Theoretical population dynamics model of a genetically transmitted disease: sickle-cell anaemia

We formulate a realistic demographic model that captures the pattern of inheritance of the S gene, which is responsible for the most common genetic defect, namely, sickle-cell anaemia (SCA), using general pair formations. The model equation is implicitly solved via the Laplace transform technique, w...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2007-02, Vol.69 (2), p.699-730
Main Author: Tchuenche, Jean M
Format: Article
Language:English
Subjects:
Anemia, Sickle Cell - genetics
Female
Hemoglobin, Sickle - genetics
Humans
Male
Models, Genetic
Population Dynamics
Selection, Genetic
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Summary:We formulate a realistic demographic model that captures the pattern of inheritance of the S gene, which is responsible for the most common genetic defect, namely, sickle-cell anaemia (SCA), using general pair formations. The model equation is implicitly solved via the Laplace transform technique, while the existence of a unique solution is proved by applying the contraction mapping principle. One of the main results is the boundedness of the solution. A fundamental reason for the persistence of SCA is probably due to the role played by the selective advantage of the abnormal S gene over the normal haemoglobin A in tropical regions, and the fact that carriers are more fertile and survive longer (a property known as hybrid vigor), because they are essentially asymptomatic. We also discuss possible public health policies.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-006-9148-y