Judul: Strategy for Controlling the Spread of Multistrain Infectious Disease with Limited Vaccination Capacity
Abstrak: Karya ilmiah ini membahas mengenai model deterministik untuk penyakit menular multistrain. Model SVEIR multistrain diperkenalkan dalam formulasi persamaan diferensial biasa nonlinear yang merepresentasikan dinamika dari subpopulasi rentan, divaksinasi, terpapar, terinfeksi, dan sembuh. Beberapa sifat seperti titik tetap bebas penyakit dan endemik beserta kestabilannya diselidiki guna menunjang proses perumusan strategi terbaik. Model SVEIR multistrain diperluas dengan penerapan teori kontrol optimal dengan variabel kontrol berupa kapasitas vaksinasi terbatas untuk dua dosis dan pengobatan. Kontrol optimal akan diterapkan dalam empat stategi pengendalian dan diimplementasikan prinsip maksimum Pontryagin untuk memperoleh solusi optimal. Simulasi numerik akan dilakukan untuk studi kasus COVID-19 dengan strain 1 merupakan COVID-19 dengan gelaja yang lebih ringan, sedangkan strain 2 adalah COVID-19 yang menimbulkan gejala lebih berat bagi penderitanya. Secara numerik, strategi 4 dengan menerapkan semua variabel kontrol secara maksimal yang menjadi strategi terbaik guna menekan angka terpapar dan terinfeksi. Strategi 4 membutuhkan biaya yang cenderung lebih mahal untuk diimpelentasikan sebagai kebijakan, mempertimbangkan kendala biaya ditentukanlah keputusan dengan melakukan analisis efektivitas biaya dengan Average Cost Effectiveness Ratio (ACER) dan Incremental Cost Effectiveness Ratio (ICER) dan diperoleh bahwa strategi 1 yang hanya menerapkan vaksinasi dosis pertama dan pengobatan yang menjadi strategi terbaik dari segi kinerja dan biaya., This thesis considers a deterministic model for multistrain infectious diseases. This problem is formulated in the multistrain SVEIR model using nonlinear ordinary differential equations representing the evolution of susceptible, vaccinated, exposed, infected, and recovered individuals. First, we investigate the population dynamics and several properties: disease-free and endemic equilibrium points and the model’s stability. Furthermore, the multistrain SVEIR model for this infectious disease will expand by applying the optimal control theory with limited vaccination capacity and treatment presented in four strategies, supported by Pontryagin’s maximum principle of obtaining optimal conditions. The numerical solution takes COVID-19 as a case study, with the first strain representing milder symptoms and the second strain expressing severe symptoms. The fourth strategy is capable and effective because the peak of endemic spike that occurs when implementing this strategy is much lower than in other scenarios and can reduce the number of individuals exposed to and infected with both strains based on numerical solutions. However, based on cost-effectiveness analysis using the Average Cost Effectiveness Ratio (ACER) and Incremental Cost Effectiveness Ratio (ICER) methods for making decisions, the first strategy is a strategy that can work optimally and cost-effectively.
Keyword: Optimal Control, Infectious Disease, Multistrain SVEIR model, Strategy

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: 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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