Abstract
The number of CD4 white blood cells has been established as an important clinical marker of disease progression to acquired immunodeficiency syndrome (AIDS) for persons infected with human immunodeficiency virus (HIV). The number of CD4 cells per unit volume is expected to decrease with time since infection by the virus. However on introduction of treatment interventions, the process is expected to reverse with the counts increasing to return to the normal level. In this study we deduce that the count per unit volume of blood of an HIV/AIDS patient has a linear relationship with the time since infection during the short period of time immediately treatment usage begins. We show one application of the model in treatment selection strategy.
Highlights
An understanding of typical course of the infection within an individual and the quantitative information about latent period, infectious period or in some cases incubation period is essential in designing effective treatment strategies
In order to describe the various stages of human immunodeficiency virus (HIV) infection one can make use of the corresponding differential equations showing the rates of changes in the number of individuals at the respective stages with the help of relevant parameters[1,2]
Simwa and Pokhariyal[3] constructed a dynamical model for stagespecific HIV incidences, using two systems of ordinary differential equations that are coupled through a delay in one of the systems
Summary
An understanding of typical course of the infection within an individual and the quantitative information about latent period, infectious period or in some cases incubation period is essential in designing effective treatment strategies. An expression for the counts per unit volume (milliliter) as a linear function of the hazard rate of the distribution of the CD4 cell lifetime on commencement of treatment is derived From these results we deduce strategies that can be used in the analysis of treatment interventions, with the analysis based on Simwa[6]. Let N τ ,t denote the number of CD4 cells per unit volume at time t in the body of an HIV patient infectedτ years ago. Let P(t,τ ) be the proportion at time t of the N CD4 cells per unit volume that are observed in an HIV patient infected τ years ago.
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