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

Abstract

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.

The Effects of Migration on the Transmission Dynamics of Sickle Cell Anaemia

“…It can also be inferred from these probabilities that δ i ii = 1. For more details on the derivation of these equations, see [14].…”

“…For example, increased international human migration has resulted to be strictly connected with an upsurge of Sickle-Cell Anaemia cases among people living in non-malaria zones (see [14]). …”

Continuous-time model and physical simulation of population dynamics of sickle cell anaemia

“…A new set of functional differential equations modeling heterosexual population dynamics with K as the polygamy factor was developed by Sowunmi (1993); there, he proved that population renewal is the product of an interaction between the reproductive males and the nongestating reproductive females. Sowunmi (1993), Tchuenche (2003) and Tchuenche (2007) were the first to use the general interaction function where contributes the major mathematical background for the formulation of birth renewal equation. Tchuenche (2003Tchuenche ( , 2007 has done a lot in the dynamics of SCA.…”

“…Sowunmi (1993), Tchuenche (2003) and Tchuenche (2007) were the first to use the general interaction function where contributes the major mathematical background for the formulation of birth renewal equation. Tchuenche (2003Tchuenche ( , 2007 has done a lot in the dynamics of SCA. He is the pioneer mathematician who made use of differential equation to model the disease (SCA).…”

“…Another beauty of population dynamics of the genetically transmitted disease (SCA) which takes age, mating behaviour and a physiological factor into account was proposed in the Theoretical Population Dynamics Model (TPDM) of a generically transmitted disease (SCA) (Tchuenche, 2007). Liddell et al (2014) made it critically clear with his mathematical model of sickle cell genome frequency in response to selective pressure from malaria that selection pressure for the carrier gene in the presence of increase in malaria death for either adult or children has higher frequencies of the gene as well as shortened time to reach these frequencies.…”