Judul: Kontrol Optimum Vaksinasi dan Pengobatan pada Penyakit Menular Tipe SIR
Abstrak: Nowadays, there are many infectious diseases that cause epidemic in the population. Therefore, an effective program is required to eliminate the infectious diseases, such as vaccination and treatment. The spread of infectious diseases can be modeled by SIR model, in which it enables us to predict the outbreak and the control rate. In this research, the SIR model is applied to analyze the population dynamic and to optimize the control of the outbreak with vaccination and treatment. As the result, the model provides two equilibrium points, i.e. dieasesfree and diseases-endemic equilibrium points. Moreover, the analysis show that if the reproduction number or ℛ0 is less than or equal 1, then the disease-free equilibrium point is globally asymptotically stable. While if ℛ0 is more than 1, then the disease-endemic equilibrium point is globally asymptotically stable. In this research the optimal control uses Pontryagin’s minimum principle with vaccination and treatment as control measures. The control objective is to find the optimal combination of vaccination and treatment that minimizes the cost of the two control measures as well as the number of infected individuals at the end of control period.
Keyword: vaccination., treatment, SIR model, Pontryagin’s minimum principle, optimal control

Judul: Masalah Kontrol Optimum Linear dan Taklinear pada Model SIR dengan Vaksinasi dan Pengobatan.
Abstrak: Dalam karya ilmiah ini dibahas masalah pengendalian penyakit yang dinamika penyebarannya dinyatakan dalam Model . Dua buah variabel kontrol ditambahkan ke dalam model, yaitu laju vaksinasi dan laju pengobatan. Ada dua model kontrol optimum yang dibahas berdasarkan bentuk fungsional objektif, yaitu model linear dan model taklinear. Prinsip maksimum Pontryagin diterapkan untuk mendapatkan kondisi optimalitas yang harus dipenuhi oleh variabel-variabel yang terlibat. Selanjutnya, metode Runge-Kutta orde empat digunakan untuk menentukan solusi numerik model kontrol optimum. Tiga skenario pengendalian diterapkan untuk melihat tingkat efektivitasnya, yaitu penerapan kontrol secara sendiri dan secara bersamaan. Solusi numerik menunjukkan bahwa seluruh skenario dapat menurunkan jumlah individu terinfeksi dengan usaha minimum. Model linear dan taklinear menghasilkan strategi pengendalian yang tidak jauh berbeda. Model linear menghasilkan fungsi kontrol optimum kontinu bagian demi bagian, sedangkan model taklinear menghasilkan fungsi kontrol kontinu dari waktu awal hingga waktu akhir.
Keyword: kontrol optimum, prinsip maksimum Pontryagin, bang-bang control, metode Runge-Kutta

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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