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Bifurkasi Pada Model Penyebaran Penyakit MERS-CoV di Dua Wilayah dengan Populasi Konstan Livia Owen
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is caused by a novel coronavirus and it can be a human-to-human transmission disease. World Health Organization (WHO) reported the disease outbreak first happened in Saudi Arabia in 2012 and the last case is reported in 2019. In 2018, MERS-CoV outbreaks were reported in the Republic of Korea, United Kingdom of Great Britain, Northern Ireland, Saudi Arabia, Uni Arab Emirates, Oman, and Malaysia. Cases that are identified outside the Middle East are usually caused by traveling people who were infected in the Middle East and then traveled back to their country. The previous research had constructed a mathematical model for the transmission of MERS-CoV in two areas by separating the human population into susceptible and infectious groups. It focused on the basic reproductive number and sensitivity analysis. In this paper, we simplify the model with the assumption that the total population of each area is constant. Using Lagrange Multiplier Method, we find some co-dimension one and co-dimension two bifurcations i.e.fold bifurcation and cusp bifurcation, respectively. We get the domain of parameters where three, two and one non-trivial equilibrium point occurs. We also find a transcritical bifurcation point such that the disease-free equilibrium point is stable on some parameter domains.

Bifurkasi Kodimensi dua dari model SIR untuk COVID-19 dan implikasi epidemiologisnya Owen, Livia; Jonathan Hoseana; Benny Yong
Communication in Biomathematical Sciences Vol. 6 No. 2 (2023)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2023.6.2.6

We study the codimension-two bifurcations exhibited by a recently-developed SIR-type mathematical model for the spread of COVID-19, as its two main parameters -the susceptible individuals' cautiousness level and the hospitals' bed-occupancy rate- vary over their domains. We use AUTO to generate the model's bifurcation diagrams near the relevant bifurcation points: two Bogdanov-Takens points and two generalised Hopf points, as well as a number of phase portraits describing the model's orbital behaviours for various pairs of parameter values near each bifurcation point. The analysis shows that, when a backward bifurcation occurs at the basic reproduction threshold, the transition of the model's asymptotic behaviour from endemic to disease-free takes place via an unexpectedly complex sequence of topological changes, involving the births and disappearances of not only equilibria but also limit cycles and homoclinic orbits. Epidemiologically, the analysis confirms the importance of a proper control of the values of the aforementioned parameters for a successful eradication of COVID-19. We recommend a number of strategies by which such a control may be achieved.

INOVASI PEMBELAJARAN MATEMATIKA MELALUI PENULISAN MATEMATIS, PEMECAHAN MASALAH MATEMATIS, DAN SOAL-SOAL MATEMATIKA BERBASIS HOTS UNTUK PARA GURU SMP DAN SMA SANTA ANGELA BANDUNG Yong, Benny; Hoseana, Jonathan; Owen, Livia; Salim, Daniel; Wijaya, Andreas Parama
JURNAL PENGABDIAN KEPADA MASYARAKAT Vol 30, No 1 (2024): JANUARI-MARET
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jpkm.v30i1.49105

Keterbatasan pengetahuan, kemampuan, dan keterampilan para guru di tingkat sekolah menengah merupakan salah satu kendala terbesar yang seringkali ditemui dalam pembelajaran matematika di Indonesia. Para guru terjebak dengan rutinitas harian tanpa dibekali dengan pelatihan, lokakarya, maupun pendampingan untuk memperbarui ilmu pengetahuan dalam rangka peningkatan kompetensi kognitif. Pada kegiatan pengabdian kepada masyarakat ini, dilakukan kegiatan pelatihan, workshop, dan pendampingan inovasi pembelajaran matematika dengan mitra SMP dan SMA Santa Angela Bandung. Kegiatan ini bertujuan untuk meningkatkan pengetahuan dan kemampuan guru akan tiga hal, yaitu penulisan matematis, strategi-strategi pemecahan masalah matematis, dan penyusunan soal-soal matematika berbasis keterampilan berpikir tingkat tinggi. Target pengabdian yang ingin dicapai adalah meningkatnya pemahaman konsep matematika para peserta yang tertuang dalam penulisan matematis yang baik dan benar, dimilikinya keterampilan dalam menyelesaikan masalah-masalah matematis dengan menggunakan strategi-strategi yang tersedia, dan perubahan jenis soal-soal yang digunakan dalam pembelajaran matematika dari soal-soal berbasis Lower Order Thinking Skills (LOTS) ke soal-soal berbasis Higher Order Thinking Skills (HOTS).

IMPLEMENTASI PROYEK PEMODELAN MATEMATIKA PADA KURIKULUM MERDEKA DI SEKOLAH KRISTEN IMMANUEL PONTIANAK Yong, Benny; Wijaya, Andreas Parama; Salim, Daniel; Owen, Livia
PAKEM : Jurnal Pengabdian Kepada Masyarakat Vol 5 No 2 (2025): Pakem : Jurnal Pengabdian Kepada Masyarakat
Publisher : Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/pakem.5.2.87-96

To prepare students for the rapidly evolving demands of the modern era, the Indonesian Ministry of Education, Culture, Research, and Technology introduced the Merdeka Curriculum. This curriculum provides schools and teachers with greater autonomy to design learning experiences tailored to local contexts, student potential, and individual characteristics. It emphasizes competency-based learning, integrating relevant skills and knowledge applicable to daily life and the labor market. The curriculum aims to foster creativity, critical thinking, and adaptability among students. Despite its progressive orientation, a significant challenge in its implementation is the readiness of educators. Addressing this issue requires collaborative efforts among schools, teachers, parents, communities, and the government. This community service program was designed to support teachers in implementing the Merdeka Curriculum, particularly in mathematics education. The program involved training and workshops on mathematical modeling projects aligned with the Pancasila Student Profile Strengthening Project (P5). The primary objective was to provide participants with a comprehensive understanding of curriculum implementation in mathematics and to assist them in designing student-centered project-based learning activities. The program was conducted in partnership with Immanuel Christian School, under the Kampung Bali Protestant Church Foundation in Pontianak, West Kalimantan. Overall, the mentoring activities have been highly positive, although certain materials require further refinement to ensure participants attain a more comprehensive understanding. The three strongest aspects of this program are the instructor’s deep mastery of the subject matter, the quality of the content presentation, and the organization of materials along with effective time allocation. Conversely, the aspects needing improvement are participants’ comprehension of the data analytics series, the overall relevance of the content to their needs, and their understanding of the matrix and Bayesian series

INOVASI PEMBELAJARAN MATEMATIKA MELALUI PENULISAN MATEMATIS, PEMECAHAN MASALAH MATEMATIS, DAN SOAL-SOAL MATEMATIKA BERBASIS HOTS UNTUK PARA GURU SMP DAN SMA SANTA ANGELA BANDUNG Yong, Benny; Hoseana, Jonathan; Owen, Livia; Salim, Daniel; Wijaya, Andreas Parama
JURNAL PENGABDIAN KEPADA MASYARAKAT Vol. 30 No. 1 (2024): JANUARI-MARET
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jpkm.v30i1.49105

Keterbatasan pengetahuan, kemampuan, dan keterampilan para guru di tingkat sekolah menengah merupakan salah satu kendala terbesar yang seringkali ditemui dalam pembelajaran matematika di Indonesia. Para guru terjebak dengan rutinitas harian tanpa dibekali dengan pelatihan, lokakarya, maupun pendampingan untuk memperbarui ilmu pengetahuan dalam rangka peningkatan kompetensi kognitif. Pada kegiatan pengabdian kepada masyarakat ini, dilakukan kegiatan pelatihan, workshop, dan pendampingan inovasi pembelajaran matematika dengan mitra SMP dan SMA Santa Angela Bandung. Kegiatan ini bertujuan untuk meningkatkan pengetahuan dan kemampuan guru akan tiga hal, yaitu penulisan matematis, strategi-strategi pemecahan masalah matematis, dan penyusunan soal-soal matematika berbasis keterampilan berpikir tingkat tinggi. Target pengabdian yang ingin dicapai adalah meningkatnya pemahaman konsep matematika para peserta yang tertuang dalam penulisan matematis yang baik dan benar, dimilikinya keterampilan dalam menyelesaikan masalah-masalah matematis dengan menggunakan strategi-strategi yang tersedia, dan perubahan jenis soal-soal yang digunakan dalam pembelajaran matematika dari soal-soal berbasis Lower Order Thinking Skills (LOTS) ke soal-soal berbasis Higher Order Thinking Skills (HOTS).

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