This research is a descriptive study that aims to describe students' critical thinking abilities carried out by online learning. This research was conducted in class VIII SMP Negeri Widyakrama involving 23 students as research subjects. Data collection was obtained from validated essay test instruments. The test instrument was used to collect data on students' mathematical critical thinking abilities with indicators (a) problem identification (b) analysis, (c) synthesis, and (d) drawing conclusions. The results showed that students' critical thinking abilities implemented through online learning at Widyakrama State Middle School were in the medium category. This is shown based on the classification of critical thinking abilities of 23 respondents. There are only 5 students who are in the high category, 14 students are in the medium category, and 4 other students are in a low category.

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.

Dinamika model Leslie-Gower dengan fungsi respon ratio-dependent yang didiskretisasi menggunakan skema Euler maju adalah fokus utama pada artikel ini. Analisis diawali dengan mengidentifikasi eksistensi dari titik ekuilibrium dan kestabilan lokalnya. Diperoleh empat titik ekuilibrium yaitu titik kepunahan kedua populasi dan titik kepunahan predator yang selalu tidak stabil, dan titik kepunahan prey dan eksistensi kedua populasi yang stabil kondisional. Selanjutnya dipelajari eksistensi dari bifurkasi periode ganda dan Neimark-Sacker di sekitar titik eksistensi kedua populasi sebagai akibat perubahan parameter h (time-step). Dari hasil analisis ditemukan bahwa bifurkasi periode ganda terjadi setelah melewati ℎ ℎ atau ℎ ℎ dan bifurkasi Neimark-Sacker terjadi setelah melewati ℎ ℎ. Di akhir pembahasan, diberikan simulasi numerik yang mendukung hasil analisis sebelumnya. Kata Kunci: model predator-prey, Leslie-Gower, proses diskretisasi, bifurkasi.

This article discusses the description of students' mathematical connection abilities in solving mathematics on the Pythagorean theorem material. This descriptive research was conducted at SMP Negeri 1 Bolaang Uki in the odd semester of the 2019/2020 school year. The technique of data collection is done by test. Description test to obtain mathematical connection ability data. The results showed that the students' mathematical connection ability to recognize and use connections between mathematical ideas was 45.14%, the indicator of understanding how mathematical ideas were connected and built on one another to produce a coherent whole was 29.63%, and indicators of the introduction and application of mathematics in daily life by 23.61%.

Forecasting the number of passengers can be a consideration for managers of Gorontalo Crossing Port regarding the provision of tickets. The number of passengers can be influenced by certain seasonal or special events. To see the special events that affect the number of passengers arriving at Gorontalo Crossing Port, the forecasting method used is the Exponential Smoothing Event Based (ESEB) method. The seasonal influences can be known through historical data patterns and using the Winter’s Exponential Smoothing (WES) method. After compared, the ESEB method is a better method of forecasting the number of arriving passengers at Gorontalo Crossing Port because it has a smaller MAPE value than the WES method.