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All Journal Square : Journal of Mathematics and Mathematics Education Jurnal Pendidikan Kewarganegaraan
Abdur Rahman Hakim
Universitas Islam Negeri Sultan Syarif Kasim Riau
Education Mathematics Social Sciences

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Model SIRS Nonlinear Incidence Rate dengan Faktor Imigrasi Terinfeksi pada Penyebaran Penyakit COVID-19 Abdur Rahman Hakim; Oktarisa Ramadhanti; Granita
Square : Journal of Mathematics and Mathematics Education Vol. 8 No. 1 (2026)
Publisher : UIN Walisongo Semarang

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Abstract

ABSTRACT COVID-19 is a rapidly spreading disease driven by high human mobility, intense social interactions, and the emergence of new variants that enable reinfection. Classical SIR models generally assume permanent immunity, utilize a linear transmission rate, and do not account for individual immigration, making them inadequate for representing waning immunity, changes in community behavior, and more complex disease transmission dynamics. Therefore, this study extends the SIR model with a nonlinear incidence rate into an SIRS model with a nonlinear incidence rate, incorporating an infected immigration factor. The mathematical analysis includes determining the disease-free and endemic equilibrium points, calculating the basic reproduction number using the Direct Method, and conducting stability analysis through the Jacobian matrix and the Routh–Hurwitz criterion. The analysis yields the disease-free equilibrium point , the basic reproduction number and the endemic equilibrium point . Stability analysis shows that when , the disease-free equilibrium is locally asymptotically stable, indicating that the disease will not spread widely and will eventually disappear from the population. Conversely, when , the endemic equilibrium is locally asymptotically stable, implying that the infection will persist and continue to spread within the population, eventually becoming endemic. Keywords: SIRS model, nonlinear incidence rate, infected immigration, COVID-19.
Pacu Jalur Sebagai Identitas Budaya Lokal: Studi Etnografi di Kabupaten Kuantan Singingi Fiona Deanovans; Putri Dayani Ginting; Siti Mey Listianti; Teguh Adzuri; Ummi Maulinda Sari; Vino Ramadhan; Hambali; Abdur Rahman Hakim
JURNAL PENDIDIKAN KEWARGANEGARAAN Volume 9 Nomor 2 Edisi Desember 2025
Publisher : UNIVERSITAS PGRI PONTIANAK

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31571/jpkn.v9i2.9764

Abstract

Pacu Jalur merupakan tradisi lomba perahu panjang khas Kuantan Singingi, Riau, yang diwariskan antargenerasi dan menjadi penanda identitas budaya masyarakat setempat. Tradisi ini tidak hanya berfungsi sebagai perlombaan, tetapi juga sebagai ruang untuk memperkuat relasi sosial serta menanamkan nilai gotong royong, solidaritas, religiusitas, dan kebersamaan. Meski memberi dampak ekonomi melalui peningkatan wisata, kajian mendalam mengenai makna budaya dan nilai sosialnya masih terbatas. Penelitian ini bertujuan mengungkap Pacu Jalur sebagai simbol identitas budaya dengan menggunakan metode kualitatif berpendekatan etnografi. Informan dipilih secara purposive, meliputi tokoh adat, pembuat jalur, peserta, panitia, dan masyarakat. Data diperoleh melalui observasi, wawancara, dokumentasi, dan studi arsip, kemudian dianalisis dengan reduksi, penyajian, dan verifikasi melalui triangulasi. Temuan menunjukkan bahwa Pacu Jalur berkembang dari alat transportasi menjadi tradisi sarat nilai sosial dan spiritual yang juga berdampak ekonomi. Tantangan seperti berkurangnya minat generasi muda dan biaya perawatan menegaskan perlunya pelestarian berbasis masyarakat, pemerintah, dan pendidikan budaya.
Co-Authors Fiona Deanovans Granita Hambali Oktarisa Ramadhanti Putri Dayani Ginting Siti Mey Listianti Teguh Adzuri Ummi Maulinda Sari Vino Ramadhan