Judul: Analisis kestabilan titik tetap pada model penyebaran penyakit menular dengan vaksinasi
Abstrak: FELICIA. Analisis Kestabilan Titik Tetap pada Model Penyebaran Penyakit Menular dengan Vaksinasi. Dibimbing oleh PAlAN SIANTURI dan BIB PARUHUM SILALAHL Setiap tahun, jutaan manusia di seluruh dunia meninggal karena penyakit menular. Memodelkan proses penyebaran penyakit menular akan mempermudah dalam mengerti dinamika penyebaran penyakit dalam suatu populasi. Ada dua pola penyebaran penyakit yang mewakili penyebaran penyakit di masyarakat yakni pola SIS dan pola SIR. Proses SIS tersebut dituangkan dalam model matematika namun ditambabkan satu kelompok populasi lagi yaitu kelompok individu-individu yang divaksinasi dan memenuhi beberapa asumsi. Modelnya adalah sebagai berikut:
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Judul: Kajian Model Epidemik SIR dengan vaksinasi Deterministik dan Stokastik dengan Waktu Diskret
Abstrak: SIR dengan vaksinasi merupakan model epidemik yang digunakan untuk memodelkan penyebaran suatu penyakit dalam suatu populasi tertutup dengan memasukkan faktor vaksinasi. SIR dengan vaksinasi terdiri atas tiga subpopulasi, yaitu individu rentan dinotasikan dengan S (susceptibles), individu terinfeksi dinotasikan dengan I (infected), dan individu yang telah sembuh dan kebal terhadap penyakit dinotasikan dengan R (recovered). Model epidemik SIR dengan vaksinasi yang dibahas dalam penelitian ini yaitu model deterministik dan model stokastik. Dari model SIR dengan vaksinasi deterministik diperoleh titik tetap beserta kestabilannya. Dari model stokastik diperoleh peluang transisi dan peluang wabah. Kestabilan titik tetap pada model deterministik bergantung nilai dari bilangan reproduksi dasar. Dari hasil simulasi yang dilakukan baik pada model SIR dengan vaksinasi deterministik maupun stokastik, perlakuan pemberian vaksin cenderung lebih efektif dalam meningkatkan jumlah individu yang sembuh. Sedangkan perlakuan penyembuhan cenderung lebih efektif dalam menurunkan wabah penyakit.
Keyword: SIR, vaksinasi, deterministik, stokasti

Judul: Xylooligosaccharide production of corncobs as prebiotic candidate by high temperature heating and enzymatic hydrolysis.
Abstrak: Corncob waste is a rich xylan source that can be utilized as raw material for xylooligosaccharides (XOS) production. XOS is a potential prebiotic and has high economic value. Two corn varieties i.e. Bisi and Pioneer were first analyzed for its hemicellulose, cellulose and lignin contents and xylan yield to choose the corn variety to be studied. Process technology for XOS production was studied using available equipment such as oven. Xylooligosaccharide (XOS) from corncob was produced in two stages i.e. xylan extraction by heating at high temperatures in oven or autoclave as comparison, followed by enzymatic hydrolysis. Analysis of two corncob varieties showed that Pioneer variety contained higher hemicellulose content (34.98%) and xylan yield (18.32%) than Bisi variety (12.28% and 10.22%, respectively), therefore Pioneer variety was chosen as raw material for XOS production. Corncob particles were soaked in dilute acid (1 g/l H2SO4) for 12 h at 60 oC, filtered and washed with tap water and then heated in oven or autoclave. Before oven heating, The corncobs were added with water at various ratios (1:1 – 1:5) and then heated in oven at various temperature (130 oC, 140 oC, 150 oC for 0.5 h) and autoclave at 121oC for 0.5, 1, 1.5 and 2 h with one and two heating cycles. During heating, the total sugar and reducing sugar were increase, while the degree of polymerization was decrease. The results showed that heating in oven to extract the xylan was affected by the ratios of corncobs and aquadest and heating temperatures. Oven heating (130-150 oC) with optimum ratio of corncobs and aquadest (1:3) successfully increased the xylan content from 3.98% up to 18.21 – 19.46% while repeated heating cycle (two cycles) did not affect the xylan content. Heating the corncobs with aquadest (at the ratio of 1:3) in oven at 130 oC for 0.5 h produced 18.98% xylan and enzymatic conversion of the xylan by xylanase significantly increased the XOS content from 19.60% up to 44.06%. Heating the corncobs in autoclave (121 oC, 0.5 h) followed by enzymatic conversion produced higher XOS content (65.67%). The corncob XOS could stimulate the growth of Lactobacillus plantarum kik and Bifidobacterium longum ATCC 15707 by 1.2 until 1.7 unit log, indicating the prebiotic properties. Cookies prebiotic produced by addition of 5% (based on wheat flour) had higher hardness texture (1256 gf) than control without XOS (1067 gf).
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