According to the needs, real systems can be modeled at various level of resolution.
It can be detailed interactions at the individual level (or at microscopic level) or a
sample of the system (or at mesoscopic level) and also by averaging over mesoscopic
(structural) states; that is, at the level of interactions between subsystems of the original
system (or at macroscopic level).
With the microscopic study one can get a detailed information of the interaction but
at a cost of heavy computational work. Also sometimes such a detailed information is
redundant. On the other hand, macroscopic analysis, computationally less involved
and easy to verify by experiments. But the results obtained may be too crude for some
applications.
Thus, the mesoscopic level of analysis has been quite popular in recent years for
studying real systems. Here we will focus on structured population models where
we can observe various level of organization such as individual, a group of population,
or a community. Due to fast movement of the individual compare of the other
demographic processes (like death and birth), the problem is multiple-scale.
There are various methods to handle multiple-scale problem. In this work we will
follow asymptotic analysis ( or more precisely compressed Chapman–Enskog method)
to approximate the microscopic model by the averaged one at a given level of accuracy.
We also generalize our model by introducing reducible migration structure. Along
with this, considering age dependency of the migration rates and the mortality rates,
the thesis o ers improvement of the existing literature. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2011.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/9760 |
| Date | January 2011 |
| Creators | Goswami, Amartya. |
| Contributors | Banasiak, Jacek. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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