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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 44 Documents
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Parameters Estimation of Generalized Richards Model for COVID-19 Cases in Indonesia Using Genetic Algorithm Maya Rayungsari; Muhammad Aufin; Nurul Imamah
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 1: June 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i1.6910

Abstract

In this research, genetic algorithm was implemented to estimate parameters in generalized Richards model by adjusting COVID-19 case data in Indonesia. Data collected were the daily new cases and cumulative number of COVID-19 case in Indonesia from early March to early June 2020, that was reported by databoks.katadata.co.id. The best pair of parameters was selected based on the lowest cost function value, determined from the distance between data with estimated model and real data. Next, model with estimated parameters is used to predict new cases and cumulative cases for upcoming days. Numerical simulations were carried out so that the peaks and ends of the COVID-19 pandemic can be seen easily.
Model matematika SMEIUR pada penyebaran penyakit campak dengan faktor pengobatan Anisa Fitra Dila Hubu; Novianita Achmad; Nurwan Nurwan
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 2: December 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i2.7970

Abstract

This study discusses the spread of measles in a mathematical model. Mathematical modeling is not only limited to the world of mathematics but can also be applied in the health sector. Measles is a disease with a high transmission rate. The spread of measles in this model was modified by adding the treated population and the treatment parameters of the exposed population. In this article, we examine the equilibrium points in the SMEIUR mathematical model and perform stability analysis and numerical simulations. In this study, two equilibrium points were obtained, namely the disease-free and endemic equilibrium point. After getting the equilibrium point, an analysis is carried out to find the stability of the model. Furthermore, the simulation produces a stable disease-free equilibrium point at conditions R01 and a stable endemic equilibrium point at conditions R01. In this study, a numerical simulation was carried out to see population dynamics by varying the parameter values. The simulation results show that to reduce the spread of measles, it is necessary to increase the rate of advanced immunization, the rate of the infected population undergoing treatment, and the proportion of individuals who are treated cured.
Revitalisasi Danau Limboto dengan Pengerukan Endapan di Danau: Pemodelan, Analisis, dan Simulasinya Sri Lestari Mahmud; Novianita Achmad; Hasan S. Panigoro
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 1: June 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i1.6945

Abstract

Limboto lake is one of assets of Province of Gorontalo that provides many benefits to the surrounding society. The main problem of Limboto lake is the silting of the lake due to sedimentation caused by forest erosion, household waste, water hyacinth, and fish farming which is not environmentally friendly. In this article, a mathematical approach is used to modeling the Limboto lake siltation by including the revitalization solution namely the lake dredging. Mathematical modeling begins by building and limiting assumptions, constructing variables and parameters in mathematical symbols, and forming them into a first order differential equation system deterministically. Furthermore, we study the dynamics of the model such as identifying the existence of equilibrium points and their stability conditions. We also give a numerical simulations to show the conditions based on the stability requirements in previous analytical results.
Discrete-time prey-predator model with θ-logistic growth for prey incorporating square root functional response P.K. Santra
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 2: December 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i2.7660

Abstract

This article presents the dynamics of a discrete-time prey-predator system with square root functional response incorporating θ-logistic growth. This type of functional response is used to study the dynamics of the prey--predator system where the prey population exhibits herd behavior, i.e., the interaction between prey and predator occurs along the boundary of the population. The existence and stability of fixed points and Neimark-Sacker Bifurcation (NSB) are analyzed. The phase portraits, bifurcation diagrams and Lyapunov exponents are presented and analyzed for different parameters of the model. Numerical simulations show that the discrete model exhibits rich dynamics as the effect of θ-logistic growth.
A Stage-Structure Rosenzweig-MacArthur Model with Effect of Prey Refuge Lazarus Kalvein Beay; Maryone Saija
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 1: June 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i1.6891

Abstract

We proposed and analyzed a stage-structure Rosenzweig-MacArthur model incorporating a prey refuge.  It is assumed that the prey is a stage-structure population consisting of two compartments known as immature prey and mature prey. The model incorporates the functional response Holling type-II. In this work, we investigate all the biologically feasible equilibrium points, and it is shown that the system has three equilibrium points. Sufficient conditions for the local stability of the non-negative equilibrium point of the model are also derived. All points are conditionally locally asymptotically stable. By constructing Jacobian matrix and determined eigenvalues, we analyzed the local stability of the trivial equilibrium and non-predator equilibrium points. Specifically for coexistence equilibrium point, Routh-Hurwitz criterion used to analyze local stability. In addtion, we investigated the effect of immature prey refuge. Our mathematical analysis exhibits that immature prey refuge have played a crucial role in the behavioral system. When the effect of immature prey refuge (constant m) increases, it is can stabilize non-predator equilibrium point, where all the species can not exists together. And conversely, if contant m decreases, it is can stabilize coexistence equilibrium point then all the species can exists together. The work is completed with a numerical simulation to confirmed analitical results
Global stability of a fractional-order logistic growth model with infectious disease Hasan S. Panigoro; Emli Rahmi
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 2: December 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i2.8135

Abstract

Infectious disease has an influence on the density of a population. In this paper, a fractional-order logistic growth model with infectious disease is formulated. The population grows logistically and divided into two compartments i.e. susceptible and infected populations. We start by investigating the existence, uniqueness, non-negativity, and boundedness of solutions. Furthermore, we show that the model has three equilibrium points namely the population extinction point, the disease-free point, and the endemic point. The population extinction point is always a saddle point while others are conditionally asymptotically stable. For the non-trivial equilibrium points, we successfully show that the local and global asymptotic stability have the similar properties. Especially, when the endemic point exists, it is always globally asymptotically stable. We also show the existence of forward bifurcation in our model. We portray some numerical simulations consist of the phase portraits, time series, and a bifurcation diagram to validate the analytical findings.
Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator Siti Maisaroh; Resmawan Resmawan; Emli Rahmi
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 1: June 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i1.5948

Abstract

The dynamics of predator-prey model with infectious disease in prey and harvesting in predator is studied. Prey is divided into two compartments i.e the susceptible prey and the infected prey. This model has five equilibrium points namely the all population extinction point, the infected prey and predator extinction point, the infected prey extinction point, and the co-existence point. We show that all population extinction point is a saddle point and therefore this condition will never be attained, while the other equilibrium points are conditionally stable. In the end, to support analytical results, the numerical simulations are given by using the fourth-order Runge-Kutta method.
Analisis dinamik model SVEIR pada penyebaran penyakit campak Sitty Oriza Sativa Putri Ahaya; Emli Rahmi; Nurwan Nurwan
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 2: December 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i2.8482

Abstract

In this article, we analyze the dynamics of measles transmission model with vaccination via an SVEIR epidemic model. The total population is divided into five compartments, namely the Susceptible, Vaccinated, Exposed, Infected, and Recovered populations. Firstly, we determine the equilibrium points and their local asymptotically stability properties presented by the basic reproduction number R0. It is found that the disease free equilibrium point is locally asymptotically stable if satisfies R01 and the endemic equilibrium point is locally asymptotically stable when R01. We also show the existence of forward bifurcation driven by some parameters that influence the basic reproduction number R0 i.e., the infection rate α or proportion of vaccinated individuals θ. Lastly, some numerical simulations are performed to support our analytical results.
Bifurkasi Hopf pada Model Lotka-Volterra Orde-Fraksional dengan Efek Allee Aditif pada Predator Hasan S. Panigoro; Dian Savitri
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 1: June 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i1.6908

Abstract

This article aims to study the dynamics of a Lotka-Volterra predator-prey model with Allee effect in predator. According to the biological condition, the Caputo fractional-order derivative is chosen as its operator. The analysis is started by identifying the existence, uniqueness, and non-negativity of the solution. Furthermore, the existence of equilibrium points and their stability is investigated. It has shown that the model has two equilibrium points namely both populations extinction point which is always a saddle point, and a conditionally stable co-existence point, both locally and globally. One of the interesting phenomena is the occurrence of Hopf bifurcation driven by the order of derivative. Finally, the numerical simulations are given to validate previous theoretical results.
Bifurkasi Hopf pada model prey-predator-super predator dengan fungsi respon yang berbeda Dian Savitri; Hasan S. Panigoro
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 2: December 2020
Publisher : Department of Mathematics, State University of 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.

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