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All Journal Kubik Square : Journal of Mathematics and Mathematics Education Journal of Intelligent Computing and Health Informatics (JICHI) KUBIK: Jurnal Publikasi Ilmiah Matematika Jurnal Pengabdian Masyarakat Intimas (Jurnal INTIMAS): Inovasi Teknologi Informasi Dan Komputer Untuk Masyarakat Journal of applied statistics and data mining Joong-Ki
Diana, Arista Fitri
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Religion Humanities Computer Science & IT Decision Sciences, Operations Research & Management Dentistry Economics, Econometrics & Finance Education Electrical & Electronics Engineering Environmental Science Mathematics Medicine & Pharmacology Public Health Social Sciences

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Analisis Kestabilan Lokal Model Transmisi Demam Berdarah Dengue Diana, Arista Fitri; Hajar, Muhammad Ibnu; Ikhtiyar, Zakaria Bani; Aulia, Lathifatul
Square : Journal of Mathematics and Mathematics Education Vol. 6 No. 1 (2024)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2024.6.1.21018

Abstract

Dengue fever transmission in Indonesia has an advanced amount. In this article, dynamic model of interaction between human and Aedes aegypti mosquitos is learned. The SEIRRD (Susceptible, Exposed, Infected, Recovered, Deceased) model is used in this article. The prurpose in this model is to describe the stability of dengue transmission, so that we can analyze the developed of epidemic model in mathemtic field. Using NGM method to analyze basic reproduction number and applying Routh-Hurwitz criteria method to show the local stability of model. Then, two equilibrium points, called endemic and non-endemic equilibrium points, are obtained. The result of basic reproduction number is described the stability analysis. If basic reproduction number less then one, the endemic equilibrium point is locally asymptotically stable and otherwise. Local stability analysis at the equilibrium point is determined through parameter analysis. Furthermore, numerical simulations are carried out by fitting the data to obtaine the result of the parameters. The results of numerical simulations explaine the spread of dengue transmission Keywords: Dynamic Model, Epidemic Model, Equilibrium Point, Local Stability, Routh Hurwitz
Model Kontrol Pada Ekosistem Perkebunan Teh Diana, Arista Fitri; Romadan, Gilang; Khumaeroh, Mia Siti; Aulia, Lathifatul; Iktiyar, Zakaria Bani
Square : Journal of Mathematics and Mathematics Education Vol. 6 No. 2 (2024)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2024.6.2.23274

Abstract

Tea plants are one of the commodities in Indonesia. In their development, the plantation ecosystem is heavily influenced by several factors, both internal and external factors. In the field of applied mathematics, mathematical modelling can be used to analyze the development of tea plant growth and their interaction each othe in their ecosystem. The mathematical model in this research is combining three main models, there are logistic model, epidemiological model, and predator prey model by adding fungicide and insecticide controls. Furthermore, local stability analysis is carried out and the optimal control problem is solved by Pontryagin maximum principle. The results of the analysis obtained five equilibrium points. Local stability analysis was carried out using the Routh Hurwitz criteria which showed the fifth equilibrium point is locally asymptotically stable. The basic reproduction number in the model is 0,99. Because  it can be concludeed that there is no spread of disease in the tea plantation ecosystem after a period of 5 years. The control provided can reduce pest and disease attacks. After being given control, the population of infected tea plants decreased by 93,21%, Empoasca pests decreased by 99,47%, and leaf roller caterpillars decreased by 99,31% compared to the model that was not given control.Keywords: Tea Plantation, Dynamical Model, Fungicide, Insecticide, Optimal Control.
Co-Authors ALYA MASITHA Aulia, Lathifatul Cahyani, Annisa Nur Diny Zulkarnaen, Diny Hajar, Muhammad Ibnu Ikhtiyar, Zakaria Bani Iktiyar, Zakaria Bani Khumaeroh, Mia Siti Mahardika, Dhimas Muhammad Sulthan, Muhammad Rahmasari, Shafira Meiria Romadan, Gilang Romadon, Gilang Sakti, Ayutdi Purbo Sari, Virgania Shiddiqie, Ichwal Afrizan Sulthan Madani, Muhammad