A Study of the anderson-may model of epidemics and its extensions
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Date
2009
Authors
Abdul Manaf, Zati Iwani
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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.
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Keywords
Anderson-May , Epidemic