnal Matematika UNAND Jurnal Abdi: Media Pengabdian Kepada Masyarakat Jambura Journal of Biomathematics (JJBM) Franconesia Journal of French Teaching, Linguistics, Literature, and Culture Indonesian Journal of Computational and Applied Mathematics
DIAN SAVITRI
Department of Child Health, Udayana University Medical School/Sanglah Hospital Denpasar
Arts Humanities Chemical Engineering, Chemistry & Bioengineering Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Materials Science & Nanotechnology Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation Other

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Bifurkasi Hopf pada model prey-predator-super predator dengan fungsi respon yang berbeda Savitri, Dian; Panigoro, Hasan S.
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 2: December 2020
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i2.8399

Abstract

This article discusses the one-prey, one-predator, and the super predator model with different types of functional response. The rate of prey consumption by the predator follows Holling type I functional response and the rate of predator consumption by the super predator follows Holling type II functional response. We identify the existence and stability of critical points and obtain that the extinction of all population points is always unstable, and the other two are conditionally stable i.e., the super predator extinction point and the co-existence point. Furthermore, we give the numerical simulations to describe the bifurcation diagram and phase portraits of the model. The bifurcation diagram is obtained by varying the parameter of the conversion rate of predator biomass into a new super-predator which gives forward and Hopf bifurcation. The forward bifurcation occurs around the super predator extinction point while Hopf bifurcation occurs around the interior of the model. Based on the terms of existence and numerical simulation, we confirm that the conversion rate of predator biomass into a new super-predator controls the dynamics of the system and maintains the existence of predator.
Implementasi algoritma genetika dalam mengestimasi kepadatan populasi jackrabbit dan coyote Savitri, Dian; Hidajati, Ninik Wahju; Panigoro, Hasan S.
Jambura Journal of Biomathematics (JJBM) Volume 3, Issue 1: June 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v3i1.11935

Abstract

This article studies about the parameter estimation using genetic algorithm for a Lotka-Volterra prey-predator model. The secondary data consist of the density of jackrabbit as prey and coyote as predator in Southwest Presscott–Arizona are used. As results, the Mean Absolute Percentage Error (MAPE) are computed to compare the results of parameter estimation and the real data. We have shown that MAPE for jackrabbit and coyote respectively given by 7.75424% and 7.95283%. This results show that the parameter estimation with genetic algorithm using Lotka-Volterra model is passably. Furthermore, some numerical simulations are portrayed to show each population density for the next 100 years.
Modeling of Abstinence Behavior on the Electoral Lists with Awareness Campaigns and Argumentative Schemes Beay, Lazarus Kalvein; Panigoro, Hasan S.; Rahmi, Emli; Savitri, Dian
Communication in Biomathematical Sciences Vol. 7 No. 2 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.2.4

Abstract

The most reasonable way to promote individual abstinence and increase voter turnout is through campaign interventions and schemes. Our paper introduces a deterministic model that captures the dynamics of citizens exercising their right to vote and the detrimental effect of abstainers on potential voters. The existence, basic reproductive number (R0) and local stability of abstinence behavior equilibrium points are determined by certain necessary conditions. The global stability of the abstaining-free point and abstaining point is achieved through the use of suitable Lyapunov functions. In addition, a sensitivity analysis of R0 was also performed. Moreover, we offer an ideal plan for an awareness program that supports politicians and officials in enhancing the registration rate of citizens on electoral lists with a level of effort. Our investigation reveals that utilizing the combination of an awareness campaign and argumentation schemes as time-dependent interventions drastically reduces abstention rates and greatly increases voter participation. By raising the values of awareness and registration rates, we can observe a decline in the basic reproductive number (R0). Our analytical results are supported by numerical simulations.
Dynamic Analysis of the Modified Leslie Gower Model with Harvesting of Prey and Holling Type II Functional Response Eghary, Nabila Kholifatul Yuniar; Savitri, Dian
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 2: June 2025
Publisher : Gammarise Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.64182/indocam.v1i2.32

Abstract

This article studies the Modified Leslie-Gower model with constant business harvesting on the prey and functional response of Holling Type II. This approach is more realistic in several phenomena, one of which is in the phenomenon of rice fields, jali snakes, and owls. The research method begins by determining the assumptions for constructing models, stability analysis, and numerical simulations. Analysis of the equilibrium points was carried out to determine the condition of its stability locally using the Jacobian approach and the Routh-Hurwitz criteria by obtaining five existing points. Analysis of stability using the Jacobian matrix shows that the equilibrium point is an asymptotic node in certain conditions. Numerical simulations are carried out to determine the suitability of the results of the analysis using the software Maple and Python. Numerical simulation results show differences in the value of environmental carrying capacity affect changes in system solutions. Thus, the change in the value of carrying capacity does not always produce the same stability because the stability of the system depends on the sensitivity of the parameter to the overall dynamic structure. This finding provides a foundation for the management of biological resources, especially in controlling harvesting so that the population remains balanced.
Dynamic Analysis of an Ecological Model with Fear Effect on Prey and Additional Food for Predator Using Ratio-Dependent Functional Response Salsabillah, Atiyah Safitri; Savitri, Dian
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 2: June 2025
Publisher : Gammarise Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.64182/indocam.v1i2.34

Abstract

This study discusses the dynamic analysis of a predator-prey model that incorporates the fear effect on prey and supplemental food for predators, using a ratio-dependent functional response. The fear effect reduces the prey’s intrinsic growth rate due to behavioral changes under predation risk, while supplemental food enables the predator to survive even when prey density is low. The analysis begins with the formulation of the model equations, followed by the identification of equilibrium points, linearization of the system, and local stability analysis using eigenvalues. Numerical simulations are carried out using \textit{Matcont} and \textit{Pplane} to verify the analytical results and to illustrate the system’s qualitative behavior. The model parameters are based on the interaction between elk (\textit{ELK}) as prey and wolves (\textit{Canis lupus}) as predators. The results reveal four equilibrium points: $E_0=(0,0)$ is an unstable nodal source, $E_1=\left(0,\dfrac{nA(c\gamma - e\alpha)}{em}\right)$ and $E_2=\left(\dfrac{r-a}{b},0\right)$ are unstable saddle points, while the coexistence equilibrium $E_3=(x^*, y^*)$ is a stable spiral sink under certain parameter conditions. Bifurcation analysis with respect to the fear parameter $f$ and the supplemental food parameter $A$ reveals the occurrence of a transcritical bifurcation, where two equilibrium branches exchange stability. The system tends toward the equilibrium point $E_1$ when either $f$ or $A$ exceeds a critical threshold, indicating that predators can persist even as prey populations decline significantly. These findings suggest that predator survival is not solely dependent on prey availability but also influenced by the availability of alternative food sources and the intensity of the prey’s fear response.
Co-Authors ABADI Akmal Ali, Muhamad Restu Andreani, Phobe APRILIA, VERNANDA Beay, Lazarus Kalvein BUDI RAHADJENG Dewi, Mifta Kharisma Dina Kartika Maharani Dini Kinati Fardah Dino, Awan Eghary, Nabila Kholifatul Yuniar Faradilla, Anisa' Hamzah, Ahmad Taufik Hasan S. Panigoro Hidajati, Ninik Wahju I Made Kardana Jakfar, Muhammad Khofifah, Rike Farikha Lydia Rohmawati Mahameru Rosy Rochmatullah Manuharawati Ni Putu Siadi Purniti Ninuk Lustyantie Phibeta, Toni Prawoto, Budi P. Putri, Laras Kinanti RADEN SULAIMAN Rahmi, Emli Ratna Salsabila, An Nisa Salsabillah, Atiyah Safitri Sri Harini Ekowati Sri Mulyani Subur Ismail, Subur Thoriq, Abil Alfath Umaroh, Siti Zulfaniah