Judul: Analisis Kestabilan Model Epidemi pada Penyebaran Virus Hepatitis B dengan Vaksinasi
Abstrak: Virus hepatitis B adalah penyebab penyakit hepatitis B. Model epidemi penyebaran virus hepatitis B dengan vaksinasi yang ditinjau adalah model SIR (Susceptible, Infected, Recovered). Penelitian ini bertujuan untuk merekonstruksi model, menentukan titik tetap dan bilangan reproduksi dasar, menganalisis kestabilan titik tetap dan sensitivitas, serta melakukan simulasi numerik. Bilangan reproduksi dasar diperoleh dengan menggunakan the next generation matrix. Simulasi numerik dilakukan dengan menggunakan software Mathematica 12.0 untuk menunjukkan pengaruh setiap parameter terhadap bilangan reproduksi dasar. Penurunan tingkat penularan mengakibatkan penurunan bilangan reproduksi dasar. Kenaikan tingkat pemulihan dan vaksinasi mengakibatkan penurunan bilangan reproduksi dasar. Perubahan bilangan reproduksi dasar berpengaruh pada kestabilan sistem., Hepatitis B virus is the cause of hepatitis B disease. The epidemic model of the spread hepatitis B virus with vaccination is the SIR (Susceptible, Infected, Recovered) model. The purpose of this research is to reconstruct the model, determining the fixed point and the basic reproduction number, analysing the stability of the fixed point and sensitivity, and perform numerical simulations. The basic reproduction number is obtained using the next generation matrix. Numerical simulations are carried out using Mathematica 12.0 software to show the effect of each parameter on the basic reproduction number. The decrease in the transmission level implies the decrease in the basic reproduction number. The increase in the rate of recovery and vaccination implies the decrease in the basic reproduction number. The changes in the basic reproduction affect the stability of the system.
Keyword: hepatitis B virus, epidemic, SIR, fixed point, basic reproduction number

Judul: Analisis Kestabilan Model SEIR COVID-19 dengan Pengaruh Vaksinasi
Abstrak: Corona Virus Disease atau COVID-19 adalah penyakit menular yang cukup serius bagi kesehatan masyarakat. COVID-19 merupakan penyakit yang disebabkan oleh virus SARS-CoV-2. Tujuan dari penelitian ini adalah menentukan serta menganalisis kestabilan dari titik tetap pada model SEIR COVID-19 dan melakukan simulasi numerik untuk mengkaji pengaruh vaksinasi. Analisis kestabilan titik tetap ditentukan dengan aturan Descartes dan fungsi Lyapunov. Bilangan reproduksi dasar (ℛ0) didapatkan dengan menggunakan matriks next generation. Hasil penelitian ini menunjukkan bahwa titik tetap bebas penyakit bersifat stabil asimtotik bilamana ℛ0 < 1. Simulasi numerik dilakukan dengan menggunakan software Mathematica 13.0. untuk mengetahui pengaruh parameter terhadap bilangan reproduksi dasar. Penurunan laju perpindahan populasi individu terpapar ke populasi individu terinfeksi mengakibatkan bilangan reproduksi dasar menurun. Kenaikan tingkat pemberian vaksinasi pada populasi individu rentan akan mengakibatkan bilangan reproduksi dasar menurun. Dengan mengontrol kedua parameter tersebut, penyebaran penyakit akan dapat dikendalikan., Corona Virus Disease or COVID-19 is an infectious disease that is quite serious for public health. COVID-19 is a disease caused by the SARS- CoV-2 virus. The purpose of this study is to determine and analyze the stability of equilibrium points in the COVID-19 SEIR model and conduct numerical simulations to assess the effect of vaccination. The analysis of equilibrium-point stability is determined by Descartes' rule and the Lyapunov function. The basic reproduction number (ℛ0) is obtained using the next generation matrix. The results of this study show that disease-free fixed points are asymptotic stable when ℛ0 < 1. Numerical simulations were carried out using Mathematica 13.0 software to find out the effect of parameters on the basic reproductive number. A decrease in population movement rate of the population of exposed individuals to the population of infected individuals causes a decrease in the basic reproductive number. An increase vaccination rate in vulnerable individual populations will causes a decrease in the basic reproductive number. By controlling parameters, the spread of the disease will be controlled.
Keyword: stability analysis, basic reproductive numbers, numerical simulation, COVID- 19

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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