Judul: Analisis model dinamika virus influensa dengan dua-galur
Abstrak: Influensa merupakan penyakit yang disebabkan oleh virus. Virus influensa digolongkan dalam kelompok virus RNA (Ribose Nucleic Acid) dan dibagi atas tiga tipe, yaitu A, B, dan C. Untuk mempertahankan keanekaragaman keturunan, virus dari penyakit influensa ini akan terpecah menjadi dua jenis antigen yaitu antigenic drift dan antigenic shift. Dalam tulisan ini dipelajari model virus influensa dengan mengadobsi keberadaan dua jenis antigen, yaitu dengan membuat sistem dua-galur. Dari analisis kestabilan diperoleh dua titik tetap yaitu titik tetap tanpa penyakit (Disease-free equilibrium-DFE) dan titik tetap endemik. Kestabilan titik tetap tersebut dipengaruhi oleh bilangan reproduksi dasar. Jika bilangan reproduksi dasar kurang dari satu, titik tetapnya akan stabil. Untuk titik tetap endemik, jika bilangan reproduksi dasar lebih besar dari satu, titik tetapnya akan stabil. Dalam tulisan ini juga ditunjukkan adanya coexistence (hidup berdampingan) antara kelompok individu yang terinfeksi primer pada galur ke-1 dan galur ke-2. Grafik solusi numerik model dinamika virus influensa dengan dua-galur untuk semua kelompok individu digambarkan menggunakan software Mathematica 6.
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Judul: Analysis of the Stability of Influenza Spread Model with Disease Resistance in Humans
Abstrak: Influenza adalah penyakit pada sistem pernapasan yang disebabkan oleh virus influenza. Pada penelitian ini, dibahas model SEIR yang menggambarkan penularan virus influenza dengan memerhatikan faktor resistensi penyakit pada manusia, yaitu suatu kondisi individu yang terpapar, terinfeksi dan sembuh kembali menjadi individu yang rentan. Berdasarkan model matematika tersebut diperoleh bilangan reproduksi dasar (ℛ0) dan dua titik tetap yaitu, titik tetap bebas penyakit dan titik tetap endemik . Analisis kestabilan titik tetap ditentukan dengan menggunakan kriteria Routh-Hurwitz dan fungsi Lyapunov. Analisis sensitivitas terhadap ℛ0 menghasilkan parameter laju kontak transmisi penyebaran virus influenza dan laju transmisi populasi manusia terpapar ke populasi manusia rentan sebagai parameter yang paling berpengaruh terhadap kenaikan bilangan reproduksi dasar. Peningkatan bilangan reproduksi dasar terjadi saat laju kontak transmisi penyebaran virus influenza diperbesar dan laju transmisi populasi manusia terpapar ke populasi manusia rentan diperkecil. Hal ini mengakibatkan kondisi endemik secara cepat terjadi sehingga pengendalian penyebaran penyakit influenza dapat dilakukan dengan mengurangi laju kontak transmisi dan meningkatkan laju transmisi populasi manusia terpapar ke populasi manusia rentan., Influenza is a disease of the respiratory system caused by the influenza virus. In this study, a SEIR model that depicts the transmission of the influenza virus is discussed by considering the factor of disease resistance in human, which is a condition of the individuals who are exposed, infected and recovered that can turn back into a susceptible individual. Based on this mathematical model, the basic reproduction number (ℛ0) is obtained. The model has two fixed points, which consist of one disease free and one endemic fixed points. Stability analysis of the fixed points are determined by using the Routh-Hurwitz criterion and the Lyapunov function. Sensitivity analysis to ℛ0 shows that the parameters of the contact rate of virus transmission and the transmission rate of the exposed to susceptible human are the most influencing parameters for the basic reproduction number. The increase of the basic reproduction number occurs when the contact rate of virus transmission is enlarged and the transmission rate of the exposed to susceptible human is reduced. It causes the endemic condition to occured rapidly. Therefore, controlling the spread of influenza virus should be done by reducing the contact rate of virus transmission and increasing the transmission rate of the exposed to susceptible human.
Keyword: basic reproduction number, disease resistance, Lyapunov, sensitivity  analysis   

Judul: Pembukaan Lahan Kelapa Sawit (Elaeis guineensis Jacq.) di Kebun Batang Toru, PTPN III (Persero) Tapanuli Selatan, Sumatera Utara
Abstrak: The internship was conducted at Batang Toru Plantation PTPN III (Persero), South Tapanuli, North Sumatera from November 2011 until February 2012. The purposes of the internship is improve knowledge, gain work experience and studying the management aspects land clearing of oil palm, both technical and managerial aspects. The primary data were obtained directly from the field by doing discussions or interviews with the foreman and assistant division as well as through direct observation in the field. The secondary data were obtained from the company data or company records. Based on observation during the internship can be conclude that the main issues in land clearing oil palm is conducting enterpasing basically been done at wetlands, this is due to stage process and work capacity of land clearing. Field observations focused on the land clearing activities which includes several parameters : the stages of land clearing process and land clearing techniques are used, it relates to land condition, the condition of vegetation, land clearing techniques, equipment requirements and time sheet working that is obtained by comparing a standard operation of PTPN III (Persero) Plantation. PT Nusantara Plantation III (Persero) as plantation companies state-owned enterprises (BUMN), which seeks to expand oil palm plantations owned. Total land area of the concession rights of exploitation (HGU) plantation development area Batang Toru PT PTPN III (Persero) Tapanuli District is an area of 1 500 hectares by Regents consent decree South Tapanuli. Status of the land is the location permits a secondary forest and other land uses (APL). Entirely divided into 2 locations and 5 work packages groups of land with an area of each location I is 548.43 ha and 775.98 ha II locations. Land clearing palm oil (Elaeis guineensis Jacq.) at Batang Toru Plantation, PTPN III (Persero), South Tapanuli, North Sumatra with the general condition of the area is the 67% of them in the form of coastal peatland with a depth of 1 – 2 m, while 33% of them are in dry area the form of land with the structure of clay soil, sand and dust. Land clearing technique used is fully mechanical engineering, non-burning and land clearing rules apply wet application of water management and road construction with the installation technique and overall gambangan in the management of most of peaty land in Batang Toru, South Tapanuli District, using standard procedures operation for peatland that has been poured in the No. Permentan. 14 of 2009. PTPN III (Persero) to cooperate with 3rd party (three) conduct land clearing by mechanical means to obtain efficient results. Occupation is conducted using a mechanical excavator with an average achievement 1 HK = 0.83 ha/HKT (8 BU/day), resulting in the complete work area 1 block area (30 ha) on average takes 37 HKT normal conditions without a hitch (weather, appliance repair).
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