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: Pengaruh Vaksinasi terhadap Kestabilan Dinamika Populasi pada Model SIS
Abstrak: Model susceptible-infected-susceptible (SIS) adalah salah satu model dinamika penyebaran penyakit menular. Salah satu upaya pengendalian penyebaran penyakit yaitu dengan vaksinasi sehingga pada model SIS dapat ditambahkan faktor vaksinasi. Dalam tulisan ini, dianalisis tiga model yaitu model (1) tanpa vaksinasi, model (2) dengan vaksinasi, dan model (3) vaksinasi terhadap individu rentan dan imigran. Setiap model masing-masing diperoleh dua titik tetap, yaitu titik tetap bebas penyakit dan titik tetap endemik. Titik tetap endemik ketiga model stabil lokal asimtotik jika masing-masing bilangan reproduksi dasar bernilai lebih dari satu. Hasil analisis sensitivitas pada model (3) menunjukkan bahwa laju kontak transmisi berbanding positif dengan penurunan bilangan reproduksi dasar, sedangkan proporsi vaksinasi individu rentan berbanding negatif dengan penurunan bilangan reproduksi dasar. Keadaan bebas penyakit dapat terjadi jika bilangan reproduksi dasar bernilai kurang dari satu yang diperoleh dengan cara mengurangi laju kontak transmisi atau meningkatkan proporsi vaksinasi individu rentan. Pemberian vaksinasi lebih efektif untuk menghambat penularan penyakit daripada tanpa vaksinasi., The susceptible–infected–susceptible (SIS) model is one of epidemic models. One of the methods to control the spread of infectious diseases is vaccination, hence in the SIS model is formulated by including the factor of vaccination. In this manuscript, three mathematical models are developed, namely model (1) without vaccination, model (2) with vaccination, and model (3) vaccination on susceptible individuals and immigrant. On each model, two equilibriums are obtained, they are the disease-free equilibrium and the endemic equilibrium. The endemic equilibrium on three models is locally asymptotically stable if basic reproduction number are large than one. Sensitivity analysis on model (3) suggests that the rate of transmission contact is positively proportional to the decrease of basic reproduction number, whereas proportion of vaccinated susceptible individuals is negatively proportional to the decrease of basic reproduction number. The diseases-free equilibrium will occur if basic reproduction number is less than one which can be acquired by reducing the rate of transmission contact or increasing vaccination for susceptible individuals. Vaccine delivery was more effective for halt the spread of diseases than without vaccine.
Keyword: basic reproduction number, equilibrium, SIS model, sensitivity analysis, vaccination

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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