Mathematical Modelling of the Effect of HIV/AIDS on Sickle Cell Genotype with Perturbation in the Production of T-Cells on the Choice of Stability

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-6
Year of Publication : 2022
Authors : I. C. Eli, A. B. Okrinya
 10.14445/22315373/IJMTT-V68I6P516

How to Cite?
I. C. Eli, A. B. Okrinya, " Mathematical Modelling of the Effect of HIV/AIDS on Sickle Cell Genotype with Perturbation in the Production of T-Cells on the Choice of Stability ," International Journal of Mathematics Trends and Technology, vol. 68, no. 6, pp. 137-144, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P516

Abstract
Sickle cell disease is a genetic disorder resulting from a mutation in the haemoglobin gene. Human immunodeficiency virus (HIV) infections destroys the body immune system, increases risks of certain pathogens, damages body organs and causes death eventually. A person with both SCD and HIV presents a management challenge particularly in a resource limited situation. Studies show that the presence of SCD helps to control the effects of HIV in an individual and its transformation into AIDS later on. This study presents a pre-existing mathematical model based on a set of differential equations. The model is formulated such that it takes into account HIV infected cells and its effect on Sickle cell disease when there is a perturbation in the production of T-cells. It is observed that the dynamical system maintained instability for both trivial and non-trivial steady state with the help of characteristics equations, linearization and ODE45 numerical approach. The results also show that the boundaries of the co-existence of both the trivial and non-trivial steady state solutions of the T-cells increases. Hence, there is no significant relationship between the genotype of a patient and the growth of the HIV.

Keywords : HIV, Infections, Genotype, Patient, Stability, Perturbation, Eigen Values, CD4 + T-Cells and ODE45.

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