The Study of Population Dynamics of Sickle Cell Anaemia by Renewal Equation and Markov Chain Process

Sickle cell Anaemia (SCA) is the most common form of sickle cell Diseases. Sickle cell anaemia is a potentially devastating condition that is caused by a defective allele (mutant form) of the gene coding for a sub unit of the haemoglobin protein. This paper investigates the dynamics of the disease by renewal equation and the probability of acquiring the S gene by Markov chain process. The renewal equation reflects the abundance of AS group (carrier) in the population at the long run. In the same vein the markov process also reflects that AS genotypic group has greater potential to dominate the population at the long run. (i.e. at 20th generation). Three absorbing states were noticed: the mating between three pairs AA&AA, AA&SS and SS&SS. Therefore, the study concludes that, with or without genotype screening before marriage, the population of AS genotypic group is expected to grow abundantly in the population. The abundance of the population of AS indicates that the relative activities of this heterogeneous group cannot be permanently zero. Hence, the study recommends that, a cheaper curative measure remains the only solution to the problem of sickle cell anaemia in our society.