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All Journal Journal of Tropical Life Science : International Journal of Theoretical, Experimental, and Applied Life Sciences The Journal of Experimental Life Sciences (JELS) CAUCHY: Jurnal Matematika Murni dan Aplikasi Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Biomathematics (JJBM)
Trisilowati Trisilowati, Trisilowati
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Agriculture, Biological Sciences & Forestry Arts Humanities Biochemistry, Genetics & Molecular Biology Computer Science & IT Decision Sciences, Operations Research & Management Environmental Science Immunology & microbiology Mathematics Medicine & Pharmacology Neuroscience

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Kontrol Optimal pada Model Epidemi SEIQR dengan Tingkat Kejadian Standar Zulaikha, Zulaikha; Trisilowati, Trisilowati; Fadhilah, Intan
Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Vol 1 No 1 (2017): Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai Islami )
Publisher : Mathematics Department

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (749.077 KB)

Abstract

Penelitian ini dilakukan dengan modifikasi model epidemik SEIQR dengan tingkat kejadian standar dan kontrol optimal. Kontrol optimal dilakukan dengan menambahkan dua variabel kontrol yaitu usaha pengontrolan kontak langsung antara populasi rentan dengan populasi terinfeksi, dan pemberian obat pada populasi terinfeksi. Tujuan penelitian ini adalah untuk meminimumkan jumlah subpopulasi yang terinfeksi, jumlah subpopulasi laten, jumlah biaya edukasi dan biaya pemberian obat. Kondisi kontrol optimal pada penelitian ini diperoleh dengan menggunakan prinsip minimum Pontryagin. Selanjutnya, simulasi numerik dilakukan dengan metode Sweep Maju-Mundur untuk menunjukkan bagaimana pengaruh adanya kontrol terhadap model epidemik. Hasil penelitian yang dilakukan menunjukkan bahwa dengan adanya kontrol terlihat efektif dalam menekan jumlah pertumbuhan subpopulasi terinfeksi dengan subpopulasi laten.
Dynamics of a Fractional Order Eco-Epidemiological Model Nugraheni, Kartika; Trisilowati, Trisilowati; Suryanto, Agus
Journal of Tropical Life Science Vol 7, No 3 (2017)
Publisher : Journal of Tropical Life Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11594/jtls.07.03.09

Abstract

In this paper, we propose a fractional order eco-epidemiological model. We considere the existence of time memory in the growth rate of the three populations. We observed the dynamical behaviour by analysing with fractional order and then simulateing using Grünwald-Letnikov approximation to support analytical results. It found that the model has five equilibrium points, namely the origin, the survival of susceptible prey, the predator free equilibria, the infected prey free equilibria, the interior equilibria. Numerical simulations show that the existence of fractional order  is a factor which affects the behaviour of solutions. 
A Dynamical Analysis on a Tumour Virotherapy Model with Standard Incident Rate Ikawati, Deasy Sandhya Elya; Kusumawinahyu, Wuryansari Muharini; Trisilowati, Trisilowati
Journal of Tropical Life Science Vol 7, No 1 (2017)
Publisher : Journal of Tropical Life Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11594/jtls.07.01.03

Abstract

This paper discusses a dynamical analysis on a model that governs the growth of tumour cell under a therapy by using oncolytic viruses, on the standard incident rate. The model is a modification of the similar one by replacing the bilinear incident rate with the standard one. The conducted dynamical analysis consists of the determination of equilibrium points and their existence conditions, followed by local as well as global stability analysis of the equilibrium points. The analytical result shows that there are two equilibrium points, namely uninfected and the endemic point, which needs a condition to exist. Stability analysis shows that there is a dimensionless basic reproduction number that marks the existence as well as the stability of equilibrium points. When basic reproduction number is less than one, there is only the uninfected equilibrium, which is global asymptotically stable. On the other hands, both of equilibrium points exist when the basic reproduction number is more than one, but the uninfected point is not stable anymore, while the endemic one is local asymptotically stable under a condition. Some numerical simulations are performed to illustrate the analytical result. Numerically, it can also be demonstrated that there is a set of parameters which indicates that tumour can be fully removed.  
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.
The Dynamics of a Predator-Prey Model Involving Disease Spread In Prey and Predator Cannibalism Ah, Nurul Imamah; Kusumawinahyu, Wuryansari Muharini; Suryanto, Agus; Trisilowati, Trisilowati
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.21495

Abstract

In this article, dynamics of predator prey model with infection spread in prey and cannibalism in predator is analyzed. The model has three populations, namely susceptible prey, infected prey, and predator. It is assumed that there is no migration in both prey and predator populations. The dynamical analysis shows that the model has six equilibria, namely the trivial equilibrium point, the prey extinction point, the disease free and predator extinction equilibrium point, the disease-free equilibrium point, the predator extinction equilibrium point, and the coexistence equilibrium point. The first equilibrium is unstable, and the other equilibria conditionally local asymptotically stable. The positivity and boundedness of the solution are also shown. The analytical result is supported by numerical simulation. It is shown that in such a high cannibalization the coexistence equilibrium is locally asymptotically stable.
The Impact of Releasing Domestic Dogs on the Spread of Rabies Disease and Its Prevention Ahmad Fitri, Afit; Marsudi, Marsudi; Trisilowati, Trisilowati
The Journal of Experimental Life Science Vol. 13 No. 2 (2023)
Publisher : Graduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.jels.2023.013.02.09

Abstract

The government's program to achieve rabies-free status by 2030 is an initiative to accelerate the eradication of rabies cases in Indonesia. Rabies is a highly contagious disease with a 100% fatality rate, and dogs are the main carriers of the virus. The government's efforts to minimize rabies cases include vaccination of susceptible animals, eliminating rabid dogs, and implementing dog population management (MPA). Field observations indicate that the practice of releasing domestic dogs allowing them to roam freely, has led to an increase in rabies cases. Using mathematical modeling, this husbandry system's impact can be simulated. Based on the model analysis, it is determined that a maximum of 15% of domestic dogs should be allowed to roam freely. If this threshold is exceeded, it becomes necessary to ensure a minimum of 20% vaccination coverage and eliminate at least 1% of rabid dogs. Keywords: Dogs, Rabies Disease, Releasing Domestic Dogs.
Dynamics of Covid-19 model with public awareness, quarantine, and isolation Syafitri, Risyqaa; Trisilowati, Trisilowati; Kusumawinahyu, Wuryansari Muharini
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.19832

Abstract

This paper presents a new COVID-19 model that contains public awareness, quarantine, and isolation. The model includes eight compartments: susceptible aware (SA), susceptible unaware (SU), exposed (E), asymptomatic infected (A), symptomatic infected (I), recovered (R), quarantined (Q), and isolated (J). The introduction will be shown in the first section, followed by the model simulation. The equilibrium points, basic reproduction number, and stability of the equilibrium points are then determined. The model has two equilibrium points: disease-free equilibrium point and endemic equilibrium point. The next-generation matrix is used to calculate the basic reproduction number R0. The disease-free equilibrium point always exists and is locally stable if R0 1, whereas the endemic equilibrium point exists when R0 1 and is locally stable if satisfying the Routh-Hurwitz criterion. Stability properties of the equilibrium confirmed by numerical simulation also show that quarantine rate and isolation rate have an impact in the transmission of COVID-19
KFCM-PSOTD : An Imputation Technique for Missing Values in Incomplete Data Classification Ilyas, Muhaimin; Anam, Syaiful; Trisilowati, Trisilowati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i1.25138

Abstract

Data mining is a very important process for finding out the data interpretation. Data preprocessing is the crucial data mining steps. The existence of missing values in the data is one of the primary issues with data preprocessing. Generally, this can be overcome with mean or median imputation because they are easy to implement. However, the use of these techniques is not recommended because they ignore the data variance. This research develops the Kernel Fuzzy C-Means Optimized by the Particle Swarm Optimizer with Two Differential Mutations (KFCM-PSOTD).  KFCM imputation is applied to obtain better estimation values due to its proven ability to recognize patterns in the data. In addition, the PSOTD algorithm is used as an optimization tool to boost the KFCM's performance. PSOTD is adopted because it has more balanced exploration and exploitation capabilities compared to classical PSO. Datasets that have been imputed on KFCM-PSOTD are classified using the Decision Tree algorithm. The results are evaluated using accuracy, precision, recall, and f1 score to determine the quality of the imputed values. The outcomes demonstrate that the KFCM-PSOTD algorithm has a better performance; even the difference in evaluation scores obtained reaches 10% better than other imputation techniques. 
Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations Puspitasari, Nurmaini; Kusumawinahyu, Wuryansari Muharini; Trisilowati, Trisilowati
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 5, No 1 (2021): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v5i1.3893

Abstract

This article discussed about a dynamic analysis of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.
Dynamical Analysis of the Symbiotic Model of Commensalism in Four Populations with Michaelis-Menten type Harvesting in the First Commensal Population Puspitasari, Nurmaini; Kusumawinahyu, Wuryansari Muharini; Trisilowati, Trisilowati
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 5, No 2 (2021): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v5i2.4727

Abstract

This study discusses the dynamical analysis of the symbiosis commensalism and parasitism models in four populations with Michaelis-Menten type harvesting in the first commensal population. This model is formed from a construction of the symbiotic model of commensalism and parasitism by harvesting the commensal population. This construction is by adding a new population, namely the second commensal population. Furthermore, it will be investigated that the four populations can coexist. The first analysis is to identify the conditions of existence at all equilibrium points along with the conditions for their existence and local stability around the equilibrium point along with the stability requirements. From this model, it is obtained sixteen points of equilibrium, namely one point of extinction in the four populations, four points of extinction in all three populations, six points of extinction in both populations, four points of extinction in one population and one point where the four populations can coexist. Of the sixteen points, only four points can be asymptotically stable if they meet the stability conditions that have been determined. Finally, a numerical simulation is performed to describe the model behavior. In this study, the method used in numerical simulation is the RK-4 method. The numerical simulation results that have been obtained support the dynamical analysis results that have been carried out previously.
Co-Authors Agus Suryanto Ahmad Fitri, Afit Ikawati, Deasy Sandhya Elya Ilyas, Muhaimin Intan Fadhilah, Intan Isnani Darti Kartika Nugraheni M.Pd S.T. S.Pd. I Gde Wawan Sudatha . Marsudi Marsudi Musafir, Raqqasyi Rahmatullah Nurul Imamah Puspitasari, Nurmaini Rois, Muhammad Abdurrahman Syafitri, Risyqaa Syaiful Anam Ummu Habibah, Ummu Wuryasari Muharini Kusumawinahyu Zulaikha Zulaikha