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All Journal Jambura Journal of Biomathematics (JJBM) Mathematical Sciences and Applications Journal
Nela Rizka
Mathematics Department, Faculty of Science, Institut Teknologi Sumatera, Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

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Analisis Model Predator-Prey Tanaman Lada, Hama Penggerek Batang, dan Penghisap Buah M. Diwa Sandika Aditama; Dear Michiko Mutiara Noor; Nela Rizka
Mathematical Sciences and Applications Journal Vol. 4 No. 2 (2024): Mathematical Sciences and Applications Journal
Publisher : Department of Mathematics, Faculty of Science and Technology Universitas Jambi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22437/msa.v4i2.28629

Abstract

Pepper (Piper nigrum L.) is one of the oldest and most popular spices in the world and one of the important plantation crops in Indonesia, especially in Lampung Province. In cultivating pepper plants, many farmers are faced with the problem of pest attacks so that the productivity of pepper plants decreases due to pest attacks. Pests that attack pepper plants in Lampung Province include stem borers and fruit suckers. This research was conducted to look at the predator-prey mathematical model between pepper plants and stem borer and fruit sucking pests and to see the effect of pesticide control on this phenomenon. Modeling was carried out using the Holling II function. The results of numerical simulations on the predator-prey model without control show that the model will be stable in conditions where there is a population of pepper plants, while the populations of stem borers and fruit suckers experience extinction. However, if the parameter values \[ \gamma \] > 0.001045 and \[ \delta \] > 0.008032, then the model will not be stable under these conditions. Furthermore, the simulation shows that the use the use of pesticide control can accelerate the reduction in pest growth.
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.
Co-Authors Dear Michiko Mutiara Noor Erianto, Elvi Syukrina Khumaeroh, Mia Siti M. Diwa Sandika Aditama Nuwari, Najmudin