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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika Mutiara Medika: Jurnal Kedokteran dan Kesehatan Medical Laboratory Technology Journal Saintifik : Jurnal Matematika, Sains, dan Pembelajarannya Griya Journal of Mathematics Education and Application Journal of Experimental and Clinical Pharmacy (JECP) Pengabdian Kampus: Jurnal Informasi Kegiatan Pengabdian Pada Masyarakat Pharmaceutical Sciences and Research (PSR) Barigas: Jurnal Riset Mahasiswa Journal of Mathematics, Computation and Statistics (JMATHCOS) Diophantine Journal of Mathematics and Its Applications
Widayati, Ratna
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Dentistry Economics, Econometrics & Finance Education Engineering Environmental Science Health Professions Immunology & microbiology Industrial & Manufacturing Engineering Materials Science & Nanotechnology Mathematics Medicine & Pharmacology Neuroscience Nursing Physics Public Health Social Sciences Other

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Journal : Griya Journal of Mathematics Education and Application

 1 
Analisis Kestabilan Global dan Analisis Sensitivitas pada Model Matematika Penyebaran Penyakit Gondongan Widayati, Ratna; Rachmawati, Ramya; Afandi, Nur
Griya Journal of Mathematics Education and Application Vol. 5 No. 2 (2025): Juni 2025
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v5i2.578

Abstract

Mumps is a contagious viral disease transmitted through respiratory droplets and close contact. It can cause symptoms like fever and salivary gland swelling. Despite the MMR vaccine, which offers partial protection, outbreaks persist, especially in college-aged individuals. Epidemiological models can aid in identifying effective prevention strategies for controlling mumps transmission. This paper proposes a mathematical model for mumps spread, considering quarantined individuals and complications. A global stability analysis of the mumps transmission model was performed, considering mortality and quarantine subpopulation. The Disease Free Equilibrium and Endemic Equilibrium Point are globally stable, confirmed by Lyapunov functions. Sensitivity analysis of the basic reproduction number shows that reducing birth rates and contact between infected and susceptible individuals effectively minimizes the infected population. However, increasing the natural death rate can reduce the total population, which may lower infections, but poses potential social and economic challenges for decision-makers.
Modifikasi Operator Weighted Backward Shift untuk Membentuk Operator Hypercyclic pada Ruang Barisan Nur Afandi; Damayanti, Septri; Widayati, Ratna
Griya Journal of Mathematics Education and Application Vol. 5 No. 2 (2025): Juni 2025
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v5i2.648

Abstract

The linear operator T: X --> X is called an hypercyclic operator if there exist such that the orbit of under the operator T is dense in X. This study aims to construct an explicit hypercyclic operator on the sequence space \(\ell^p\), by modifying the backward shift operator using a non-constant weight sequence. This approach differs from Rolewicz's classical method, which used constant weights. The method applied is constructive and formal, relying on deductive reasoning in mathematical proofs. Two operators—weighted left and right shifts—are introduced and their properties are analyzed, including their composition and iterative behavior. The main result is the construction of a specific operator \(S_\bold{a}\) weighted by \(\bold{a}=(a_n)\) that is proven to be hypercyclic. The proof involves demonstrating the existence of a vector whose orbit under \(S_\bold{a}\) is dense in \(\ell^p\).
Co-Authors Adelia, Sirli Adryannoor, Muhammad Rafli Arif Rahman Jabal Arini Ratnasari Augustina, Indria Balyas, Abi Bakring Dian Mutiasari, Dian Eka Susilowati, Eka Elsa Trinovita Fatmaria, Fatmaria Frethernety, Agnes Hamim Muntoha, Renal Hanasia, Hanasia Handayani, Septi Kristiani, Friska Merilia Dwi Lestarisa, Trilianty Ma'rifah, Umi Maulia, Desi Rahma Mizan Ahmad Natalia Sri Martani Nita Yulianti, Nita Nugrahini, Sintha Nuha, Alya Firyal Nur Afandi Patricia, Tisha Permatasari, Silvani rachmawati, Ramya Rakhman, Farizky Ranintha br Surbakti Ranti, Dalia Reviladi, Intrada Rian Ka Praja Savitri, Dilasari Septri Damayanti Sibarani, Juliet Valeria Sitorus, Elisabeth Prihana Rotua Sofiyati, noor Toemon, Agnes Immanuela Turnip, Oktaviani Naulita