STOCHASTIC MODELS OF PERTUSSIS EPIDEMIC WITH IMPERFECT VACCINE
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 o...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/22537 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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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