Judul: Analisis Model Epidemik SIS dengan Mengakomodasi Perubahan Suhu Lingkungan
Abstrak: Dalam karya ilmiah ini dikembangkan model epidemik SIS yang dipengaruhi oleh perubahan suhu lingkungan dengan menggunakan Markovian switching. Hasil penelitian menunjukkan bahwa penggabungan dua kondisi suhu lingkungan yang berbeda dapat menyebabkan perubahan banyaknya individu terinfeksi dalam rentang yang cukup besar. Selain itu, perubahan nilai parameter laju penularan penyakit berbanding lurus dengan banyaknya individu terinfeksi, perubahan nilai parameter rata-rata lamanya waktu individu terinfeksi berbanding lurus dengan banyaknya individu terinfeksi. Sedangkan perubahan nilai parameter total penduduk berbanding terbalik dengan banyaknya individu terinfeksi.
Keyword: model epidemik SIS, perubahan suhu lingkungan, Markovian switching

Judul: Analisis Model Epidemik SIS Stokastik Rantai Markov Waktu Kontinu dengan Adanya Migrasi
Abstrak: Model epidemik adalah model matematika yang digunakan untuk mengetahui perilaku penyebaran penyakit menular. Salah satu model epidemik adalah model epidemik SIS (Susceptible Infective Susceptible). Model epidemik SIS yang dibahas adalah model stokastik rantai Markov waktu kontinu dengan menambahkan faktor migrasi. Model SIS dengan adanya migrasi terdiri atas dua subpopulasi, yaitu individu rentan dinotasikan dengan ��������� (susceptible) dan individu terinfeksi dinotasikan dengan ��������� (infected). Dalam penelitian ini dibahas mengenai distribusi peluang stasioner dan nilai harapan waktu wabah penyakit. Simulasi numerik dilakukan untuk membandingkan penyebaran penyakit pada model epidemik SIS ketika terjadi migrasi dan ketika tidak terjadi migrasi. Dari hasil analisis dapat disimpulkan bahwa semakin kecil laju kontak penderita dapat menyebabkan meningkatnya peluang terjadinya bebas penyakit. Begitu juga dengan nilai laju migrasi, semakin kecil laju migrasi dapat menyebabkan semakin besarnya peluang terjadinya bebas penyakit.
Keyword: migrasi, stokastik, rantai Markov waktu kontinu, model SIS

Judul: Synthesis of Chicken Eggshells-Based β-Tricalcium Phosphate Bioceramics and Their Biocompatibility Test as A Tooth Filler
Abstrak: Preservation of alveolar bone following tooth extraction is an important step in dental practices before dental implant placement. This study reported synthesis of β-Tricalcium Phosphate (β-TCP) bioceramics and its biocompatibility test as a tooth filler to maintain the desired alveolar ridge dimension and stimulate the bone healing processes in the area of tooth loss. β-TCP bioceramics was resulted directly from precipitation of calcinated chicken eggshells as calcium source and phosphoric acid. The corresponding β-TCP was mixed with chitosan 2% to get β-TCP pellet for biocompatibility testing. Biocompatibility testing of β-TCP on lower incisor was performed in rabbits and sheep as animal model. In this study, the x-ray diffraction (XRD) profiles showed that 1000 oC calcinated chicken eggshells correspond to calcium oxide (CaO). There was also transformation phase of CaO into Ca(OH)2 observed after more than three months stored. The XRD profiles proved that obtained β-TCP bioceramics by precipitation has the same pattern with that of reference data base and commercial β-TCP. Fourier transform infrared (FTIR) spectra were completely consistent with the result of crystallization processes observed by XRD measurements. Moreover, the purity of the product shown by the atomic absorption spectroscopy (AAS) resulted in Ca/P ratio of 1.48 which was closed to that of standard β-TCP ceramics. The repeatable XRD peaks patterns and FTIR spectra obviously showed the sample reproducibility. Sheep’s alveolar socket that is filled with the corresponding β-TCP demonstrated the expected results. The x-ray radiograph of sheep’s jaw indicated no change on mesio-distal of the edentulous area. Moreover, the histological results were completely consistent with the x-ray radiograph and macroscopic result which is proved by the formation of new bone. In the contrary with sheep’s result, histological results showed no tooth growth on rabbit proved by the presence of lipid and collagen on the extraction site. This result did not correspond to the x-ray radiograph and macroscopic results that demonstrated the tooth growth and erupted tooth. It is clear that the corresponding β-TCP could minimize the bone loss and maintain the dimension of alveolar ridge.
Keyword: β-tricalcium phosphate, chicken eggshells, rabbit, sheep, tooth filler