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 (IJMTT)
© 2022 by IJMTT Journal
Volume-68 Issue-6
Year of Publication : 2022
Authors : I. C. Eli, A. B. Okrinya

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,

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.


[1] Burden, R. L. and Faires, J. D. (2011). Numerical Analysis, Ninth edition, Canada.
[2] Lange, F. R, Snyder, Lozovsky D, Kaistha V, Kaczaniuk M. A, and Jaffe J. H, (1998). Geographic distribution of human immune deficiency virus markers in parenteral drug abusers. AMJ Public Health 78, pp446.
[3] Kassim O, Ejezie G. ABO blood groups in Malaria and Schistosomiasis haematobium. Acta Trop …. 1982; 39.179-84.
[4] Tursen U, Tiffik E, Unal S, Gunduz O, Kaya T1, et al. Relationship between ABO blood groups and skin cancers Dermatol. On line J, 2005; 11:pp44.
[5] Opera K. Onchocerciasis and ABO blood group status: a field based study. Int. J. Trop. Med, 2007: 2(4):123-125.
[6] Abdulazeez A, Alo E, Rebecca S. Carriage rate of Human Immuno Deficiency Virus (HIV) infection among different ABO and Rhesus blood groups in Adamawa State, Nigeria. Biomed Res.., f2008:19:pp41-44.
[7] Ndambaa J, Gomoa E, Nyazemab N, Makazaa N, relations to the ABO blood groups among school children in Zimbabwe. Acta Trop., 1997;65. Pp181-190.
[8] Blackwell cc, Dundas S, James vs, Mackenzie Ac, Braun JM, et al. Blood group and susceptibility to disease caused by Eschetichia coli 0 157. J. Infect. Dis; 2002, 185 (3): 393-396.
[9] Garraty G. Dzik W, Issitt P. Lubin D, Reid M, et al. Terminology for blood group antigens and genes-historical origin and guideline in the new millennium. Transfusion, 2000, 40:477-489.
[10] Rahman M. Lodlu Y. Frequency of ABO and Rhesus blood groups in blood donors in Punjab Pak J. Med. Sci, 2004;20:315-318.
[11] Lease M, Bazuaye G. Distribution of ABO and Rh-D blood groups in the Benin area of Niger-Delta: Implication for regional blood transfusion. Asian J. Transfus, Sci., 2008; 2(1):3-5.
[12] Ahmad J, Taj A, Rahim A, Shah A, Rheman M. Frequency of Hepatitis B and Hepatitis C in health blood donors of NWFP: A single centre experience J. Post grad Med. Inst, 2004; 18(3): 343-352.
[13] Wazirali H, Ashfane RA Herzig JW. Association of blood group A with increased risk of coronary heart disease in the Pakistan population. Pak J. Physiol, 200; 1:(1-2):1-3.
[14] Eli I. C. and Bunonyo K. W. Mathematical Modelling of the effect of HIV/AIDS on Sickle Cell Genotype. International Journal of Scientific Engineering and Applied Science (IJSEAS). Volume 6, Issue 6, June 2020. ISSN:2395-3470.