A Study of the anderson-may model of epidemics and its extensions
| dc.contributor.author | Abdul Manaf, Zati Iwani | |
| dc.date.accessioned | 2015-07-30T02:16:14Z | |
| dc.date.available | 2015-07-30T02:16:14Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | Every year, millions of people worldwide die from infectious diseases such as AIDS, Dengue, SARS and others. So, the mathematical models can provide much insight into the dynamics of epidemics and help the public health authorities to make decision to control and eradicate the infectious disease involving with immigrants, especially. In this dissertation, we demonstrate how the mathematical model can describe the epidemiological phenomena. Firstly, we discussed the classical epidemic models and the Anderson.. ,a.,n d May model. Next, we introduced the extension model by extending the model of Anderson and May to take care of vaccination among immigrants. This model was set up by using the system of nonlinear ordinary differential equations. From extension model, we found the equilibrium and done with the stability analysis in order to test whether the equilibrium is stable or not. This model have shown that the free-disease equilibrium is stable for Ro < I and unstable for R0 > 1. But, the endemic..disease equilibrium shown that the equilibrium is stable for R0 > 1 and unstable for Ro < 1. For the vaccination threshold, we proved that for large vaccination level, the free...<fisease equilibrium is stable when p > Pc. And, for the weak vaccination level, the endemic...<fisease equilibrium is stable when p < Pc· Finally, the numerical result has shown that the vaccination strategies are possible to reduce the infected population. These evaluations are carried out by using the numerical simulations with Mathematica. However, the improved model may have some limitations and needed to reconsider in further research. Some recommendations are given in this dissertation to perform the better vaccination strategies in order to eradicate the infectious disease. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/913 | |
| dc.language.iso | en | en_US |
| dc.subject | Anderson-May | en_US |
| dc.subject | Epidemic | en_US |
| dc.title | A Study of the anderson-may model of epidemics and its extensions | en_US |
| dc.type | Thesis | en_US |
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