Mathematical Population Dynamics of a Genetic Disease: a Deterministic Approach

A realistic deterministic demographic model that captures the pattern of inheritance of the gene responsible for the most common genetic defect is formulated using general pair formations and analyzed using various approaches including a numerical semi-discretization scheme. The patterns of inheritance of the disease are carefully derived. Polygamy is captured in the application and it is shown to be partially responsible for the widespread of this defect. This book is therefore a basic introduction to the mathematics of SCA at the population level, taking into account the genotype of individuals in the mating pattern. Minimizing mating which produces SCA sufferers can theoretically be achieved if some carriers of the trait as well as SCA patients agree to remain childless or choose celibacy (a difficult social condition indeed!). The analysis helps shed some light on this genetic defect and should be especially useful to senior undergraduates and graduate students as well as scientists working at the interface between mathematics and biological sciences interested in genetically transmitted disorders.