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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 4, Issue 2: December 2023" : 7 Documents clear
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.
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.
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.
Transmission Dynamics of Tuberculosis Model with Control Strategies Olaosebikan, M. L.; Kolawole, M. K.; Bashiru, K. A.
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.v4i2.21043

Abstract

Tuberculosis (TB) is a global health concern, with a significant proportion of the population at severe risk of infection. Mathematical models can provide valuable insights into the transmission dynamics of TB, especially with the use of vaccination and the mixed proportional incidence rate. In this study, we developed a compartmental model to analyze the impact of mixing proportional incidence rates with vaccination on TB transmission. We conducted a qualitative study on the mathematical model, which included showing that it is unique, positively invariant, and bounded, showing that it is epidemiologically sound to study the physical transmission of TB. We used the homotopy perturbation method to obtain numerical solutions to the model. Using python software, we simulated the obtained results, and our results show that increasing vaccination coverage is an effective measure for reducing TB incidence. Furthermore, our analysis suggests that the mixing proportional incidence rate can be used to predict the spatial spread of TB in a population. It was concluded that vaccination and proportional incidence rate mixing are critical factors to be considered when developing effective TB control strategies.
The Dynamics of a Predator-Prey Model Involving Disease Spread In Prey and Predator Cannibalism Ah, Nurul Imamah; Kusumawinahyu, Wuryansari Muharini; Suryanto, Agus; Trisilowati, Trisilowati
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.v4i2.21495

Abstract

In this article, dynamics of predator prey model with infection spread in prey and cannibalism in predator is analyzed. The model has three populations, namely susceptible prey, infected prey, and predator. It is assumed that there is no migration in both prey and predator populations. The dynamical analysis shows that the model has six equilibria, namely the trivial equilibrium point, the prey extinction point, the disease free and predator extinction equilibrium point, the disease-free equilibrium point, the predator extinction equilibrium point, and the coexistence equilibrium point. The first equilibrium is unstable, and the other equilibria conditionally local asymptotically stable. The positivity and boundedness of the solution are also shown. The analytical result is supported by numerical simulation. It is shown that in such a high cannibalization the coexistence equilibrium is locally asymptotically stable.
Hybrid ARIMA-Spatial Autocorrelation (Moran Index and LISA) for Covid-19 Vaccination in All Indonesian Provinces Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
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.v4i2.20915

Abstract

Numerous issues arise from stochastic processes with temporal and spatial index parameters. From 2020, Covid-19 has occurred worldwide. Combining time series with geographical analysis is crucial. ARIMA and spatial autocorrelation analysis using Moran's Index and LISA are prominent models for the two analyses. ARIMA predicts future values. The ARIMA model is applied to all recorded locations since it involves a stochastic process with a time and location parameter index. Then the prediction results at each location were examined using spatial autocorrelation, starting with the Moran index to see global relationships, then LISA (to look at the relationship between locations locally, to see which locations have a significant effect). The Queen Contiguity weight matrix calculates spatial autocorrelation (assuming that locations that are directly adjacent to each other have a spatial effect). Spatial autocorrelation will divide each place into four quadrants: High-High (HH), High-Low (HL), Low-High (LH), and Low-Low (LL). This approach was applied to 2021 Indonesian vaccination rates in all 34 provinces (354 days). Hence, the ARIMA model was applied to the 34 provinces, and each location received three forecasting. Moran's Index revealed spatial autocorrelation in the 354th and 355th time forecasts. LISA shows that Aceh (LL), West Sumatra (LH), South Sumatra (HH), Lampung (LH), and North Maluku (LL) influence other provinces (LH).

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