MODEL POPULASI NYAMUK DENGAN MELIBATKAN FAKTOR KONTROL DAN VARIASI MUSIM

Nyamuk merupakan serangga yang mengalami metamorfosis sempurna, dimuali dari telur, pupa, larva (fase akuatik) hingga nyamuk dewasa (fase nonakuatik). Proses perkembangbiakan nyamuk, khususnya pada fase akuatik (air sebagai habitatnya) sangat dipengaruhi oleh kondisi cuaca. Model matematik dibangun untuk mengetaui dinamika populasi nyamuk dengan melibatkan faktor cuaca. Penggunaan temephos dan fumigasi juga dilibatkan dalam konstuksi model sebagai kontrol terhadap pertumbuhan nyamuk. Analisis kestabilan pada titik kesetimbangan disajikan untuk mengetahui kondisi populasi nyamuk seiring berjalannya waktu. Dari hasil simulasi diperoleh bahwa pengaruh musim mengakibatkan dinamika populasi larva dan nyamuk berosilasi setiap tahunnya dengan puncak pertumbuhan terjadi pada musim hujan. Disamping itu, penggunaan temephos da fumigasi secara signifikan dapat mengurangi jumlah populasi dari larva dan nyamuk.

Analisis Dinamik Model SIR Pada Kasus Penyebaran Penyakit Corona Virus Disease-19 (COVID-19)

Corona Virus Disease-19 (COVID-19) merupakan salah satu virus yang menyebabkan penyakit pada manusia dan hewan. Penyakit ini menyebabkan gangguan saluran pernapasan sedang atau berat. Telah dilakukan penelitian untuk mengetahui dinamika perkembangan COVID-19 dengan menggunakan model persamaan diferensial SIR. Model SIR merupakan salah satu pemodelan matematika yang menghubungkan antara individu yang rentan, terinfeksi dan individu yang sembuh. Berdasarkan hasil analisis dinamik model SIR dengan parameter laju infeksi dan laju kesembuhan berturut-turut yaitu beta = 0.5 dan gama=0.3 . Model SIR memiliki dua titik kesetimbangan yaitu kesetimbangan bebas penyakit pada titik E_0=(0,0,0) dan titik kesetimbangan endemik pada titik E_1=(gama/beta,0,0) . Analisis kestabilan perilaku dinamik model S dan I pada titik kesetimbangan E_0=(0,0,0) memiliki sifat semi stabil dan E_1=(gama/beta,0,0) memiliki sifat konstan. Hal ini menunjukkan bahwa akan terjadi epidemi COVID-19 dalam kurun waktu tertentu. Solusi dinamik model SIR pada titik kesetimbangan menggunakan solusi numerik metode runge-kutta orde 4 dengan solusi analitik menunjukkan suatu perbedaan yang tidak terlalu besar saat mencapai titik kestabilan.

Analisis Hubungan Kepadatan Penduduk dengan Pola Penyebaran COVID-19 Provinsi DKI Jakarta menggunakan Regresi Robust

COVID-19 pandemic have been spread around the world since the first outbreak on Desember 2019 in Wuhan, China. DKI Jakarta as one of the highest population density among 34 provinces in Indonesia, has become an endemic area of COVID-19 with the rate of new cases show some fluctuation for each month along 2020. This is a secondary data research which drawn from Health Ministry of Indonesia as well as Center of Statistics for DKI Jakarta. Focus and the scope of this paper is on analyzing the relation between new cases of COVID-19 with population density of Jakarta’s districts. Descriptive and inferential analysis that combined with Robust Regression Test are conducted due to some outliers data. This unbiased method shows a good regression model of spreading new positive cases. M-Estimator Robust Regression with Tukey Bisquare function, shows the best result with the least Residual Standar Error (RSE), that is 0.411. Analysis on statistical test for the chosen model shows that population density has significant impacts on outbreak pattern of COVID-19 in Jakarta. But mobilities and interactions betweeen citizens has also give a great impact.

Analisis Rantai Markov dalam Memprediksi Status Pasien COVID-19 di Indonesia

COVID-19 is an infectious disease caused by a new type of corona virus, beta coronavirus. The spread of COVID-19 can occur through human interactions. On March 9, 2020 the WHO (World Health Organization) officially declared COVID-19 a pandemic. This means that COVID-19 has spread widely in the world. Until now, there has not been found a drug to treat COVID-19. So, it is necessary to predict when the COVID-19 pandemic will end. This study discusses the Markov chain method in predicting the status of COVID-19 patients in Indonesia. The prediction of the number of people who are positive for COVID-19, recovered, and die can be one of the government's bases for determining when the large-scale social restrictions (PSBB) will end. The results of the study stated that the COVID-19 pandemic in Indonesia would end at the end of 2020. On December 5, 2020 there were no more people infected with COVID-19 with a cure rate of 29.815% of patients with COVID-19 and a death rate of 3, 5933%.

Penerapan Program Linear Fuzzy dalam Optimalisasi Jumlah Produksi dan Keuntungan di K-Bakery

K-Bakery is a bakery located in Bandar Lampung City, Lampung. K-Bakery produces various types of bread, namely brown bread, nuts, greentea, mocha, and tiramisu bread which involve various raw material resources. Unstable market demand creates obstacles for K-Bakery in formulating the number of each type of bread to be produced so as to produce maximum profit. However, in determining the amount of production must pay attention to the limited supply of raw materials. In this case, there is a need for production planning so that all available resources can be used optimally and produce a combination of production that provides maximum profit. One way to solve this problem is to optimize production using a fuzzy linear program with a tolerance of 10% as the capability of K-Bakery. The use of the fuzzy linear program generates greater profits than the usual linear program, the profit obtained is Rp. 11.247.972,1708by producing 320 chocolate breads, 449,75 peanut breads, 365,667 greentea breads, 250 moka breads fruit, 449,925 srikaya bread, and 499,975 tiramisu breads. In addition, the value of l = 0,5 is obtained, or in other words, the maximum addition of each raw material is 50% of the available safety stock.