We consider a mathematical model to describe the interaction between predator and prey that includes predator cannibalism and refuge. We aim to study the dynamics and its long-term behavior of the proposed model, as well as to discuss the effects of crucial parameters associated with the model. We first show the boundedness and positivity of the solution of the model. Then, we study the existence and stability of all possible equilibrium points. The local stability of the model around each equilibrium point is studied via the linearized system, while the global stability is performed by defining a Lyapunov function. The model has four equilibrium points. It is found that the equilibrium point representing the extinction of both prey and predator populations is always unstable, while the other equilibrium points are conditionally stable. In addition, there is forward bifurcation phenomena that occur under certain condition. To support our analytical findings, we perform some numerical simulations.

In this paper, we propose a fractional-order COVID-19 epidemic model with a quarantine and standard incidence rate using the Caputo fractional-order derivative. The model consists of six classes: susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and deceased (M). In our proposed model, we simultaneously consider the recovery rate and quarantine rate of infected individuals, which has not been considered in other fractional-order COVID-19 epidemic models. Furthermore, we consider the standard incidence rate in the model. For our proposed model, we prove the existence, uniqueness, non-negativity, and boundedness of the solution. The model has two equilibrium points: disease-free equilibrium and endemic equilibrium. Implementing the spectral radius of the next-generation matrix, we obtain the basic reproduction number (${\mathcal{R}}_0$). The disease-free equilibrium always exists and is locally and globally asymptotically stable only if ${\mathcal{R}}_0<1$. On the other hand, endemic equilibrium exists and is globally asymptotically stable if ${\mathcal{R}}_0>1$. Our numerical simulation confirms the stability properties of the equilibrium. The smaller the order of the derivative, the slower the convergence of the solution of the model. Both the recovery rate and quarantine rate of the infected class are important parameters determining the stability of the equilibrium point. Based on parameter estimation from COVID-19 data in Indonesia, the fractional-order model has better performance than the first-order model for both the calibration and 20-day forecasting of confirmed daily active cases of COVID-19.

Ethnomathematics has experienced rapid development recently and has become a trend in mathematics. This research uses a systematic literature review method to analyze the relationship between mathematics and culture, trends in mathematical findings, and conformity with ethnomathematics theory. The articles from Sinta's accredited journals over the last five years. The research results show that there is no practical connection between mathematical and cultural concepts in temple ethnomathematics research. Second, mathematical findings tend to be convergent, with most studies referring to the same material without uniqueness or novelty across cultures. Third, Indonesia's natural diversity is not always relevant in ethnomathematics, which focuses more on cultural aspects. In conclusion, there is a gap in ethnomathematics research, and it is suggested that further studies utilize Mathematical Landscape in addressing mathematics in various broader aspects of life that are not directly related to ethnomathematics. This research can serve as a foundation and be further developed to benefit society and education worldwide.

Kegiatan penguatan literasi bagi guru dan tenaga kependidikan di SMA Negeri 1 Purwosari pada tanggal 18 Agustus 2023 diselenggarakan sebagai implementasi dari Program 1D1S (1 Dosen 1 Sekolah) Universitas PGRI Wiranegara (Uniwara). Kegiatan ini bertujuan untuk meningkatkan pengetahuan dan keterampilan guru dalam menyusun buku sederhana dan publikasi artikel ilmiah. Metode yang digunakan meliputi ceramah, demonstrasi, praktik, dan konsultasi. Hasil menunjukkan bahwa tingkat kepuasan peserta terhadap materi dan alokasi waktu pelatihan tinggi. Pelatihan ini juga memotivasi dan meningkatkan produktivitas peserta dalam membuat buku sederhana dan menyusun artikel ilmiah. Output dari pelatihan ini adalah satu draf buku sederhana dan tiga draf artikel ilmiah. Direkomendasikan agar kegiatan ini dapat dilanjutkan di sekolah-sekolah lain; dibuat program pendampingan untuk membantu guru dan tenaga kependidikan dalam menerapkan ilmu yang diperoleh dari pelatihan; serta dilakukan penelitian untuk mengkaji lebih lanjut tentang dampak pengabdian ini terhadap kualitas pembelajaran. Kata Kunci: Guru dan tenaga kependidikan, penguatan literasi, penyusunan buku sederhana, program 1D1S, publikasi artikel ilmiah

Predator-prey models are essential for understanding ecological dynamics, and fractional-order models provide a more realistic approach by considering memory effects. This study aims to analyze the discrete dynamics of a predator-prey model, incorporating predator cannibalism, refuge, and memory effects with a Caputo-type fractional-order. The Piecewise Constant Argument (PWCA) method was employed for discretization, followed by an analysis of the equilibrium points and their stability. Four equilibrium points were identified: the origin, prey extinction, predator extinction, and coexistence. It was found that the origin point was unstable, while the prey extinction, predator extinction, and coexistence points were conditionally locally asymptotically stable, depending on the parameter values. The order of the fractional derivative and step size significantly influenced the stability of these equilibrium points. Numerical simulations confirmed the theoretical findings, showing how parameter variations affect system behavior.