Path: TopS2-ThesesMathematics2009

MODEL STOKASTIK UNTUK EPIDEMI PERTUSSIS DENGAN VAKSIN TAK SEMPURNA

STOCHASTIC MODELS OF PERTUSSIS EPIDEMIC WITH IMPERFECT VACCINE

Master Theses from JBPTITBPP / 2017-01-18 14:44:30
Oleh : I MADE SUARSANA (NIM: 20107002), S2 - Mathematics
Dibuat : 2009, dengan 7 file

Keyword : Bilangan reproduksi tervaksin, bifurkasi mundur, rantai markov waktu kontinu, matriks generator, waktu antarkejadian, persamaan diferensial stokastik, drift, difusi.

Sebelum vaksin ditemukan, pertussis merupakan penyebab utama sakit dan kematian pada bayi. Bahaya pertussis lebih diakibatkan oleh infeksi sekunder yang timbul. Kasus pertussis turun hingga 99% sejak vaksin ditemukan. Data terakhir menunjukkan bahwa pertussis masih menjadi endemik pada sebagian besar wilayah dan sewaktu-waktu dapat memicu munculnya epidemi. Salah satu faktor penyebab belum punahnya pertussis adalah vaksin yang digunakan belum sempurna yaitu masih memungkinkan individu tervaksin terinfeksi. Masa inkubasi pertussis berkisar antara 3-12 hari. Setelah periode ini barulah individu terinfeksi bersifat menular. Dalam tesis ini, adanya periode laten diperhatikan dan juga disusun model stokastik berupa model rantai markov waktu kontinu dan model persamaan diferensial stokastik. Analisis kualitatif dan kuantitatif dilakukan untuk model deterministiknya kemudian dibandingkan dengan model stokastiknya.

Deskripsi Alternatif :

Before vaccine was found, pertussis was the main cause for illness and deaths of infants. The danger of pertussis is more as a result of a second infection that occurs. Case of pertussis have decreased by 99% since the invention of vaccine. Recent data shows that pertussis is still endemic in most of area in the world, which can anytime become a trigger for the existence of an epidemic. One of the factors why pertussis cannot totally be disappeared, is the fact that the vaccine is still imperfect, which makes an already vaccinated individual still vulnerable to infection. Incubation (latent) period ranges from 1 to 12 days. After that, an infected individual becomes infectious. In this thesis, latent period was considered and two stochastic models were formulated for pertussis epidemic, which included continuous time markov chain model and stochastic di®erential equation model. The analysis was done both qualitative and quantitatively for the deterministic model, which was then compared with the result of stochastic models.

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