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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 7 Documents
 1 
Search results for , issue "Volume 5, Issue 2: December 2024" : 7 Documents clear
Mathematical Model of the Impact of Home-Based Care on Contagious Respiratory Illness Under Optimal Conditions Wanjala, Henry Milimo; Okongo, Mark; Ochwach, Jimrise
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.v5i2.27611

Abstract

Mathematical models are vital for understanding real-world phenomena without direct experimentation, particularly in epidemics, as they predict and analyze the effectiveness of various mitigation strategies. Given the rapid transmission of infectious respiratory diseases, public health measures aim to curb spread while managing impacts. This study assesses rapid contact tracing and testing, focusing on isolating confirmed cases through home-based care or traditional methods, on coronavirus transmission within a community.A deterministic mathematical model using ordinary differential equations segments the population into seven compartments: susceptible, exposed, asymptomatic, symptomatic, home-based care, hospitalized, and recovered. The basic reproduction number is determined via the next generation matrix. Local stability of the disease-free equilibrium is analyzed using the trace-determinant method, while global stability is confirmed with the Lyapunov-Krasovskii approach. A Python-based numerical simulation on NumPy and PyPlot uses parameters calibrated to previous studies and estimated for this research. Simulations indicate home-based care delays peak infection days and reduces peak population, providing time to bolster healthcare facilities. Optimal control methods, including media awareness, reduce susceptibility and encourage asymptomatic individuals to choose home-based care. Using Pontryagin's Maximum Principle, the study identifies optimal strategies, highlighting that media awareness effectively lowers susceptibility and optimal control directs asymptomatics to home-based care, reducing strain on healthcare facilities. In conclusion, home-based care is effective for managing mild symptomatic and asymptomatic cases, alleviating pressure on healthcare resources and prioritizing severe cases. Combining home-based care with other non-pharmaceutical strategies is recommended for maximum effectiveness.
Mathematical Model of SAR-CoV-2 and Influenza A Virus Coinfection within Host with CTL-Mediated Immunity Khumaeroh, Mia Siti; Nuwari, Najmudin; Erianto, Elvi Syukrina; Rizka, Nela
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.v5i2.27782

Abstract

Coinfection of SARS-CoV-2 and Influenza A virus within a host poses a unique challenge in understanding immunological dynamics, especially the role of cytotoxic T lymphocytes (CTL) in mediating the immune response. This work present a mathematical model to examine the dynamics of coinfection within a host, highlighting CTL-mediated immunity. Generally, this model encompasses several compartments, including epithelial cells, free viruses, and CTLs specific of both SARS-CoV-2 and Influenza A. The basic properties of the model, equilibrum state analysis, stability using the Lyapunov function, and numerical simulations are examined to investigate the dynamics behavior of the model. Eight equilibrium states are identified: the virus-free equilibrium (E0), single SARS-CoV-2 infection without CTLs (E1), single Influenza A virus infection without CTLs (E2), single SARS-CoV-2 infection with SARS-CoV-2-specific CTLs (E3), single Influenza A virus infection with Influenza A virus-specific CTLs (E4), SARS-CoV-2 and Influenza A virus coinfection with SARS-CoV-2-specific CTLs (E5), SARS-CoV-2 and Influenza A virus coinfection with Influenza A virus-specific CTLs (E6), and SARS-CoV-2 and Influenza A virus coinfection with both SARS-CoV-2-specific and Influenza A virus-specific CTLs (E7). The existence and stability regions for each equilibrium state are determined and represented in the R1-R2 plane as threshold functions within the model. Numerical simulations confirm the results of the qualitative analysis, demonstrating that CTLs specific to SARS-CoV-2 and Influenza A virus can be activated, reducing the number of infected epithelial cells as well as inhibiting virus transmission within epithelial cells. Furthermore, analysis of parameter changes shows that increasing the proliferation rate of epithelial cells and CTLs, while lowering the virus formation rate, can shift the system's stability threshold and stabilize it at the virus-free equilibrium.
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.
Optimizing Algal Bloom Through Bioenzyme and Harvesting Control for Bioenergy Purposes in Eutrophic Water Bodies Akbar, Fadilah; Mardlijah, Mardlijah
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.v5i2.26938

Abstract

This article discusses the optimization of algae growth for bioenergy purposes in eutrophic water bodies through bioenzyme control and harvesting. The study explores innovative approaches to manage algae growth in such water bodies. A mathematical model based on dynamical systems, specifically the NASC (Nutrients, Algae, Detritus, and Dissolved Oxygen) algae growth model, was used for the analysis. The results indicate that the system used is unstable, given the needs of algae growth over time. To optimize algae growth, this study proposes controlling the bioenzyme (u1) feeding to decompose detritus into nutrients and harvesting algae using (u2). The Pontryagin Maximum Principle (PMP) method was used to obtain optimization with control parameters u1=0.093 and u2=0.32. The results show that the optimal time to harvest algae is every 84 days or 2.8 months, with an estimated harvestable amount of 16.3667  . This discovery enhances our understanding of controlling algae growth in the context of renewable energy and reinforces the mathematical approach to managing eutrophic aquatic ecosystems.
A Fractional Mathematical Model for Controlling and Understanding Transmission Dynamics in Computer Virus Management Systems Yunus, Akeem Olarewaju; Olayiwola, Morufu Oyedunsi; Ajileye, Adewole Mukaila
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.v5i2.25956

Abstract

The constant danger of computer viruses and malware makes it difficult to safely simulate the management of computer systems over time for both networks and individual users. The present study proposes a novel six-compartment fractional model that builds on existing classical frameworks and examines the existence and uniqueness of its solution, indicating that it is both mathematically and biologically well-posed. Additionally, we compute the fundamental reproduction number R0 and use sensitivity analysis to investigate the impact of various factors on the model's behavior. The Laplace Adomian Decomposition Method is employed for numerical analysis, and its findings have the potential to transform computer security and network management by providing robust countermeasures and eradication tactics. The complex properties of the fractional-order model are further explored by examining the memory effect of fractional order on system dynamics. The research findings offer valuable insights for virus managers in developing and implementing effective management methods and can successfully prevent the spread of computer viruses by leveraging these discoveries. In conclusion, this study provides significant insights and solutions for protecting the integrity of digital domains and network infrastructure.
Forward and Backward Bifurcation Analysis From an Imperfect Vaccine Efficacy Model With Saturated Treatment and Saturated Infection Fatahillah, Hakan Ahmad; Aldila, Dipo
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.v5i2.28810

Abstract

This paper aims to study the saturation effect on the infection and recovery process within a Susceptible-Vaccination-Infected model featuring an imperfect vaccine efficacy. First, we nondimensionalized the model under the assumption of a constant population, resulting in the reduction of the model from three to two-dimensional differential equations. The analysis indicates the presence of a disease-free equilibrium (DFE) and potentially multiple endemic equilibria (EE) within the model. The calculation of the basic reproduction number further explains the model's solution conditions. In particular, we discovered that a backward bifurcation is possible under specific saturation effect values. Dulac's criterion confirmed the absence of a closed orbit in the solution region, suggesting the global stability of the endemic equilibrium when the basic reproduction number exceeds one. To supplement the analytical study, a numerical simulation was conducted to generate a bifurcation diagram, autonomous simulation, and global sensitivity analysis. The global sensitivity analysis revealed that changing the vaccination rate or recovery rate could significantly impact the basic reproduction number. Moreover, the bifurcation diagram depicting the relationship between the transmission rate and vaccination rate demonstrated that increasing the vaccination rate while maintaining the transmission rate can reduce the proportion of infected individuals within the population.

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