The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

Sickle Cell Anaemia (SCA) is a serious inherited blood disorder where the red blood cells, which carry oxygen around the body develop abnormally. The mathematical dynamics of the disease remain poorly understood, as such this paper investigates the mathematical inheritance pattern of the disease by the application of Monte Carlos simulation technique which is a complementary approach to physical simulation Smith's statistical package was used as random number generator in which the simulated birth from different mating indicates that SS has an average of 2.4% neonates, AS has 29.9% and AA has 67.7%. We thus, conclude that eradication of SCA is not visible. However, curative measure of SCA remains paramount.

Sickle Cell Disease (SCD) is a potentially devastating condition that is caused by an autosomal recessive inherited hemoglobinopathy which results in the vaso-occlusive phenomena and hemolysis. Sickle Cell Anaemia (SCA) is the most common form of SCD. As such, this paper provides an insight on the mathematical transmission dynamics of SCA and develops a physical realistic model. A female dominant renewal equation of birth dynamics was developed. Hardy-Weinberg equation is applied to obtain the frequency of different genotype groups for the physical simulation. We realized an average of 70% neonates normal (AA), 27% carrier (AS), and 3% sicklers (SS), which is typically the real world result. This implies that physical simulation is an effective tool in predicting the genetic make-up of any population.

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