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: 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: Studi pembuatan bambu lapis daeri anyaman bambu tali, Gigantochloa apus(J.A.& J.H. Schultes)Kurz) dengan menggunaklan perekat UF dan PF
Abstrak: Nilai rata-rata keteguhan rekat sejajar serat bambu lapis dengan perlakuan perebusan sebesar 7,73 kg/cm² dengan kisaran antara 1,72 kg/cm² sampai 14,80 kg/cm². Berdasar nilai yang didapat maka nilai keteguhan rekat sejajar serat dengan perekat PF telah memenuhi standar SNI, JAS, dan ASTM karena nilainya lebih dari 7 kg/cm². Bambu lapis dengan perekat UF yang tidak mendapat perlakuan sudah memenuhi standar SNI, JAS, dan ASTM, sedangkan untuk bambu lapis dengan perlakuan perebusan nilainya kurang dari nilai yang telah dipersyaratkan sehingga tidak memenuhi persyaratan keteguhan rekat sesuai standar. Hal ini diduga oleh sifat dari perekat UF yang tidak tahan terhadap perlakuan air panas sehingga menyebabkan kerusakan pada bambu lapis, rusaknya bambu lapis dapat menyebabkan kekuatan rekatnya berkurang.
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