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Hasan S Panigoro
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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 96554, Gorontalo, Indonesia
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Jambura Journal of Biomathematics (JJBM)
Published by Universitas Negeri Gorontalo
ISSN : -     EISSN : 27230317     DOI : https://doi.org/10.37905/jjbm
Core Subject : Health, Science, Education,
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Public Health
The Jambura Journal of Biomathematics JJBM is a peer reviewed academic journal published by the Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo, Indonesia. The journal is established with the vision of becoming a leading scientific publication in Southeast Asia and serves as a platform for researchers, academicians, and practitioners to publish original research articles and review papers. JJBM focuses on explaining complex biological phenomena through mathematical approaches and acts as a bridge between theoretical mathematics and the life sciences. JJBM has a broad and interdisciplinary scope covering various research areas. The journal welcomes high quality submissions involving mathematical analysis, computational modeling, and statistical methods to generate biological insights. The main areas include population dynamics, evolutionary dynamics, epidemiology, infectious disease modeling, systems biology, ecological modeling, and optimal control in biological systems. Through this scope, JJBM aims to support innovation in both mathematics and biological applications. To ensure scientific quality and originality, every submitted manuscript undergoes a single blind peer review process by experts in the field. The journal applies a strict policy against plagiarism and uses tools such as Turnitin to ensure originality. All accepted manuscripts are required to be prepared using LaTeX to maintain consistency and quality in mathematical formatting. JJBM is published quarterly in March, June, September, and December. The journal follows an open access policy, allowing all published articles to be freely accessed by the public. This approach supports wider dissemination of knowledge and increases the visibility and impact of published research. JJBM is committed to publication ethics and accessibility. The journal follows the guidelines of the Committee on Publication Ethics COPE. To support inclusivity, JJBM provides waiver options for article processing charges for authors from low and lower middle income countries.
Arjuna Subject : Matematika - Matematika Terapan
Articles 35 Documents
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Optimal Control Strategy and Dynamical Analysis of AI-Supported Mutated Computer Viruses in Network Systems Mehmet Kocabiyik
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 3: September 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i3.28

Abstract

Computer viruses continue to be a serious problem on network infrastructure, with the ability to use AI to self-mutate and optimize its propagation. These virus variants that are influenced by AI are capable of adapting their attack method by themselves, which makes the known defense methods ineffective and necessitates advanced defense arrangements. The paper introduces a deterministic mathematical model with six compartments: Susceptible, Protected, Latent, Infected, Mutated, Recovered to study the macroscopic population dynamics of computer viruses based on the AI model. The basic reproduction number is calculated and a complete stability analysis of the equilibrium points is performed. An optimal control framework is developed to identify the best mitigation strategies with regard to proactive patching and reactive cleaning. An explicit existence theorem is proved and Pontryagin's Minimum Principle is used to describe the optimal control pair. To check the validity of the theoretical results, numerical simulations are carried out, which are based on the fourth-order Runge-Kutta method and the Forward-Backward Sweep Method. Our results show that AI-influenced viruses can be an endemic threat due to their increased mutation rate, but the dual-control strategy is a very reliable and cost-effective model for viral suppression. Sensitivity analyses, including 3D cost surfaces, also further validate this finding that synchronized proactive and reactive controls do an effective job of minimizing viral persistence and optimizing defense resource allocation.
Comparing Unstructured Kinetic Growth Models of Debaryomyces hansenii in Xylitol Production from Oil Palm Empty Fruit Bunch Hydrolysis Alvioni Bani; Kasbawati Kasbawati; Syamsuddin Toaha; Efri Mardawati; Misri Gozan; Yeyen Nurhamiyah; Biqiong Chen
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 3: September 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i3.34

Abstract

This study aims to determine the optimal growth model for xylose fermentation using Debaryomyces hansenii with a substrate derived from oil palm empty fruit bunch (OPEFB) hydrolysate. An unstructured model was developed by observing the dynamics of Debaryomyces hansenii as biomass, xylose as the substrate, and xylitol as the product, utilizing both growth-associated and non-growth-associated product formation approaches. Four kinetic models for the specific growth rate (Aiba, Blackman, Monod, and Moser) were evaluated to fit the experimental data. The fitting process was performed by minimizing the Root Mean Square Error (RMSE) and validated using the coefficient of determination (R2) and the Normalized Root Mean Square Error (NRMSE). The evaluation results indicate that xylitol production by \textit{Debaryomyces hansenii} is predominantly decoupled from active cell growth and occurs primarily during the stationary phase. The Moser model proved to be the best-fitting model, exhibiting the lowest RMSE value (0.1789) and high predictive accuracy (R2 for biomass = 0.96; xylitol = 0.89). Parameter perturbation-based sensitivity analysis demonstrated that a 50\% increase in the maximum specific growth rate ($\mu_{max}$) and the ratio between the yield coefficients for xylitol production and biomass formation from the substrate (Y2) could double xylitol production by the end of fermentation, whereas a 50\% decrease in the maintenance coefficient (m) could increase the product concentration by more than two-fold.
Multiple Coexistence Equilibria, Stability Switching, and Bifurcations in a Plant-Pest-Predator Model Eduart Wolok; Resmawan Resmawan; Mehmet Yavuz; Olumuyiwa James Peter; Sharifah Sakinah Syed Ahmad
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 3: September 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i3.107

Abstract

This study formulates and analyzes a three-dimensional plant-pest-predator model with logistic plant growth and nonlinear trophic interactions. The main objective is to investigate how pest conversion efficiency influences population persistence, equilibrium stability, and changes in long-term dynamics. The model is shown to preserve nonnegativity and boundedness of solutions, ensuring its biological feasibility. Several equilibrium states are identified, including the pest-free equilibrium, the predator-free equilibrium, and two possible coexistence equilibria. Local stability analysis reveals that the pest-free state is stable when the pest cannot invade the plant population, whereas the predator-free state may become stable when the pest persists but the predator cannot establish. The two coexistence equilibria exhibit different dynamical properties: the branch associated with the lower plant density is unstable, while the branch associated with the higher plant density can be locally asymptotically stable. Bifurcation analysis shows that variation in pest conversion efficiency generates multiple transcritical bifurcations connecting the pest-free, predator-free, and coexistence states. The stable coexistence equilibrium may subsequently lose stability through a Hopf bifurcation, leading to oscillatory population dynamics. Numerical simulations support the analytical findings and illustrate the transitions from pest extinction to predator-free persistence, stable coexistence, and oscillatory behavior. These results demonstrate that pest conversion efficiency plays a central role in determining predator invasion, coexistence stability, and the effectiveness of biological pest control.
Fractional Order Derivative Model and Analysis of Tuberculosis Transmission Kumama Cheneke; Fatmawati Fatmawati
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 3: September 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i3.158

Abstract

This paper constructs a fractional derivative model of TB in the Caputo sense. By using the Laplace definition in fractional derivative and fractional integral along with the stated Lipschitz condition, the proposed model's mathematical acceptability and biological significance are confirmed. The basic reproduction number is calculated by incorporating the spectral radius of the next-generation matrix. We compute steady states and demonstrate the local stability of the TB-free equilibrium. Sensitivity index is computed and the most contributor parameter to TB disease persistence and extinction is identified. Analytical and numerical simulation analysis results are consistent with one another. Furthermore, the TB fractional model solutions demonstrate that a higher order of fractional derivative corresponds to a lower population infection rate. Since the population's memory is correlated with the order of fractional derivative, a higher level of activation of memory toward tuberculosis infection means that the disease will spread and advance less. The interactive numerical scheme is derived and the fractional TB model is solved to support the analytical results.
Numerical Simulation for The Dynamical Interaction of Aphids and Ladybugs Using Micken's Finite Difference Scheme Viska Noviantri; Eloise Sari; Dani Suandi
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 3: September 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i3.162

Abstract

Significant agricultural losses worldwide can be caused by pests, such as aphids, especially in tropical regions like Indonesia. It is interesting to analyze aphid population growth to determine the proper steps in controlling plant pests to minimize these losses. Pesticides are a common way to reduce aphid populations. In this study, a mathematical model is used to predict aphid growth when pesticides and the presence of ladybugs, their natural predator, are considered. This model consists of three nonlinear differential equations with four equilibrium points, one of which is the interior equilibrium point. The stability characteristics of the interior equilibrium point are evaluated using Monte Carlo simulations, as the system's complexity renders analytical methods impractical in this context. Additionally, the robustness of the stability is examined by analyzing its sensitivity to parameter variations, providing insights into the system's stability under different conditions. The model was then solved numerically using Micken's Non-Standard Finite Difference (NSFD) scheme. NSFD is a more robust and reliable option than standard finite-difference methods, especially for modeling complex dynamics. In this numerical scheme, the time step size is adjusted based on the eigenvalues of the Jacobian matrix for a nonlinear system model. As a result, the numerical scheme shows higher accuracy than the 4th-order Runge-Kutta scheme. Several simulations were carried out here and validated analytically using the equilibrium points. Furthermore, this paper analyzes the model's sensitivity to examine the behaviour of aphids and ladybugs under parameter changes, thereby minimizing the trial-and-error process of controlling plant pests that may not be effective.

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