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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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Mathematical Model and Simulation of the Spread of COVID-19 with Vaccination, Implementation of Health Protocols, and Treatment Manaqib, Muhammad; Mahmudi, Mahmudi; Prayoga, Galuh
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.19162

Abstract

This research develops the SVEIHQR model to simulate the spread of COVID-19 with vaccination, implementation of health protocols, and treatment. The population is divided into twelve subpopulations, resulting in a mathematical model of COVID-19 in the form of a system of twelve differential equations with twelve variables. From the model, we obtain the disease-free equilibrium point, the endemic equilibrium point, and the basic reproduction number (R0). The disease-free equilibrium point is locally asymptotically stable when R0 1 and ∆5 0, where âˆ†5 is the fifth-order Routh-Hurwitz matrix of the characteristic polynomial of the Jacobian matrix. Additionally, an endemic equilibrium point exists when R0 1. The results of numerical simulations are consistent with the conducted analysis, and the sensitivity analysis reveals that the significant parameters influencing the spread of COVID-19 are the proportion of symptomatic infected individuals and the contact rate with asymptomatic infected individuals.
Factors causing Dengue Hemorrhagic Fever (DHF) in Sikka District, East Nusa Tenggara Province Kleden, Maria Agustina; Atti, Astri; Talahatu, Anna Henny
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.19460

Abstract

Dengue Hemorrhagic Fever (DHF) is a disease caused by infection of the Dengue virus. The incidence of Dengue Fever in Sikka District is the highest in East Nusa Tenggara Province and even in Indonesia at the beginning of 2020. The condition of DHF occurrence in Sikka District is designated as an Extraordinary Event (EE). This study aims to identify some factors including the home environment, biological environment, and social environment that might lead to the occurrence of DHF in Sikka Regency and to determine the risk of a person getting DHF based on the factors. There were 170 respondents from the community of Sikka Regency, where 85 of them have suffered from DHF while the other 85 have never had DHF. The instrument used was a questionnaire containing 22 questions that have been tested for validity and reliability. This is a quantitative study, where the analytical method used is the logistic regression analysis. The results of the analysis showed that the factors that affect a person suffering from DHF are the size of the house, the color of the walls of the house, the habit of draining water reservoirs, the habit of using mosquito repellent, and the participation in cleaning mosquito nests. Based on the value of the odds ratio, it is known that a person with a house area of 36 m2 is more at risk of contracting dengue fever than someone with a house area of 36 m2. Likewise, households that did not participate in cleaning mosquito nests were compared to those who did participate. It is also found that house members who have light wall colors, have a habit of draining water reservoirs, and have a habit of using mosquito repellent are more at risk of contracting DHF than family members whose walls are dark in color, do not have the habit of draining water reservoirs, and do not participate in cleaning mosquito nests.
Two isolation treatments on the COVID-19 model and optimal control with public education Rois, Muhammad Abdurrahman; Fatmawati, Fatmawati; Alfiniyah, Cicik
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.19963

Abstract

This study examines a COVID-19 mathematical model with two isolation treatments. We assume that isolation has two treatments: isolation with and without treatment. We also investigated the model using public education as a control. We show that the model has two equilibria based on the model without control. The basic reproduction number influences the local stability of the equilibrium and the presence of an endemic equilibrium. Therefore, the optimal control problem is solved by applying Pontryagin's Principle. In the 100th day following the intervention, the number of reported diseases decreased by 85.5% when public education was used as the primary control variable in the simulations.
Sensitivity Analysis and Optimal Control of Covid 19 Model Firmansyah, Firmansyah; Rangkuti, Yulita Molliq
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.19025

Abstract

Coronavirus infection is a disease that causes death and threatens human life; for prevention, it is necessary to quarantine susceptible, exposed, and infected populations and vaccinate the entire population. This kind of quarantine and vaccination is intended to reduce the spread of coronavirus. Epidemiological models are a strategy used by public health practitioners to prevent and fight diseases. However, to be used in decision making, mathematical models must be carefully parameterized and validated using epidemiological and entomological data. Epidemiological models: susceptible, symptomatic, contagious, and recovering. In this study, sensitivity analysis and optimal control were performed to determine the relative importance of the model parameters and to minimize the number of infected populations and control measures against the spread of the disease. Sensitivity analysis was carried out using a sensitivity index to measure the relative change in the basic reproduction number for each parameter, and this control function was applied to the dynamic modeling of the spread of COVID-19 using the Pontryagin Minimum Principle. We will describe the formulation of a dynamic system for the spread of COVID-19 with optimal control and then use Pontryagin's Minimum Principle to find optimal control solutions. In this article, COVID-19 cases in the USA and India serve as examples of the efficiency of control measures. The results obtained revealed that the parameters that became the basis for reducing the number of infected with COVID-19 for the two countries, the USA and India, are effective transmission rates from S to E, (β), transmission rates from E to I, (α), and transmission rates from S to R, (ps), which are the main parameters to watch for growth with respect to Basic Reproduction rates (R0). Finally, three controls were simulated in cases I (in the USA) and II (in India) in the interval t ∈ [0, 15]. For all controls, the effectiveness was close to 50% in India and 100% in the USA to reduce the spread of COVID 19. According to the findings, if these three controls were implemented ideally from the start of the pandemic, the number of sufferers.
Exploring of Homotopy Perturbation Method (HPM) for Solving Spread of COVID-19 Nasution, Hamidah; Mulyono, Mulyono; Surbakti, Nurul Maulida; BR Sihaholo, Ruth Salisa
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.21560

Abstract

This article discusses the solution to the non-linear differential equation system for the spread of COVID19 with SEIR (Susceptible, Exposed, Infected, Recovered) model using the Homotopy Perturbation Method. Specifically, this article examines the impact of moving the recovered subpopulation back to the susceptible subpopulation on the spread of COVID-19 in the city of Medan. The data used is real data for the city of Medan in 2021. The results of constructing a model for the spread of COVID-19 were analyzed to obtain a disease-free critical point. By using the Next Generation Matrix method, the Basic Reproduction number R0 = 4.61 is obtained, this indicates that COVID-19 is still possible to spread in Medan City. Simulations using the Homotopy Perturbation Method numerical approach and the results compared with the Runge Kutte Order 4 method show results that accurately describe the dynamics of the spread of COVID-19 in Medan City. The very small error indicates that the Homotopy Perturbation Method is very suitable for use in solving non-linear differential equation systems, especially in the SEIRS model of the spread of COVID-19. The simulation results show that the impact of the movement of recovered sub-populations to susceptible sub-populations results in accelerated transmission of COVID-19. The greater the number of movements higher the rate of spread of COVID-19.
Prediction of the Change Rate of Tumor Cells, Healthy Host Cells, and Effector Immune Cells in a Three-Dimensional Cancer Model using Extended Kalman Filter Fitriyati, Nina; Faizah, Salma Abidah; Sutanto, Taufik Edy
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.24672

Abstract

In this study, we develop and implement the Extended Kalman Filter (EKF) to forecast the rate of change in tumor cells, healthy host cells, and effector immune cells within the Itik-Banks model. This novel application of EKF in cancer dynamics modeling aims to provide precise real-time estimations of cellular interactions, especially in constructing a new state space representation from the Itik-Banks model. We use a first-order Taylor series to linearize the model. The numerical simulations were performed to analyze the accuracy of this new state space with data from William Gilpin's GitHub repository. The results show that the EKF predictions strongly align with actual data, i.e., in the prior and posterior steps for tumor and healthy host cells, there is a strong agreement between the predictions and the actual data. The EKF captures the oscillatory nature of the tumor and healthy host cell population well. The peaks and troughs of the predictions align closely with the actual data, indicating the EKF's effectiveness in modeling the dynamic behavior of the tumor and healthy host cells. However, for effector immune cells, the oscillatory nature of the data in these cells gives rise to slight deviations. This represents a significant challenge in the future for updating the state space representations. Despite minor discrepancies, the EKF demonstrates a strong performance in both the training and testing data, with the posterior step estimates significantly improving the prior step accuracy. This study emphasizes the importance of data availability for accurate predictions, noting a symmetric Mean Absolute Percentage Error (sMAPE) of 35.92% when data is unavailable. Prompt correction with new data is essential to maintain accuracy. This research underscores the EKF's potential for real-time monitoring and prediction in complex biological systems.
Bifurcation analysis of phytoplankton-fish model through parametric control by fish mortality rate and food transfer efficiency Das, Kalyan; Madhusudanan, V.; Srinivas, M. N.; Kabir, Md Humayun; Gani, Md Osman; Islam, Sardar M. N.
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.21480

Abstract

An Algae-zooplankton fish model is studied in this article. First the proposed model is evaluated for positive invariance and boundedness. Then,the Routh-Hurwitz parameters and the Lyapunov function are used to determine the presence of a positive interior steady state and the criteria for plankton model stability (both local and global). Taylor's sequence is also used to discuss Hopf bifurcation and the stability of bifurcated periodic solutions. The model's bifurcation analysis reveals that Hopf-bifurcation can occur when mortality rate and food transfer efficiency are used as bifurcation parameters. Finally, we use numerical simulation to validate the analytical results.
Dynamical Behavior in Prey-Predator Model with Mutualistic Protection for Prey Putri, Laras Kinanti; Savitri, Dian; Abadi, Abadi
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.21541

Abstract

This article reconstructs the model of predator-prey mutualistic protection based on a journal written by Revilla and Krivan (2022). The predator-prey model considers mutualistic protection for the prey. The model focuses on the analysis of equilibrium points and combines an adaptive model to study the influence of both models on predator-prey dynamics. This research continues the stability analysis and numerical simulations of the predator-prey model with mutualistic protection to examine the impact of mutualistic protection on prey dynamics in the model. The research process begins with a literature review, reconstructing the predator-prey model, determining equilibrium points, analyzing stability at the equilibrium points, conducting numerical simulations including bifurcation diagrams and phase portraits of the model solutions, and drawing conclusions. The analysis yields three equilibrium points: the unstable co-extinction of both populations, predator extinction, and the conditionally stable coexistence of both populations. Based on the analysis results, there are changes in the system solutions, with the originally stable E3 becoming unstable. There is also a change in E2 from being unstable to stable. Through numerical continuation with variations in the parameter representing the mutualistic protector's preference for prey resources (u), a transcritical bifurcation (Branch Point) is obtained at u = 0.888889. The simulation results demonstrate that (u) can influence the stability of predator and prey populations.
Comparison of Optimal Control Effect from Fungicides and Pseudomonas Fluorescens on Downy Mildew in Corn Ludji, Dian Grace; Hurit, Roberta Uron; Manek, Siprianus Septian; Ndii, Meksianis Z
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.23153

Abstract

Downy mildew is a disease that continues to infect corn crops in Timor Tengah Utara regency, reducing the amount of crop production and making corn farmers suffer losses. Farmers continue to look for ways to control downy mildew. Two treatments are commonly used by farmers, namely spraying Fungicides and Pseudomonas Fluorescens simultaneously in one unit of time, but have not resulted in optimal production. Therefore, this research is important to get a more optimal way to control find downy mildew. In this paper, we determine the optimal model of downy mildew control in corn plants by comparing the use of Fungicides and Pseudomonas Fluorescens. This research begins by forming a dynamic mathematical model consisting of six populations, namely four corn populations (Sh, F , P , Ih) and two populations of infecting fungi (Sv , Iv ). Then they obtained the basic reproduction number (R0) and two equilibrium points, namely the disease-free equilibrium and the disease-endemic equilibrium which has asymptotic stability. Numerical simulation results based on optimal control analysis with the minimum Pontryagin principle show that using fungicides can reduce the number of plants infected with downy mildew. Therefore, control by using fungicides is necessary and recommended increasing the number of downy mildew infected plants.
A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator Beay, Lazarus Kalvein; Leleury, Zeth Arthur; Rijoly, Monalisa E.; Lesnussa, Yopi Andry; Wattimena, Abraham Zacaria; Rahakbauw, Dorteus Lodewyik
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.22047

Abstract

The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results.

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