Judul: Solusi Numerik Masalah Kontrol Optimum Penyebaran Penyakit Influenza A
Abstrak: Influenza A is an acute respiratory disease caused by a virus H1N1. The virus is mainly transmitted by air and can be contagious from human to human. In this work, a mathematical model of SIR is used to describe the disease transmission, where the population is divided into three classes namely susceptible, infected, and recovered. Analysis was performed on two cases, those are models without and with control, i.e. vaccination treatments. The model of H1N1 transmission is applied at regency and city of Bogor with a total population of six million people. Model without control provides two equilibrium points, where from stability threshold for disease free equilibrium point is obtained a basic reproductive number . The disease will die out if and may become endemic if . On the model with administration of control we minimized the infected population and the vaccination cost. Numerical solutions of nonlinear system of differential equations derived from the conditions of Pontryagin minimum principle are conducted by Runge-Kutta 4th order method. The results of numerical simulation show that the model without control administration, basic reproductive number causes more infected individuals than that of . Meanwhile, the effect of the treatment above decreased the number of H1N1 infected down to .
Keyword: Runge-Kutta 4th order, Pontryagin minimum principle, optimal control, influenza A (H1N1), stability analysis

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: Penggunaan Tanin Kulit Kayu Tusam (Pinus merkusii Juugh et de Vricst) Sebagai Perekat Kayu Lapis Eksterior
Abstrak: Perekat merupakan salah satu komponen penentu dalam industri kayu lapis. dewasa ini perekat yang umum digunakan dalam industri kayu lapis adalah perekat sintetis yang bahan bakunya diolah secara kimia dari hasil minyak bumi. Selain harganya mahal sumberdaya untuk perekat sintetis ini bersifat tidak dapat pulih yang akan habis dalam jangka waktu tertentu, sehingga perlu dicari alternatif pengganti untuk bahan perekat tersebut.
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