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Hasan S Panigoro
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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 30 Documents
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Mathematical Analysis Of The Two-Patch SIRS-SIW Model For The Dynamical Transmission Of Dengue Fever Involving Wolbachia Fitriana Saptaningtyas; Fugo Takasu; Hartono; Fithri Lathifah; Ikha Parwitasari
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 2: June 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i2.87

Abstract

A promising, biologically safe approach to controlling dengue hemorrhagic fever (DHF) is the release of Wolbachia-infected mosquitoes. The use of mathematical modelling to identify optimal control strategies has been the focus of numerous studies. However, the dynamics of human movement between areas where Wolbachia is applied and areas where it is not remain poorly understood. In this study, the spread of dengue fever is examined through a two-patch autonomous ordinary differential equation system encompassing two human population patches, along with Aedes aegypti mosquitoes and Wolbachia, to characterise the dynamics of dengue transmission between humans interacting from two separate patches, alongside the mosquito populations. The Wolbachia strategy has been implemented in portions of the DIY region. We use a two-patch framework to model this issue. We propose developing a mathematical model to investigate the relationship between mosquito bite rates and the proportion of Wolbachia mosquitoes, while accounting for temporary population movements between spatially distinct patches. We assume that the human population is divided into two distinct patches: one in an area where Wolbachia has been implemented and the other in an area where it has not, with a temporary visit between the patches. We compute the local and global stability criteria for the disease-free equilibrium and the basic reproduction number for each patch. In addition, we conducted a thorough analysis of the key parameters related to the proportion of Wolbachia mosquitoes that affect the stability of this equilibrium point. These parameters may serve as vital references to aid in eradicating dengue hemorrhagic fever (DHF) within each patch. Our findings demonstrate that increasing the number of Wolbachia strains significantly limits the spread of dengue in Yogyakarta. The spread of dengue fever can be suppressed by targeting at least 69.9\% of Wolbachia mosquitoes from the total mosquito population.
Modeling Tuberculosis Transmission and Control Using Game Theory and Optimal Strategies Incorporating Migration Flow Dynamics Md. Abu Salek; Mehmet Yavuz; Md. Humayun Kabir; Jannatun Nayeem; Muhammad Hossain; Md. Fayz-Al-Asad
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 2: June 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i2.88

Abstract

A Tuberculosis (TB) transmission model,which optimizes the control strategy with migration dynamics utilizing evolutionary game theory, has been introduced in this work. Besides, the population dynamics is categorized into susceptible, vaccinated, migratory, exposed, infectious, treated, and recovered individuals, while three dynamic controls,distancing, vaccination, and treatment,modulate the spread of disease. Each control measure is considered within the range of 0 to 1 for the governing parameters,namely, migration rate ($\lambda$), treatment rate ($\gamma$), recovery rate ($\delta$) and transmission rate ($\beta$).This study develops a migration-integrated tuberculosis transmission model incorporating susceptible, vaccinated, migratory, exposed, infectious, treated, and recovered populations. Three intervention strategies, namely distancing, vaccination, and treatment, are included to examine their effects on TB transmission. The basic reproduction number is derived, and the positivity and boundedness of the model are established. Numerical simulations are performed using an Adams–Bashforth–Moulton predictor–corrector method. A formal evolutionary game-theoretic framework is introduced through payoff functions and replicator dynamics to evaluate the behavioral preference among the control strategies. The results indicate that treatment produces the strongest reduction in infection prevalence when applied as a single control, while combined strategies provide stronger epidemic suppression when sufficient resources are available. Cost-effectiveness analysis is used to compare the economic efficiency of the intervention strategies. The findings highlight the importance of incorporating migration and behavioral responses into tuberculosis control planning.
Mathematical Modeling of Malaria Transmission in Remote and Underserved Regions: Integrating Healthcare Access and Environmental Management Strategy Sigit Sugiarto; Gusti Arviana Rahman; Taufan Talib
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.v7i3.7

Abstract

Mathematical modeling of malaria transmission remains essential for understanding disease dynamics in remote and underserved regions, where limited access to healthcare and environmental conditions jointly sustain vector-borne transmission. This study develops a mathematical model of malaria transmission that integrates healthcare access constraints and environmental management strategies as key intervention components. The transmission dynamics are formulated as a coupled eight-dimensional nonlinear system representing human SEIRS dynamics and mosquito populations across aquatic and adult (SEI) stages. The model is analyzed by establishing positivity and boundedness of solutions, characterizing equilibrium points, and deriving the basic reproduction number $\mathcal{R}_0$ using the next-generation matrix method. Local stability analysis is conducted using the Routh–Hurwitz criterion, while bifurcation behavior is examined following the Castillo–Chavez and Song framework. The results show that the disease-free equilibrium is locally asymptotically stable when $\mathcal{R}_0 < 1$, whereas endemic persistence occurs when $\mathcal{R}_0 > 1$. Sensitivity analysis indicates that mosquito-related parameters, particularly transmission rate and mortality rates, are the dominant factors that influence $\mathcal{R}_0$. Importantly, integration of healthcare access improvement and environmental management produces a nonlinear synergistic reduction in $\mathcal{R}_0$, with aquatic-stage environmental interventions having a stronger marginal effect on transmission reduction. These findings suggest that effective malaria control in remote and underserved regions requires a balanced integration of clinical access improvement and environmental vector control strategies. Numerical simulations confirm the analytical results and demonstrate the existence of a combined intervention threshold under which malaria elimination becomes achievable in remote and underserved regions. The proposed model provides a more realistic and policy-relevant framework for understanding malaria transmission dynamics and supports integrated control strategies that combine healthcare access and environmental management in geographically constrained settings.
Dynamics of a Mathematical Model of Coral Reef Ecosystems with Harvesting of the Crown-of-Thorns Starfish Alya Saphira; Dian Savitri; Riska Wahyu Romadhonia
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.v7i3.31

Abstract

This study develops a marine ecosystem model involving three species: coral as the prey, Crown-of-Thorns Starfish (CoTS) as the intermediate predator, and Giant Triton as the top predator. The model is formulated to investigate the ecological dynamics associated with CoTS outbreaks, which have become a critical environmental issue due to their significant impact on coral cover and their association with the decline of natural predators. A tritrophic predator–prey model incorporating CoTS harvesting as a population control strategy is developed based on Holling Type I and Type II functional responses. The model is analyzed through equilibrium analysis, local stability analysis, and bifurcation analysis. The results identify three biologically relevant equilibrium points: the extinction of the intermediate predator and top predator populations ($E_1$), the equilibrium between the prey and the intermediate predator in the absence of the top predator ($E_2$), and the coexistence equilibrium of all three species ($E_3$). Numerical simulations show that the stability of $E_3$ is regulated by the harvesting parameter ($H$). A supercritical Hopf bifurcation occurs at $H \approx 0.007968$, leading to the emergence of stable periodic oscillations when the harvesting rate is below this critical threshold. Stable coexistence of the three species is maintained within an intermediate harvesting range of $0.007968 < H < 0.338462$. However, excessive harvesting beyond the upper critical threshold disrupts the trophic structure and causes the system to transition to the top-predator-free equilibrium ($E_2$) through the extinction of the Giant Triton population. These findings highlight the importance of appropriate harvesting intensity in maintaining ecosystem stability. Insufficient CoTS harvesting results in persistent oscillatory dynamics, whereas excessive harvesting destabilizes trophic interactions by reducing prey availability for the top predator. Therefore, maintaining CoTS harvesting within an appropriate range is essential for preserving stable species coexistence and supporting the long-term resilience of coral reef ecosystems.
Exploring the Dynamics of Two Prey and One Predator System with Fear Effect Nithya Dakshnamoorthy; Buddana Murty; Madhusudanan Vasudevan; Dadi Saraswathi
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.v7i3.118

Abstract

This research focuses on analyzing a predator–prey system consisting of two prey species and one predator, where the prey experience fear due to the predator’s presence. The predator interacts with Prey I through a Holling Type I response and with Prey II through a Holling Type II response. Predators play a multifaceted role in shaping prey populations, as supported by biological research, by combining direct predation with indirect effects such as fear-induced stress and increased intraspecific competition. We analyzed the positivity, boundedness and condition for persistence of the system and investigate the presence of positive equilibrium points as well as their practicality. The Routh – Hurwitz condition is used to determine the stability locally at all equilibrium points. We show that the model's stability globally exists. Numerical simulations are performed to examine the system dynamics and the sensitivity to key parameters, including the fear response intensity and conversion coefficient. The results indicate that higher parameter values tend to produce oscillatory behavior, whereas lower carry-over effects promote system stability. Furthermore, the interaction between competition among Prey I and Prey II and predator-induced fear leads to a reduction in the long-term population sizes of both species. As the level of fear increases beyond a threshold, the system shifts from persistent oscillations to a stable equilibrium.
Two-patch malaria transmission model: The impact of temperature variability, human mobility and relapse mechanism Beza Aga; Temesgen Keno; Chernet Deressa
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.v7i3.14

Abstract

Malaria remains a major vector-borne infectious disease, particularly in tropical and subtropical regions, where transmission is driven by the bite of \textit{Anopheles} mosquitoes. Human mobility plays a critical role in shaping the spatial spread of malaria, while temperature variability significantly affects mosquito biting and mortality rates. In this study, we develop and analyze a two-patch compartmental model to investigate the combined impact of temperature variability, human movement, and relapse mechanisms on malaria transmission dynamics across regions with differing endemicity levels. We first verify that the model solutions are non-negative and bounded, confirming the well-posedness of the model from both mathematical and epidemiological perspectives. The next-generation matrix method is used to determine the basic reproduction number, $\mathcal{R}_{0}^{m}$. According to stability analysis, the malaria-free equilibrium is unstable when $\mathcal{R}_{0}^{m} \geq 1$ and locally and globally asymptotically stable when it is less than unity. This work makes a significant contribution by calibrating the model using reported malaria case data from Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025, which allows for the estimate of critical transmission parameters and model validation. Numerical simulations demonstrate that malaria prevalence is sensitive to both human mobility between patches and temperature variability. The movement of ignorant individuals between patches significantly affects transmission dynamics, as they carry parasites undetected into low-transmission areas and seed new outbreaks. The results further highlight the role of relapse in sustaining transmission. Our findings suggest that targeted control of human movement between high- and low-prevalence regions, combined with environmental monitoring, could significantly reduce the malaria burden.
Modelling Tuberculosis Dynamics with Optimal Control Time-Dependent Interventions Mahsa Hamidi; Omid Solaymani Fard; Olumuyiwa James Peter; Zahra Dayheem; Rantiola Famutimi; Hasan S Panigoro
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.v7i3.23

Abstract

Tuberculosis (TB) remains a major global health challenge, particularly in low- and middle-income countries. This study evaluates the impact of vaccination on TB dynamics using a mathematical model that incorporates two susceptible classes. The model examines the interplay between population characteristics, transmission pathways, treatment strategies, and intervention measures. The basic reproduction number, a key threshold parameter, is derived, and the global stability of both the disease-free and endemic equilibria is established. Furthermore, the model is extended to formulate an optimal control problem incorporating three time-dependent control functions: vaccination of susceptible individuals, public health education for the exposed population, and home-based treatment for infected individuals. Numerical simulations illustrate the theoretical results and show that, among the strategies considered, combining preventive measures with targeted vaccination is most effective in reducing TB infections. The findings provide insights into TB control and offer practical guidance for designing effective public health interventions.
Stability and Optimal Control of a Nonlinear Tourism--Environment Dynamic System for Sustainable Tourism Management Ida Ayu Putu Ari Utari; Subchan Subchan; Nikenasih Binatari; Fugo Takasu
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.v7i3.47

Abstract

The rapid growth of the tourism sector has generated several challenges, including increased tourist pressure, environmental degradation, and economic imbalances. These challenges can be addressed by developing mathematical models for sustainable tourism. This study develops a nonlinear dynamic model to describe the interactions among tourist numbers, economic growth, investment in the tourism sector, and environmental quality within the framework of sustainable tourism management. The model is formulated as a system of nonlinear ordinary differential equations that accounts for the impact of environmental quality on the growth of the tourism and economic sectors. In this study, a dynamic analysis was conducted, including the formulation of a well-posed model, the determination of equilibrium points, and a local stability analysis in their vicinity. Next, to develop an effective tourism system management strategy, an optimal control approach was employed using two control variables. The results of the numerical simulation show that the model can qualitatively represent the dynamics of a sustainable tourism system and that the application of optimal control can improve the balance among the number of tourists, economic growth, investment, and environmental sustainability.
A Mathematical Model for Rumor Propagation Considering Awareness Effect Venn Yan Ishak Ilwaru; Lazarus Beay; Lusye Bakarbessy; Maryone Saija; Meilly Silalily; Serli Ilela
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.v7i3.54

Abstract

Nowadays, the prevalence of social networks in our societies is well-established, as are their positive and negative implications. The effect of misinformation can lead to detrimental consequences in various aspects of life. This emphasizes the importance of proper control over information. Next, we present a new rumor model in this publication, distinguished by its consideration of irresolute individuals. A basic reproduction number (R0) is the threshold for rumor propagation, which is determined through a next-generation matrix approach. Additionally, we utilize the Jacobian matrix method alongside Lyapunov stability theory to provide a rigorous proof for the local and global asymptotic stability of both the rumor-free and rumor equilibria. The analysis results show that the rumor-free equilibria will be locally and globally stable for R0 < 1, and vice versa. Any change in the parameters of human consciousness (v) or human unconsciousness (w) significantly affects population dynamics. Moreover, a set of numerical simulation experiments and the subsequent analysis of their results are presented to validate the effectiveness of the model under consideration. Finally, the effects of various parameters within the proposed model have been examined.
Dynamics of a predator-prey system incorporating a saturated prey refuge and a fear-induced Allee effect Debasis Mukherjee
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.v7i3.142

Abstract

This study focuses on a predator-prey system featuring saturated prey refuges and an Allee effect arising from the prey's fear response. Analytical investigation reveals various aspects, including positivity, the bounds of solutions, and local stability of the coexistence equilibrium point. The local bifurcations (Hopf and transcritical) are discussed. The nature of the limit cycle resulting from a Hopf bifurcation is stated. It is shown that the increasing amount of fear and the Allee effect can produce complicated dynamics that can be controlled by refuge use. Moreover, fear and the Allee effect do not influence the prey density, though they can decrease the predator density at the equilibrium level. Refuge can increase the prey density, but no thet predators. The numerical simulations validate the theoretical outcomes, providing practical insights into the model's behaviour. The novelty of the work is how fear and the Allee effect reduce predator numbers without altering prey numbers at equilibrium density. It also assures that prey refuges raise prey numbers but not the predators.

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