In quest to contain and subsequently eradication Human Immunodeficiency virus (HIV) in the society, mathematical modelling remains an important research tool. In this paper, we formulated a mathematical model to study the effects of cortisol on immune response to HIV capturing the roles played by dendritic cells, T helper cells, regulatory T cells and cytotoxic T cells in the virus replication dynamics. The primary source of concentration of cortisol in this work is through psychological stress. Numerical experiments are performed to examine the effect of cortisol on selective inhibition of antigen presentation activities and up-regulation of naive cytotoxic T cells activation in the case of acute and persistent stressful conditions.
In this paper, we developed a new family of self starting second derivative Simpson’s type block methods (SDSM) of uniform order for step number. The new block methods forwere seen to possess good stability property as they possessed good regions of absolute stability. They were also found to be consistent, zero stable and A-stable (Fig.4). This essential property made them suitable for the solution of stiff system of ordinary differential equations. Four numerical examples were considered and results obtained show improved accuracy in terms of their Maximum absolute errors when compared with the work of existing scholars. The newly developed block methods were seen to approximate well with the stiff Ode Solver (Fig. 5, 6, 7 and 8).
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