Theoretical Population Dynamics Model of a Genetically Transmitted Disease: Sickle-Cell Anaemia

摘要

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.