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All Journal Kubik Teorema: Teori dan Riset Matematika M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Square : Journal of Mathematics and Mathematics Education KUBIK: Jurnal Publikasi Ilmiah Matematika Jambura Journal of Biomathematics (JJBM) Journal of Fundamental Mathematics and Applications (JFMA)
Khumaeroh, Mia Siti
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Mathematics

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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.
SEIHR-SEI Mathematical Model of Zika Virus Transmission with Vector Control Shiddiqie, Ichwal Afrizan; Khumaeroh, Mia Siti; Zulkarnaen, Diny; Diana, Arista Fitri
KUBIK Vol 9 No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i2.30948

Abstract

Zika virus (ZIKV) is transmitted by Aedes Aegypti mosquito, which is recognized as a vector for viruses causing dengue fever and chikungunya. This study uses SEIHR‐SEI mathematical model to analyze the dynamics of Zika virus transmission. In this model, human population (host) is classified into five compartments: Susceptible Humans (Sh), Exposed Humans (Eh), Infected Humans (Ih), Hospitalized Humans (Hh) and Recovered Humans (Rh). Meanwhile, the mosquito population (vector) is divide into three compartments: Susceptible Vectors (Sv), Exposed Vectors (Ev), and Infected Vectors (Iv). Stability analysis is conducted using Routh‐Hurwitz criteria for assessing local stability and Lyapunov function for evaluating global stability. Moreover, Basic Reproduction Number (R0), which represents the average number of new infections produced by one infected individual in a susceptible population, is derived by using the Next Generation Matrix (NGM) method. The result shows that the equilibrium point for disease‐free conditions is globally asymptotic stable when R0 < 1, meanwhile the equilibrium point for endemic conditions is stable when R0 > 1. The simulation result using endemic data and sensitivity analysis of three parameters, including contact rate between susceptible humans and infected humans (c), hospitalization rate of infected individuals (τ ), and mosquito control rate (ω), reveals that c and ω exert a more significant effect on changes in R0 compared to τ . Therefore, minimizing contact with infected individuals or implementing vector control is more effective than isolating or hospitalizing infected patients.
Panel Data Analysis of Two Level Mixed Linear Models for Factors Affecting The Health Index in West Java Awalluddin, Asep Solih; Khumaeroh, Mia Siti; Amalia, H.; Wahyuni, Inge
KUBIK Vol 9 No 1 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i1.31369

Abstract

The purpose of this study is to construct a multilevel mixed linear model for panel data by estimating parameters and testing the hypothesis of fit of the model with case studies in determining the prediction of the health index for the marginal and conditional models on the factors that influence the prediction of the health index in West Java for 2016 data. -2021, with time (year) and region (district and city) variables as factors involved in the model. Multilevel mixed linear model is the development of a mixed linear model that can be used to analyze correlated panel data. Parameter estimation uses the Maximum Likelihood (ML) method to estimate fixed effect parameters and Restricted Maximum Likelihood (REML) to estimate covariance parameters. The results obtained by the health index prediction model in West Java, both for the marginal and conditional prediction models and goodness of fit model.
Co-Authors Amalia, H. Asep Solih Awalluddin, Asep Solih Aulia, Lathifatul Diana, Arista Fitri Diny Zulkarnaen, Diny Elis Ratna Wulan Erianto, Elvi Syukrina Esih Sukaesih, Esih Fahrudin Muhtarulloh Iktiyar, Zakaria Bani Ilahi, Fadilah Juwita, Rhenata Nela Rizka Nurhakim, Resa Aida Nuwari, Najmudin Romadan, Gilang Shalehah, Mar Atus Shiddiqie, Ichwal Afrizan Wahyuni, Inge