Parametric sensitivity analysis of a mathematical model of HIV infection of CD4+ T-Cells

Abstract

Background: In this complex mathematical model of a system of continuous nonlinear first order ordinary differential equations of HIV infection of CD4+ T-Cells, the scientific problem of determining the sensitivity of model parameters, s and a over the model parameter d is yet to be tackled.

Aim: To determine the sensitivity of model parameters , s and a over the model parameter d by using the one-at-a-time type of sensitivity analysis over a chosen time range.

Methods:  In this  bio-medical study, we used the tool of a sensitivity analysis to select the most sensitive model parameters of this multi-parameter system. This method is based on a variation of a model parameter one-at-a-time when other model parameters are fixed.

Results: We have found that the maximum proliferation rate'a' of target cells, the T population density 'Tmax' at which proliferation shuts off and the rate's' at which new T cells are created from sources within the body such as thymus are selected using the three  mathematical norms of 1-norm, 2-norm and infinity norm as the most sensitive parameters while the death rate'd' of the T cells is selected as the least sensitive.

Conclusion: The implications of these contributions for further data validation, parameter estimation and HIV mitigation policy in a Nigerian population are suggested. The details of the sensitivity properties of other model parameters will be the subject of a future publication.

Keywords:  parametric,  Sensitivity analysis, Mathematical model, HIV/AIDS model, Policy implications, T cells