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

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)

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	4430/3959
Uncontrolled Keywords:	Markov chain, quadratic stochastic operator, blood type, rhesus factor, heredity
Subjects:	Q Science > QP Physiology
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Science
Depositing User:	Assoc.Prof.Dr Jamal Daoud
Date Deposited:	28 Sep 2011 13:04
Last Modified:	08 May 2012 12:17
URI:	http://irep.iium.edu.my/id/eprint/3959

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