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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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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.
A Qualitative Analysis of Leukemia Fractional Order SICW Model Das, Kalyan; Kumar, G. Ranjith; Ramesh, K.; Biswas, Md. Haider Ali
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.v5i1.24961

Abstract

Using a series of fundamental differential equations, including the Caputo derivative, which makes it easier to specify the initial conditions of the differential equations, we present a fractional order concept of leukemia in this study. The universality, positivity, and boundedness of solutions are first established. The local stability properties of the equilibrium are studied using the fractional Routh-Hurwitz stability criteria. The differential equation system has been solved using unconventional finite difference techniques. The Leukemia Fractional Order SICW model introduces several innovative elements compared to traditional epidemiological and disease models. This stands out due to its integration of fractional-order differential equations, inclusion of leukemic cells and immune cells compartments, simulation of treatment strategies, consideration of waning immunity, and its application to leukemia-specific scenarios. These elements collectively make it a valuable tool for studying leukemia dynamics, exploring treatment options, and improving our understanding of how the immune system interacts with cancer cells in leukemia patients. Numerical simulations of the model are shown at the conclusion to interpret our theoretical outcomes in support of various fractional orders of derivative   options. From there, we can observe how the evolution of the system components is impacted by the fractional derivative .
Comparison of Fractional-Order Monkeypox Model with Singular and Non-Singular Kernels Musafir, Raqqasyi Rahmatullah; Suryanto, Agus; Darti, Isnani; Trisilowati, Trisilowati
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.v5i1.24920

Abstract

The singularity of the kernel of the Caputo fractional derivative has become an issue, leading many researchers to consider the Atangana-Baleanu-Caputo (ABC) fractional derivative in epidemic models where the kernel is non-singular. In this context, the objective of this study is to compare the calibration and forecasting performance of fractional-order monkeypox models with singular and nonsingular kernels, represented by the model with respect to the Caputo operator and the ABC operator, respectively. We have proposed a monkeypox epidemic model with respect to the ABC operator (MPXABC), where the model with respect to the Caputo derivative (MPXC) has been proposed in previous research. We have analyzed the existence and uniqueness of the solution. Three equilibrium points of the model are endemic, human endemic, and monkeypox-free, and their global stability has been investigated. The global dynamics of the MPXABC are the same as those of the MPXC. In evaluating the performance, we collected secondary data on weekly monkeypox cases from June 1 to November 23, 2022, in the USA. Parameter estimation has been performed using the least squares method, while the solutions of the model have been determined numerically using a predictor-corrector scheme. The benchmark for performance has been determined based on the root mean square error. Data calibration and forecasting indicate that the MPXC generally has the best performance for each value of the derivative order. For certain values of derivative order, the MPXABC performs better than the corresponding firstorder model. However, generally, the corresponding first-order model performs better than the MPXABC. Depending on the data trends and the specified orders, the MPXC outperforms the MPXABC. Thus, the singularity issue of the Caputo derivative does not always have a negative impact on model fitting to data.
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.
Unveiling SIR Model Parameters: Empirical Parameter Approach for Explicit Estimation and Confidence Interval Construction Susyanto, Nanang; Arcede, Jayrold P.
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.v5i1.26287

Abstract

We propose a simple parameter estimation method for the Susceptible-Infectious-Recovered (SIR) model. This method offers explicit estimates of parameters using second-order numerical derivatives to construct empirical parameters. In addition, the method constructs confidence intervals, providing a robust assessment of parameter uncertainty. To validate the accuracy of our method, we applied it to simulated data, in order to demonstrate its effectiveness in accurately estimating the true model parameters. Furthermore, we applied this method to actual COVID-19 case data from the USA, Indonesia, and the Philippines. This application enables the estimation of parameters and reproductive numbers, along with their confidence intervals, thus underscoring the efficacy of our technique. Notably, the parameter estimates obtained through our approach successfully predicted the case numbers in all three countries, confirming its predictive reliability. Our method offers significant advantages in terms of simplicity and accuracy, making it an invaluable tool for epidemiological modeling and public health planning.
Dynamical System for Tuberculosis Outbreak with Vaccination Treatment and Different Interventions on the Burden of Drug Resistance MA, Ratnah Kurniati; Sugiarto, Sigit; Nurwijaya, Sugian
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.v5i1.21903

Abstract

Tuberculosis, a highly contagious and lethal infectious disease, remains a global health concern with challenging treatment options. To combat its widespread impact, prevention strategies, such as vaccination, are imperative. This research focuses on developing a mathematical model with the addition of a vaccination compartment to understand the dynamics of tuberculosis transmission with vaccination. Subsequently, the study proceeds to identify the equilibrium points and calculate the basic reproduction number (ℜ0). Following this, a comprehensive stability analysis is conducted, and a numerical simulation is executed to observe the population dynamics. Furthermore, parameter sensitivity analysis is undertaken to assess the extent to which these parameters impact ℜ0. Preliminary analysis shows that the modified model has a solution that remains in the non-negative and bounded region. Furthermore, model analysis reveals two equilibrium points, namely the disease-free equilibrium and the endemic equilibrium. It is established that the disease-free equilibrium exhibits local asymptotic stability when ℜ0 1. Remarkably, the numerical simulation aligns with the analytical findings, reinforcing the robustness of the results. Analysis of the sensitivity of the parameter to ℜ0 shows that the parameter of the proportion of susceptible population entering the vaccination class has a significant effect on the value of ℜ0. The parameter of proportion of susceptible population entering the vaccination class has a negative effect on the number of populations with infection.
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).
Sensitivity Analysis of SI1I2RS Model for Dengue Fever Transmission Blante, Trianty Putri; Jaharuddin, Jaharuddin; Nugrahani, Endar Hasafah
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.v5i1.23132

Abstract

Dengue fever is a disease caused by dengue virus transmitted through Aedes aegypti mosquitoes. This study discusses the SI1I2RS epidemic model in the spread of dengue fever, assuming that people with this disease can experience severe and mild symptoms. The analysis in this research aims to determine the stability of the equilibrium point, primary reproduction number, parameter sensitivity, and numerical simulation to determine the effect of parameters on the dynamics of the spread of dengue fever. The results of this analysis show two equilibrium points, namely the disease-free equilibrium point, which is locally asymptotically stable when R0 1 and the endemic point, which is locally asymptotically stable when R0 1. Numerical simulations show that the change in the parameter of the average bite of individual mosquitoes in humans has a significant effect on the primary reproductive number where when the moderate acidity of individual mosquitoes in humans is 0.05 and the contact rate of disease transmission from infected mosquitoes to susceptible humans is 0.025, it can suppress the spread of dengue fever. Therefore, individuals must maintain cleanliness and take precautions against the spread of dengue fever.
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.

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