<span class="fontstyle0">The study was aimed to introduce a new model construction regarding the transmission of Coronavirus Disease (henceforth, COVID-19) in human population. The mathematical model was constructed by taking into consideration several epidemiology parameters that are closely identical with the real condition. The study further conducted an analysis on the model by identifying the endemicity parameters of COVID-19, i.e., the presence of disease-free equilibrium (DFE) point and basic reproduction number. The next step was to carry out sensitivity analysis to find out which parameter is the most dominant to affect the disease’s endemicity. The results revealed that the parameters </span><span class="fontstyle2">𝜂, 𝜁</span><span class="fontstyle2">𝑠𝑒</span><span class="fontstyle2">, 𝛼,, </span><span class="fontstyle0">and </span><span class="fontstyle2">𝜎 </span><span class="fontstyle0">in sequence showed the most dominant sensitivity index towards the basic reproduction number. Moreover, the results indicated positive index in parameters </span><span class="fontstyle2">𝜂 </span><span class="fontstyle0">and </span><span class="fontstyle2">𝜁</span><span class="fontstyle2">𝑠𝑒 </span><span class="fontstyle0">that represented transmission chances during contact as well as contact rate between vulnerable individuals and exposed individual. This suggests that an<br />increase in the previous parameter value could potentially enlarge the endemicity of COVID-19. On the other hand, parameters </span><span class="fontstyle2">𝛼 </span><span class="fontstyle0">and </span><span class="fontstyle2">𝜎</span><span class="fontstyle0">, </span><span class="fontstyle0">representing movement rate of exposed<br />individuals to the quarantine class and proportion of quarantined exposed individuals, showed negative index. The numbers indicate that an increase in the parameter value could decrease the disease’s endemicity. All in all, the study concludes that treatments for COVID-19 should focus on<br />restriction of interaction between individuals and optimization of quarantine.</span> <br /><br />

The descriptive study aims to elaborate on the effectiveness of multimedia-based mathematics learning process in a lesson on the rectangular shape in 7th-grade students in SMP Negeri 11 Gorontalo. There are four indicators investigated in this study, i.e., 1) Teacher’s competence in learning management, 2) Students’ activity during the learning process, 3) Students’ learning outcome, and 4) Students’ response. The result shows that the implementation of rectangular multimedia in the mathematics learning process is categorized effectively. The teachers’ competence in learning management results in effective criteria, included in quite good category. Moreover, the students’ activity is categorized in effective criteria, as the overall percentage meets the minimum effectiveness criteria set. Further, the students’ learning outcome passes the classical competence, as 85 percent achieve score of 70 or more. The students’ response on the learning process also meets the effectiveness criteria; 84 percent of students respond positively or very positively towards the learning multimedia.

Abstract:Reasoning based research generally examines the application of learning models or learning methods. So far, there are still rarely studies that examine the use of teaching materials to improve the quality of learning. This study aims to develop teaching materials related to the central angle and the circumference of the circle based on reasoning. The development model used is the ADDIE development model, namely Analysis, Design, Development, Implementation and Evaluation. The analysis was conducted by involving students of SMPN 1 Kabila as research subjects. The results showed the quality of teaching materials was declared valid with a percentage of 75%. Practicality of teaching materials based on the results of student questionnaire responses reached very good categories with a percentage of 82.82%. This shows that reasoning based teaching materials can be used in the learning process. Abstrak:Penelitian berbasis penalaran umumnya mengkaji tentang penerapan model atau metode pembelajaran. Sejauh ini, masih jarang penelitian yang mengkaji tentang penggunaan bahan ajar untuk meningkatkan kualitas pembelajaran. Penelitian ini bertujuan untuk mengembangkan bahan ajar materi hubungan sudut pusat dan sudut keliling lingkaran berbasis penalaran. Model pengembangan yang digunakan adalah Model pengembangan ADDIE, yaitu Analysis (Analisis), Design (Desain), Development (Pengembangan), Implementation (Implementasi) dan Evaluation (Evaluasi).  Analisis dilakukan dengan melibatkan siswa SMPN 1 Kabila sebagai subjek penelitian. Hasil penelitian menunjukan kualitas bahan ajar dinyatakan valid dengan persentase 75%. Kepraktisan bahan ajar berdasarkan hasil angket respon siswa mencapai kategori sangat baik dengan persentase 82,82%. Hal ini menunjukkan bahwa bahan ajar berbasis penalaran dapat digunakan dalam proses pembelajaran.

Penelitian ini dilakukan untuk menganalisis kestabilan model eko-epidemiologi dengan pemanenan konstan terhadap predator. Populasi dalam model terbagi atas tiga populasi yaitu populasi prey rentan  populasi prey terinfeksi , dan populasi predator . Dikonstruksi model eko-epidemiologi dengan pemanenan konstan terhadap predator. Diperoleh dua titik kesetimbangan, yaitu titik kesetimbangan kepunahan populasi prey terinfeksi, dan titik kesetimbangan interior atau semua populasi ada. Eksistensi dari masing-masing titik kesetimbangan bergantung pada  atau akar-akar realnya masing-masing. Sebelum mencari kestabilan dari titik-titk kestimbangan, ditentukan terlebih dahulu matriks Jacobi. Kestabilan dari masing-masing titik diuraikan pada syarat kestabilannya masing-masing. Simulasi numerik dari titik kesetimbangan dilakukan agar terlihat lebih jelas kestabilan dari masing-masing titik kesetimbangan. Simulasi numerik dilakukan menggunakan metode Runge-Kutta orde 4 dan dibantu software Phyton 3.7.

The dynamics of predator-prey model with infectious disease in prey and harvesting in predator is studied. Prey is divided into two compartments i.e the susceptible prey and the infected prey. This model has five equilibrium points namely the all population extinction point, the infected prey and predator extinction point, the infected prey extinction point, and the co-existence point. We show that all population extinction point is a saddle point and therefore this condition will never be attained, while the other equilibrium points are conditionally stable. In the end, to support analytical results, the numerical simulations are given by using the fourth-order Runge-Kutta method.

Penelitian ini bertujuan untuk mendeskripsikan penggunaan multimedia interaktif pada pembelajaran matematika bangun ruang sisi lengkung. Bangun ruang sisi lengkung yang dibahas, difokuskan pada topik tabung dengan siswa SMP Negeri 2 Gorontalo sebagai subjek penelitian. Data penelitian diperoleh melalui observasi proses pembelajaran dan melalui angket respon peserta didik. Hasil penelitian menunjukkan bahwa penggunaan multimedia interaktif pada pembelajaran matematika bangun ruang sisi lengkung tabung mencapai kategori “sangat baik”, dengan indikator: kemampuan guru dalam menggunakan multimedia interaktif dalam pembelajaran sebesar 84%, aktifitas peserta didik dalam pembelajaran menggunakan multimedia interaktif sebesar 84%, dan respon positif peserta didik terhadap multimedia interaktif sebesar 85%.

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AbstrakDalam artikel ini dibahas model matematika penyebaran malaria tipe SEIRS-SEI.Modifikasi model dilakukan dengan pemberian perlakuan pada manusia, berupa treatment vaksinasi dan pengobatan. Dalam model ini, populasi manusia dibagi menjadi empat kelas, yaitu rentan, terpapar, terinfeksi, dan pulih. Adapun populasi nyamuk dibagi menjadi tiga kelas, yaitu rentan, terpapar dan terinfeksi. Selanjutnya dilakukan konstruksi bilangan reproduksi (R 0 ) yang merupakan nilai harapan banyaknya infeksi tiap satuan waktu. R 0 dalam artikel ini ditentukan dengan menggunakan pendekatan matriks generasi mendatang. Pada bagian akhir dalam artikel ini diberikan simulasi numerik untuk menunjukkan efektifitas vaksinasi dan pengobatan pada manusia untuk menekan laju penularan penyakit. Hasil simulasi menunjukkan bahwa peningkatan efektifitas vaksinasi maupun pengobatan pada manusia mampu menurunkan bilangan reproduksi. Hal tersebut menunjukkan bahwa jumlah individu yang terinfeksi semakin berkurang dan dalam jangka waktu tertentu penyakit akan menghilang dari populasi.Kata kunci:Bilangan Reproduksi, Model Malaria, SEIRS-SEI , Vaksinasi, Pengobatan. AbstractThis article discusses the mathematical model of SEIRS-SEI type malaria spread. Modification of the model is done by giving the treatment in humans, in the form of vaccination and medication treatment. In this model, the human population is divided into four classes, namely susceptible, exposed, infected, and recovered. The mosquito population is divided into three classes, namely susceptible, exposed and infected. Furthermore, the reproduction number (R 0 ) is constructed, which is the expected number of infections per unit of time. R 0 in this article is determined by using a next-generation matrix approach. At the end of this article is provided numerical simulations to show the effectiveness of vaccination and treatment in humans to suppress the rate of transmission of disease. The simulation results show that the increase of vaccination effectiveness and treatment in humans can reduce the reproduction number. It shows that the number of infected individuals is decreasing and within a certain time the disease will disappear from the population.