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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Biomathematics (JJBM) ISTEK
Erianto, Elvi Syukrina
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Decision Sciences, Operations Research & Management Electrical & Electronics Engineering Mathematics

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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.
Drug-Drug Interactions Pharmacokinetic Models with Extravascular Administration: Estimation of Elimination and Absorption Rate Constants Zulkarnaen, Diny; Irfani, Muhammad Syifa; Erianto, Elvi Syukrina
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16479

Abstract

One and two-compartment pharmacokinetic models with drug-drug interactions are proposed. Two drugs are given orally simultaneously, so that their interaction affects the drug absorption process and subsequently the elimination process. The aim of this paper is to estimate the elimination and absorption rate constants by evaluating the data set of time and drug concentration. This data set was divided into two time phases: large-time elimination phase to estimate the elimination rate constant, and small-time absorption phase to estimate the absorption rate constant. Since the models are nonlinear, the Taylor expansion is employed to so that the Wagner-Nelson and the Loo-Riegelman methods can be used for estimation. Finally, simulations were performed using the generated arbitrary data set of time and concentration, instead of an actual data set, to derive the solution of drug concentration concerning time numerically. In these simulations we compared the original parameter values with their estimates for the one and two-compartment models, and we concluded that the two-compartment model produced better estimates than the one-compartment model. Qualitatively, the two-compartment model gives smaller drug concentration curve deviations between the original and the estimated curve compared with the one-compartment model.
Numerical Simulation of Fluid Flow on An Open Channel with Parabolic Cross-section Erianto, Elvi Syukrina; Aprilia, Nadya Zulfani; Khumaeroh, Mia Siti
ISTEK Vol. 14 No. 2 (2025)
Publisher : Fakultas Sains dan Teknologi UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/istek.v14i2.2447

Abstract

Water is a vital resource whose movement is influenced by various factors such as gravity and frictional force. The cross-sectional shape of a channel can significantly influence the friction force,consequently, affect the flow characteristics. One of the interesting cross-sectional shapes to analyze is parabolic because of its unique geometric properties. This study aims to conduct a numerical simulation of open channel flow within a parabolic cross-section using a modified Shallow Water Equation and the Finite Volume Method implemented with a staggered grid scheme. The mathematical model used takes into account the influence of the parabolic shape through the calculation of Manning's friction, which depends on the hydraulic radius. The Shallow Water Equations, consisting of the continuity and momentum equations, are solved numerically through spatial and temporal discretization. The simulations are perfomed using Scilab to generate visualizations of the water depth and flow velocity distribution under various geometric conditions. This study produces simulations of one-dimensional (1D) and two-dimensional (2D) dam-break flows with a parabolic cross section and compares them with the rectangular cross-section. The simulation results show that the finite volume method with the staggered grid scheme provides stable solutions and is capable of accurately describing the flow behavior across different channel geometries.
Co-Authors Aprilia, Nadya Zulfani Diny Zulkarnaen, Diny Irfani, Muhammad Syifa Khumaeroh, Mia Siti Nela Rizka Nuwari, Najmudin