Interpolasi menggunakan splin trigonometri dengan satu parameter bentuk
| dc.contributor.author | Razali, Noor Khairiah | |
| dc.date.accessioned | 2015-05-21T08:07:44Z | |
| dc.date.available | 2015-05-21T08:07:44Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | Infectious diseases are a major health problem throughout the world. Each year, millions of people die from infectious diseases such as measles, tuberculosis, malaria, HIV/AIDS, and so on. Measles is a severe and highly contagious viral infection of the respiratory tract, though its most prominent symptom is a skin rash. Its virus spreads through direct contact with an infected person. Usually, measles is not considered as a fatal disease in most developed countries. However, some reports claim that measles is the most contagious of all infectious diseases. Measles epidemics occur when the virus spreads rapidly through a susceptible population. In this dissertation, we compare two models; seasonally forced nonlinear SEIR model, and seasonally nonlinear SEIR model. We derive the seasonally nonlinear models by following works done by previous reports of Liu et.al as stated in the bibliography to determine the steady states and basic reproductive rates. We incorporate seasonality by allowing the contact or transmission ra.te , 13 to vary over the course of the year . Periodic contact rate implies the model with seasonal forcing. We used the simplest possible form of the sinusoidal contact rate, f3(t) = 130(1 + 8 cos 21ft), which has been widely used in studies of the dynamics of the epidemic models, also been used by the numerous researchers likes Ira B.Schwartz. We then analyze the stability of the equilibrium and the steady states. The "epidemic threshold" is the point at which the percentage of unvaccinated people is high enough to risk an epidemic. The model then was evaluated by using Mathematica. From the results, we can see clearly that IX the domain is positively invariant. Moreover, solutions exist for all positive time as no solution path leave through any boundary and initial value problems have unique solution that exists on maximal intervaL Clearly, the domain always have a diseasefree equilibrium given by E = I = R = 0 so that S = 1 where S, E, I, and R are susceptible, exposed, infectives, and recovered respectively. Basic reproductive rate is denoted by Q. By linearization, if Q > 1, the disease-free equilibrium is locally asymptotically stable. But then, if Q :$ 1, the disease-free equilibrium is globally asymptotically stable in the domain, D, since the origin is the only positively invariant subset of the set, and all path in the origin will approach the origin. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/665 | |
| dc.language.iso | en | en_US |
| dc.title | Interpolasi menggunakan splin trigonometri dengan satu parameter bentuk | en_US |
| dc.type | Thesis | en_US |
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