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All Journal Journal of Tropical Life Science : International Journal of Theoretical, Experimental, and Applied Life Sciences MATEMATIKA The Journal of Experimental Life Sciences (JELS) CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Mahasiswa Matematika Journal of Innovation and Applied Technology Natural B Journal of Mathematical and Fundamental Sciences JTAM (Jurnal Teori dan Aplikasi Matematika) Limits: Journal of Mathematics and Its Applications Indonesian Journal of Electrical Engineering and Computer Science Jambura Journal of Biomathematics (JJBM) Jurnal Matematika Integratif Limits: Journal of Mathematics and Its Applications
Wuryasari Muharini Kusumawinahyu
Jurusan Matematika, Fakultas MIPA, Universitas Brawijaya
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Environmental Science Immunology & microbiology Mathematics Mechanical Engineering Medicine & Pharmacology Neuroscience Physics Transportation

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Dynamical Analysis and Optimal Control of Breast Cancer Patient Model Muniroh, Kunnisai; Habibah, Ummu; Kusumawinahyu, Wuryansari Muharini
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): 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/cauchy.v10i1.31514

Abstract

This research studied the dynamics model of breast cancer patients that was built as a dynamical system. The model had five compartments, including the subpopulations of stage 1 and 2 breast cancer patients, stage 3 cancer patients, stage 4 cancer patients, recovered individuals due to chemotherapy treatment, and patients who suffered cardiotoxicity. Equilibrium points and local stability were determined. The dynamical analysis resulted in one equilibrium point that exists and is stable under certain conditions. The model was constructed with the assumption that all patients undergo intensive chemotherapy treatment. This treatment caused side effects in the form of cardiotoxicity. Therefore, optimal control of additional treatment and ketogenic diet was applied. Additional treatment control is applied to prevent cardiotoxicity, while ketogenic diet control is used to reduce tumor cell growth. The aim of optimal control was to find out the treatment strategy that is effective in reducing cardiotoxicity and treatment costs. Numerical simulations were conducted to support the analysis results.
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 Andonowati Andonowati Ani Budi Astuti Deasy Sandhya Elya Ikawati Fitroh Aulani Hadinata, Nadia Agus Hidayatulloh, Muhammad Rif’an Ikawati, Deasy Sandhya Elya Isnani Darti Khozaimi, Ach. Kwardiniya Andawaningtyas Lu’luul Wardah Muna Afdi Muniroh Muna Afdi Muniroh Muniroh, Kunnisai Ni’matur Rohmah Nurul Imamah Purnomo, Anna Silvia Puspitasari, Nurmaini Shofiyya, Nada Syafitri, Risyqaa Syaiful Anam Trisilowati Trisilowati Trisilowati Trisilowati Trisilowati, Trisilowati Trisilowati, Trisilowati Ummu Habibah, Ummu Yuni Ayu Anita