Judul: Pengaruh vaksinasi terhadap dinamika populasi pada model SIR (Susceptible-Infected-Recovered)
Abstrak: SIR model can be used to model the spread of diseases in a closed population based on certain assumptions. In this research, the SIR model is formulated by including the factor of vaccination. As the result, the model has been shown to have two equilibrium points, i.e. disease free and endemic equilibrium. A simulation study is carried out to illustrate the model. The results show that some equilibrium points are asymptotically stable. Moreover, a minimum level of vaccination has been defined. For the vaccination level less than the minimum level, increase in the vaccination level results in decrease of the proportion of infected individuals in the corresponding equilibrium point. On the other hand, for the vaccination level greater than the minimum level, increase in the vaccination level results in decrease the proportion of susceptible individuals in the corresponding equilibrium point. Furthermore, when vaccination level is greater than the minimum level, it is found that the time needed for the disease to extinct is shorter.
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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: Sifat Pulp Campuran antara Pulp Asli Bambu dan Pulp Karton Bekas (Old Corrugated Containers)
Abstrak: OCC was soaked for 7 days and disintegrated afterward. Soda pulping of bamboo was carried out following the pulping parameters of 35% NaOH charge, L/W of 4/1, maximum temperature of 170 oC and total cooking time of 3 hours. Kappa number and pulping yield were determined based on TAPPI T236 cm-85 standard. Bamboo and OCC pulp was bleached following the method of D0ED1D2. Bleached bamboo pulp was beaten up to the freeness of 100, 200, 300, and 400 ml CSF. While that of OCC was up to 400 ml CSF only. The composisitions of bamboo/OCCpulp mixture (B/K) were 0/100, 20/80, 40/60, 60/40, 80/20 and 100/0. Physical and optical properties of pulp mixture were determined based on TAPPI T205 sp-02 standard. The pulp composition of (B/K) 20/80 at freeness level of 400 ml CSF was resulted in the highest strength properties based on Duncan scoring. Pulp beating was able to decrease the composition of bamboo pulp in pulp mixture while retaining the strength properties
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