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Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96119, Gorontalo, Indonesia
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Jambura Journal of Biomathematics (JJBM)
Published by Universitas Negeri Gorontalo
ISSN : -     EISSN : 27230317     DOI : https://doi.org/10.34312/jjbm.v1i1
Core Subject : Science, Education,
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics
Jambura Journal of Biomathematics (JJBM) aims to become the leading journal in Southeast Asia in presenting original research articles and review papers about a mathematical approach to explain biological phenomena. JJBM will accept high-quality article utilizing mathematical analysis to gain biological understanding in the fields of, but not restricted to Ecology Oncology Neurobiology Cell biology Biostatistics Bioinformatics Bio-engineering Infectious diseases Renewable biological resource Genetics and population genetics
Arjuna Subject : Matematika - Matematika Terapan
Articles 99 Documents
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Dynamical Analysis of Holling Tanner Prey Predators Model with Add Food in Second Level Predators Salsabila, An Nisa; Savitri, Dian
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 2: December 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i2.25753

Abstract

This article discusses the Holling Tanner prey predator model and Holling type II response function with additional food in the second level predator. The dynamic analysis of the system begins with determining the equilibrium point, analyzing the stability of the equilibrium point, and numerical simulation with python. The results of the dynamic analysis obtain seven equilibrium points, namely E1 extinction in three populations, point E2 extinction in the population of prey and first level predator, point E3 extinction in the first and second level predator populations, point E4 extinction in the second level predator population, point E5 extinction in the first level predator population, and point E6 the three populations are not extinction. The results of the stability analysis around the equilibrium point E1, E2, E3 are shown to be saddle unstable, then E4, E5, E6 are asymptotically stable with certain conditions. Numerical simulation is applied to determine the validity of the analytical results. The simulation results illustrate changes in the system solution in the form of phase portraits. The bifurcation diagram of the numerical continuation of the maximum predation rate parameter of the second-level predator (β) shows the existence of Hopf bifurcation when maximum predation rate parameter of the second-level predator with β = 2.1014232 and Transcritical bifurcation when maximum predation rate parameter of the second-level predator with β = 3.197.
Complex dynamics in a discrete-time model of two competing prey with a shared predator Mukherjee, Debasis
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 2: December 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i2.27453

Abstract

This paper concentrates on the study of a discrete time model of two competing prey with a shared predator. The condition for the existence and local stability of positive fixed point are derived. By using an iteration scheme and the comparison principle of difference equations, it is possible to obtain the sufficient condition for global stability of the positive fixed point. The sufficient criterion for Neimark-Sacker bifurcation and flip bifurcation are established. The system admits chaotic dynamics for a certain choice of the system parameters which is controlled by applying hybrid control method. The intra-specific competition among predators and the intrinsic growth rate of prey species have major impact for different bifurcation. For continuous system, handling time spent for prey population plays an important role for obtaining limit cycle behaviour. The decrease amount of this rate makes the system stable. Global convergence of the solutions to the coexistence equilibrium point is possible for a particular choice of system parameters. The obtained results for discrete system are verified through numerical simulations. Also some diagrams are presented for continuous system.
Modeling the Impact of Toxicants on a Plankton-Fish System with Gompertz Growth Function Annavarapu, Raveendra Babu; Makwana, Kavita; Jadon, Bhanu Pratap Singh
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 2: June 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i2.30824

Abstract

This study develops a mathematical model to investigate the dynamics of an aquatic ecosystem, incorporating key ecological features such as Gompertz growth, prey refuge, Holling Type II predation, and the Beddington-DeAngelis functional response. The primary objective is to analyze the effects of toxicant accumulation and population interactions on ecosystem stability. Analytical techniques, including the Jacobian matrix, Routh-Hurwitz criteria, and Lyapunov functions—are employed to examine equilibrium points, stability conditions, and bifurcation behavior. A Hopf bifurcation is observed when the carrying capacity  exceeds a critical threshold, indicating a transition from stable to oscillatory behavior. Intraspecific competition among fish is found to dampen chaotic dynamics, thereby enhancing system stability. Numerical simulations confirm the theoretical findings and highlight that increased toxicant levels disrupt energy flow through the food chain, causing population decline. These results underscore the importance of ecological regulation in preserving ecosystem balance and mitigating the impact of environmental stressors.
A Non-linear Fractional Model for Analyzing the Impact of Vaccination on the Dynamics of COVID-19 in Indonesia Akanni, John Olajide; Abidemi, Afeez; Fatmawati, Fatmawati; Chukwu, Chidozie Williams
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 2: June 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i2.30383

Abstract

COVID-19, yang disebabkan oleh virus corona baru SARS-CoV-2, masih menjadi tantangan kesehatan masyarakat global. Studi ini mengusulkan dan menganalisis model matematika untuk memantau perkembangan COVID-19 dan menilai dampak upaya imunisasi. Model tersebut menggabungkan faktor-faktor epidemiologi utama dan dikalibrasi menggunakan data yang tersedia untuk umum tentang kasus harian kumulatif COVID-19 di Indonesia, yang berlangsung dari 1 Juli 2021 hingga 21 Juli 2022. Angka reproduksi dasar, , diturunkan dan keadaan ekuilibrium ditetapkan. Analisis bifurkasi dilakukan menggunakan Teorema Manifold Pusat untuk memahami potensi dinamika transisi penyakit. Analisis sensitivitas lokal mengungkapkan bahwa tingkat penularan efektif (), tingkat kematian alami (), tingkat vaksinasi () dan tingkat pengobatan untuk individu bergejala () adalah parameter yang paling berpengaruh. Simulasi model menunjukkan bahwa mengurangi penularan, meningkatkan pengobatan, dan meningkatkan penyerapan vaksin secara signifikan mengurangi beban penyakit. Untuk lebih menangkap efek memori yang melekat dalam penularan penyakit, model diperluas ke kerangka turunan Caputo orde fraksional. Keberadaan, keunikan, dan stabilitas model fraksional ditetapkan melalui teori titik tetap. Hasil numerik menunjukkan bahwa penurunan dalam orde fraksional sedikit menggeser dinamika, yang menunjukkan perubahan perilaku dalam menanggapi wabah sebelumnya. Temuan ini memberikan informasi berharga tentang strategi pengendalian penyakit dan menyoroti pentingnya langkah-langkah kesehatan masyarakat yang berkelanjutan.
Mathematical Modeling, Optimal Control and Cost-Effectiveness Analysis of Diphtheria Transmission Dynamics Afolabi, Ayodeji Sunday; Miswanto, Miswanto
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 2: June 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i2.30851

Abstract

Diphtheria remains a serious public health concern in regions with low vaccination coverage and limited access to timely treatment, highlighting the urgent need for effective modeling and control strategies to guide intervention efforts. A nonlinear mathematical model is developed to describe the transmission dynamics of diphtheria. The well-posedness of the model is analyzed by investigating the positivity and boundedness of its solutions. The solutions of the disease-free equilibrium points are obtained analytically. The basic reproduction number () is determined using Diekmann-Heesterbeek-Metz Next Generation Matrix approach. The stability of the disease-free and endemic equilibrium points are rigorously analyzed. Sensitivity analysis of the model parameters with respect to  is conducted to assess the relative impact of each parameter on the transmission dynamics of the disease. Based on the results of the sensitivity analysis, the proposed diphtheria model is extended into an optimal control problem by introducing four time-dependent control variables: personal protection, booster vaccine administration, detection/treatment of the asymptomatic infected humans and reduction of bacteria concentration. Four different scenarios with each involving at least three of the control variables are examined. We evaluated the cost-effectiveness of each control strategy using IAR, ACER and ICER methods in order to identify the most economically efficient strategy. The findings demonstrate that Strategy A is the most cost-effective startegy that can significantly reduce diphtheria transmission throught optimal personal protection, detection/treatment of the asymptomatic infected humans and reduction of bacteria concentration.
Cost-effectiveness with Optimal Strategies for Enhancing Population Birth Rate Trends in Japan Kundu, Pulak; Mallick, Uzzwal Kumar
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 2: June 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i2.30983

Abstract

Japan faces one of the major challenges as its declining birth rate and aging population threaten long-term demographic and economic stability. To address this challenge,  a mathematical model with optimal control has been formulated, employing awareness programs and incentives to maximize population growth at minimal policy costs. Along with analyzing the model’s positivity, boundedness, existence of a unique solution, and stability at equilibrium points, the optimal control was characterized using Pontryagin’s Maximum Principle. Using the forward-backward sweep method, the numerical simulation demonstrated that the objective is maximized by applying awareness programs and incentives at full capacity until 2042 and 2046, respectively, before gradually reducing them. Then, a cost-effectiveness analysis was conducted to determine the most efficient approach, revealing that awareness programs are more cost-effective than the alternative strategy. Therefore, the findings of this study provide valuable guidance for policymakers to develop practical, cost-effective strategies that address Japan’s demographic challenges and promote sustainable population growth for society.
A Reinforcement Learning Based Decision-Support System for Mitigate Strategies During COVID-19: A Systematic Review Rifanti, Utti Marina; Aryati, Lina; Susyanto, Nanang; Susanto, Hadi
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.30513

Abstract

The past threat of the COVID-19 pandemic has challenged policymakers to develop effective decision-support systems. Reinforcement learning (RL), a branch of artificial intelligence, has emerged as a promising approach to designing such systems. This systematic review analyzes 20 selected studies published between 2020 and 2024 that apply RL as a decision-making tool for COVID-19 mitigation, focusing on environment models, algorithms, state representation, action design, reward functions, and challenges. Our findings reveal that Q-learning is the most frequently used algorithm, with most implementations relying on SEIR-based models and real-world COVID-19 epidemiological data. Policy interventions, particularly lockdowns, are commonly modeled as actions, while reward functions are health-oriented, economic, or hybrid, with an increasing trend toward multi-objective designs. Despite these advancements, key limitations persist, including data uncertainty, computational complexity, ethical concerns, and the gap between simulated performance and real-world feasibility. This review further identifies a research opportunity to integrate epidemic model formulations with explicit control inputs into RL frameworks, potentially enhancing learning efficiency and bridging the gap between simulation and practice for future pandemic response systems.
Effect of Toxicant on One Prey and Two Competing Predators with Beddington-DeAngelis Functional Response Makwana, Kavita; A., Raveendra Babu; Jadon, B.P.S.
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.30686

Abstract

This study investigates the dynamical behaviour of a prey-predator system with two competing predators, incorporating the Beddington–DeAngelis functional response and the effects of environmental toxicants. Analytical analysis ensures the boundedness of solutions, guaranteeing biologically feasible population dynamics. Equilibrium points are identified, and their stability is examined using local and global stability analyses. Numerical simulations validate the analytical findings, demonstrating that as the competition coefficient b1 increases, the system transitions from a stable equilibrium to periodic oscillations and eventually to chaotic behaviour. Furthermore, the impact of the toxicant uptake rate d1 is explored to assess its role in system stability. The results indicate that low levels of toxicant absorption promote oscillatory dynamics, while higher values of d1 suppress population growth and restore stability. This highlights the dual role of toxicants in ecological systems, where moderate exposure disrupts equilibrium, but excessive accumulation can lead to stabilization. Bifurcation diagrams and time-series simulations further reinforce these transitions, revealing critical thresholds where stability is lost or regained. The study provides valuable insights into the complex interplay between toxicant dynamics, predator-prey interactions, and bifurcation phenomena. The findings emphasize the ecological implications of toxicant exposure and interspecies competition, offering potential applications in environmental management and conservation strategies.
Implementation of non-standard finite difference on a predator prey model considering cannibalism on predator and harvesting on prey Luis, Prisalo; Kamalia, Putri Zahra; Peter, Olumuyiwa James; Aldila, Dipo
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.30550

Abstract

The type of interaction between two different species in the same ecosystem plays an important role in the coexistence between these species. One type of interaction between species is predator-prey interaction. Several important factors are crucial to guarantee the existence of predator and prey in the same ecosystem, such as the carrying capacity of the ecosystem for the survival of prey, the intensity of predation, cannibalism in the predator population, and many other factors. External factors such as human intervention, such as harvesting, increase the complexity of the problem. Here in this article, we discuss a predator-prey model that takes predation and harvesting in prey populations into account. We implement a Non-Standard Finite Difference (NSFD) numerical scheme to solve our model due to it good performance on stability and approximation. Mathematical analysis on the existence and stability of equilibrium points from the discrete model was analyzed in detail. We implement a Nonstandard Finite Difference (NSFD) scheme to ensure numerical stability across various simulation scenarios. It is shown that NSFD has a better numerical stability compared to the standard numerical scheme like Euler or fourth-order Runge-Kutta method. From the sensitivity of autonomous simulation, we have shown that increases of cannibalism in predator populations will reduce predator populations, and as a result, the population of prey will increase due to the lack of number of predators. We also showed that increasing harvesting in prey populations may cause extinction in prey and predator populations. Furthermore, we have shown how periodic harvesting on prey populations may cause a critical condition on the existence of prey populations that takes a longer period to get recovered.
A Discrete Predator-Prey Model with Cannibalism, Refuge, and Memory Effect: Implementation of Piecewise Constant Argument (PWCA) Method Rayungsari, Maya; Nurmalitasari, Dewi; Pamungkas, Edy Tya Gullit Duta
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.29391

Abstract

Predator-prey models are essential for understanding ecological dynamics, and fractional-order models provide a more realistic approach by considering memory effects. This study aims to analyze the discrete dynamics of a predator-prey model, incorporating predator cannibalism, refuge, and memory effects with a Caputo-type fractional-order. The Piecewise Constant Argument (PWCA) method was employed for discretization, followed by an analysis of the equilibrium points and their stability. Four equilibrium points were identified: the origin, prey extinction, predator extinction, and coexistence. It was found that the origin point was unstable, while the prey extinction, predator extinction, and coexistence points were conditionally locally asymptotically stable, depending on the parameter values. The order of the fractional derivative and step size significantly influenced the stability of these equilibrium points. Numerical simulations confirmed the theoretical findings, showing how parameter variations affect system behavior.

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