Judul: Analisis Sensitivitas Model Penyakit Demam Berdarah Dengue dengan Faktor Curah Hujan Studi Kasus: Kabupaten Bogor
Abstrak: Demam berdarah dengue adalah penyakit yang disebabkan oleh gigitan nyamuk Aedes Aegypti yang sudah terinfeksi virus dengue. Pada penelitian ini dianalisis model demam berdarah dengue dengan adanya faktor curah hujan dengan kasus di Kabupaten Bogor. Tujuan penelitian ini adalah untuk melihat pengaruh parameter terhadap penyebaran penyakit. Penentuan bilangan reproduksi dasar menggunakan matrix the next generation. Peningkatan laju kematian nyamuk, peningkatan pergerakan curah hujan, penurunan tingkat gigitan nyamuk, penurunan peluang terjadinya transmisi virus dengue dari nyamuk ke manusia, penurunan peluang terjadinya transmisi virus dengue dari manusia ke nyamuk, dan penurunan tingkat curah hujan menyebabkan bilangan reproduksi dasar menurun. Parameter-parameter tersebut dapat digunakan untuk mengendalikan laju penyebaran penyakit demam berdarah dengue., Dengue hemorrhagic fever is a disease caused by the bite of the Aedes Aegypti mosquito which has been infected with the dengue virus. In this research, the dengue hemorrhagic fever model was analyzed with rainfall factor with cases in Bogor Regency. The purpose of this research was to see the effect of parameters on the spread of the disease. Determination of the basic reproduction number was using the next generation matrix. The increase in the death rate of mosquito, the increase in the movement of rainfall, the decrease in the rate of mosquito bites, the decrease in the transmission probabilities of dengue virus from mosquito to human, the decrease in the transmission probabilities of dengue virus from human to mosquito, and the decrease in the rainfall rate, cause the decrease of the basic reproduction number. These parameters can be used to control the rate of spread of dengue hemorrhagic fever.
Keyword: analisis kestabilan, analisis sensitivitas, bilangan reproduksi dasar, curah hujan, demam berdarah dengue, basic reproduction number, dengue hemorrhagic fever, rainfall, sensitivity analysis, stability analysis

Judul: Analisis Model Asimtomatik Penyebaran Penyakit Demam Berdarah Dengue
Abstrak: Demam Berdarah Dengue adalah penyakit yang disebabkan oleh gigitan nyamuk Aedes aegypti dan Aedes albopictus . Penyakit ini memiliki empat jenis virus yaitu DEN-1, DEN-2, DEN-3, dan DEN-4. Individu yang terinfeksi memiliki gejala yang berbeda-beda bahkan ada yang tidak menunjukkan gejala atau asimtomatik. Karya ilmiah ini membahas model penyebaran penyakit dengan adanya pengaruh asimtomatik pada suatu populasi manusia yang tertutup. Berdasarkan analisis terdapat dua titik tetap yaitu titik tetap bebas penyakit dan titik tetap endemik. Untuk menentukan nilai parameter yang mempengaruhi penanggulangan penyebaran penyakit DBD, dilakukan analisis sensitivitas dan simulasi numerik. dst..., engue Fever is a disease caused by the bite of the Aedes aegypti and Aedes albopictus mosquito. This disease has four types of viruses namely DEN-1, DEN-2, DEN-3, and DEN-4. Infected individuals have different symptoms and some even show no symptoms or asymptomatic. This scientific work discusses the model of the spread of disease with an asymptomatic influence on a closed human population. Based on the analysis there are two fixed points, namely the fixed point free of disease and the endemic fixed point. To determine the value of parameters that affect the prevention of the spread of dengue disease, sensitivity analysis and numerical simulations are carried out. etc ...
Keyword: SIR type, dengue fever, basic reproduction number, sensitivity analysis

Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm