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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 1: June 2024" : 7 Documents clear
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.
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 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.
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.
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.

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