Stability of Some Models in Mathematical Biology

Lately there has been an increasing awareness of the adverse side effect from the use of pesticides on the environment and on human health. As an alternative solution attention has been directed to the so-called "Biological Control" where pests are removed from the environment by the us...

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Main Author:	Aldaikh, Abdalsalam B. H.
Format:	Thesis
Language:	English English
Published:	1998
Subjects:	Biology - Mathematical models Biomathematics Biological pest control agents
Online Access:	http://psasir.upm.edu.my/id/eprint/9454/1/FSAS_1998_40_A.pdf
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id	my-upm-ir.9454
record_format	uketd_dc
spelling	my-upm-ir.94542013-09-25T07:29:28Z Stability of Some Models in Mathematical Biology 1998-12 Aldaikh, Abdalsalam B. H. Lately there has been an increasing awareness of the adverse side effect from the use of pesticides on the environment and on human health. As an alternative solution attention has been directed to the so-called "Biological Control" where pests are removed from the environment by the use of another living but harmless organism. A detailed study of biological control requires a clear understanding on the types of interaction between the species involved. We have to know exactly the conditions under which the various species achieve stability and live in coexistence. It is here that mathematics can contribute in understanding and solving the problem. A number of models for single species are presented as an introduction to the study of two species interaction. Specifically the following interactions are studied: -Competition -Predation -Symbiosis. All the above interactions are modelled based on ordinary differential equations. But such models ignore many complicating factors. The presence of delays is one such factor. In the usual models it is tacitly assumed that the coefficients of change for a given species depend only on the instantaneous conditions. However biological processes are not temporally isolated, and the past influences the present and the future. In the real world the growth rate of a species does not respond immediately to changes in the population of interacting species, but rather will do so after a time lag. This concept should be taken into account, and this leads to the study of delay differential equations. However the mathematics required for the detailed analysis of the behaviour of such a model can be formidable, especially for biologists who share the subject. By the aid of computer and using Mathematica software (version 3.0), the main properties of the solutions of many models related to the various interactions can be clarified. Biology - Mathematical models Biomathematics Biological pest control agents 1998-12 Thesis http://psasir.upm.edu.my/id/eprint/9454/ http://psasir.upm.edu.my/id/eprint/9454/1/FSAS_1998_40_A.pdf application/pdf en public masters Universiti Putra Malaysia Biology - Mathematical models Biomathematics Biological pest control agents Faculty of Science and Environmental Studies English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Biology - Mathematical models Biomathematics Biological pest control agents
spellingShingle	Biology - Mathematical models Biomathematics Biological pest control agents Aldaikh, Abdalsalam B. H. Stability of Some Models in Mathematical Biology
description	Lately there has been an increasing awareness of the adverse side effect from the use of pesticides on the environment and on human health. As an alternative solution attention has been directed to the so-called "Biological Control" where pests are removed from the environment by the use of another living but harmless organism. A detailed study of biological control requires a clear understanding on the types of interaction between the species involved. We have to know exactly the conditions under which the various species achieve stability and live in coexistence. It is here that mathematics can contribute in understanding and solving the problem. A number of models for single species are presented as an introduction to the study of two species interaction. Specifically the following interactions are studied: -Competition -Predation -Symbiosis. All the above interactions are modelled based on ordinary differential equations. But such models ignore many complicating factors. The presence of delays is one such factor. In the usual models it is tacitly assumed that the coefficients of change for a given species depend only on the instantaneous conditions. However biological processes are not temporally isolated, and the past influences the present and the future. In the real world the growth rate of a species does not respond immediately to changes in the population of interacting species, but rather will do so after a time lag. This concept should be taken into account, and this leads to the study of delay differential equations. However the mathematics required for the detailed analysis of the behaviour of such a model can be formidable, especially for biologists who share the subject. By the aid of computer and using Mathematica software (version 3.0), the main properties of the solutions of many models related to the various interactions can be clarified.
format	Thesis
qualification_level	Master's degree
author	Aldaikh, Abdalsalam B. H.
author_facet	Aldaikh, Abdalsalam B. H.
author_sort	Aldaikh, Abdalsalam B. H.
title	Stability of Some Models in Mathematical Biology
title_short	Stability of Some Models in Mathematical Biology
title_full	Stability of Some Models in Mathematical Biology
title_fullStr	Stability of Some Models in Mathematical Biology
title_full_unstemmed	Stability of Some Models in Mathematical Biology
title_sort	stability of some models in mathematical biology
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science and Environmental Studies
publishDate	1998
url	http://psasir.upm.edu.my/id/eprint/9454/1/FSAS_1998_40_A.pdf
_version_	1747810959314911232

Stability of Some Models in Mathematical Biology

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