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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi DEDIKASI: Community Service Reports
Noorma Yulia Megawati
Universitas Gadjah Mada
Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Education Environmental Science Mathematics Mechanical Engineering Physics Social Sciences Other

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A Mathematical Model of Human-to-Human Transmission of Monkeypox with Reinfection Eka Widia Rahayu; Noorma Yulia Megawati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40140

Abstract

Monkeypox is a zoonotic disease caused by the monkeypox virus and remains a public health concern due to its potential for sustained human-to-human transmission. This study analyzes the transmission dynamics of monkeypox by developing a deterministic compartmental model that explicitly incorporates reinfection arising from waning immunity. The model is analyzed by deriving the basic reproduction number and determining the disease-free and endemic equilibrium points, whose local and global stability properties are rigorously investigated. A sensitivity analysis is conducted to identify key parameters driving transmission dynamics. Motivated by these results, an optimal control problem is formulated in which vaccination is implemented as a time-dependent control, and the optimal strategy is characterized using Pontryagin’s Minimum Principle. Numerical simulations reveal that even low reinfection rates can sustain endemic transmission in the absence of control, while appropriately timed vaccination strategies significantly reduce infection levels and prevent long-term persistence.
Workshop Peningkatan Kompetensi Guru Matematika SMA/MA Kabupaten Banyumas melalui Pelatihan Materi Olimpiade Matematika SMA Made Tantrawan; Erni Widiyastuti; Sri Wahyuni; Nanang Susyanto; Noorma Yulia Megawati; Zenith Purisha; Ari Dwi Hartanto; Uha Isnaini; Iwan Ernanto; Hadrian Andradi; Rahmasari Nur Azizah
DEDIKASI: Community Service Reports Vol 7, No 2 (2025): DEDIKASI: Community Service Report - July
Publisher : FKIP Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/dedikasi.v7i2.95193

Abstract

Dalam rangka meningkatkan kompetensi dan kemampuan mengajar guru-guru dalam bidang matematika, sejalan dengan standar kompetensi guru yang ditetapkan pemerintah dalam Permendiknas Nomor 16 Tahun 2007, Departemen Matematika Universitas Gadjah Mada (UGM) bekerja sama dengan Universitas Muhammadiyah Purwokerto mengadakan workshop pelatihan olimpiade matematika yang ditujukan kepada guru-guru Matematika yang tergabung dalam MGMP Matematika SMA/MA Kabupaten Banyumas. Workshop ini telah dilaksanakan pada tanggal 9 Oktober 2024 di SMAN 3 Purwokerto. Kegiatan ini merupakan keberlanjutan dari program PkM yang telah diinisiasi oleh Departemen Matematika UGM sejak 2017. Dukungan berkelanjutan ini diharapkan dapat memperkuat keterampilan guru dalam penguasaan konsep matematika dan aplikasinya dalam pembelajaran di kelas, sehingga berkontribusi pada peningkatan kualitas pendidikan di Indonesia, khususnya di kabupaten Banyumas.
Co-Authors Ari Dwi Hartanto Eka Widia Rahayu Erni Widiyastuti Hadrian Andradi Iwan Ernanto Made Tantrawan Nanang Susyanto Rahmasari Nur Azizah Ratna Widayati Sholikhatun Sholikhatun Sri Wahyuni Uha Isnaini Zenith Purisha