Linear and nonlinear models of heredity for blood groups and rhesus factor

We consider linear and nonlinear stochastic models for transmission of blood types and Rhesus factor from parents to their offspring and investigate long run behavior of these models. In this study we will consider an application of the theory of Markov chains and the theory of nonlinear transformat...

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Main Authors:	Ganikhodjaev, Nasir, Jamal Ibrahim, Daoud, Usmanova, Maksuma
Format:	Article
Language:	English
Published:	Asian Network for Scientific Information 2010
Subjects:	QP Physiology
Online Access:	http://irep.iium.edu.my/3959/ http://irep.iium.edu.my/3959/ http://irep.iium.edu.my/3959/ http://irep.iium.edu.my/3959/1/1748-1754_%281%29.pdf

id	iium-3959
recordtype	eprints
spelling	iium-39592012-05-08T04:17:32Z http://irep.iium.edu.my/3959/ Linear and nonlinear models of heredity for blood groups and rhesus factor Ganikhodjaev, Nasir Jamal Ibrahim, Daoud Usmanova, Maksuma QP Physiology We consider linear and nonlinear stochastic models for transmission of blood types and Rhesus factor from parents to their offspring and investigate long run behavior of these models. In this study we will consider an application of the theory of Markov chains and the theory of nonlinear transformations in medicine. It is well known that the gene which determines blood group in humans has three different alleles, A, B, C and that there are four groups of blood, A, B, AB and O. The aim is to investigate the transmission of blood groups from parents to their offspring. For simplicity, we will consider only positive Rhesus factors, since the portion of the population with negative Rhesus is around 1%. It is well known that the blood groups of parents do not determine unambiguously their offspring’s blood group. To describe this transmission, we have rather extensive statistics for blood groups of parents and their offspring. In connection with these statistics, we construct the following two Markov chains. The first Markov chain describes the transmission from a father to his sons; the second Markov chain describes the transmission from a mother to her daughters. Lastly we construct and study a quadratic stochastic operators that describe the transmission of blood groups from parents to their offspring. Asian Network for Scientific Information 2010 Article PeerReviewed application/pdf en cc_by_nc http://irep.iium.edu.my/3959/1/1748-1754_%281%29.pdf Ganikhodjaev, Nasir and Jamal Ibrahim, Daoud and Usmanova, Maksuma (2010) Linear and nonlinear models of heredity for blood groups and rhesus factor. Journal of Applied Sciences, 10 (16). pp. 1748-1754. ISSN 1812-5662 (O), 1812-5654 (P) http://scialert.net/archivedetails.php?issn=1812-5654&issueno=144 10.3923/jas.2010.1748.1754
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QP Physiology
spellingShingle	QP Physiology Ganikhodjaev, Nasir Jamal Ibrahim, Daoud Usmanova, Maksuma Linear and nonlinear models of heredity for blood groups and rhesus factor
description	We consider linear and nonlinear stochastic models for transmission of blood types and Rhesus factor from parents to their offspring and investigate long run behavior of these models. In this study we will consider an application of the theory of Markov chains and the theory of nonlinear transformations in medicine. It is well known that the gene which determines blood group in humans has three different alleles, A, B, C and that there are four groups of blood, A, B, AB and O. The aim is to investigate the transmission of blood groups from parents to their offspring. For simplicity, we will consider only positive Rhesus factors, since the portion of the population with negative Rhesus is around 1%. It is well known that the blood groups of parents do not determine unambiguously their offspring’s blood group. To describe this transmission, we have rather extensive statistics for blood groups of parents and their offspring. In connection with these statistics, we construct the following two Markov chains. The first Markov chain describes the transmission from a father to his sons; the second Markov chain describes the transmission from a mother to her daughters. Lastly we construct and study a quadratic stochastic operators that describe the transmission of blood groups from parents to their offspring.
format	Article
author	Ganikhodjaev, Nasir Jamal Ibrahim, Daoud Usmanova, Maksuma
author_facet	Ganikhodjaev, Nasir Jamal Ibrahim, Daoud Usmanova, Maksuma
author_sort	Ganikhodjaev, Nasir
title	Linear and nonlinear models of heredity for blood groups and rhesus factor
title_short	Linear and nonlinear models of heredity for blood groups and rhesus factor
title_full	Linear and nonlinear models of heredity for blood groups and rhesus factor
title_fullStr	Linear and nonlinear models of heredity for blood groups and rhesus factor
title_full_unstemmed	Linear and nonlinear models of heredity for blood groups and rhesus factor
title_sort	linear and nonlinear models of heredity for blood groups and rhesus factor
publisher	Asian Network for Scientific Information
publishDate	2010
url	http://irep.iium.edu.my/3959/ http://irep.iium.edu.my/3959/ http://irep.iium.edu.my/3959/ http://irep.iium.edu.my/3959/1/1748-1754_%281%29.pdf
first_indexed	2023-09-18T20:11:58Z
last_indexed	2023-09-18T20:11:58Z
_version_	1777407537758339072

Linear and nonlinear models of heredity for blood groups and rhesus factor

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