Abstract

Mathematical models of HIV-1 infection can help interpret drug treatment experiments and improve our understanding of the interplay between HIV-1 and the immune system. We develop and analyze an age- structured model of HIV-1 infection that allows for variations in the death rate of productively infected T cells and the production rate of viral particles as a function of the length of time a T cell has been infected. We show that this model is a generalization of the standard differential equation and of delay models previously used to describe HIV-1 infection, and provides a means for exploring fundamental issues of viral production and death. We show that the model has uninfected and infected steady states, linked by a transcritical bifurcation. We perform a local stability analysis of the nontrivial equilibrium solution and provide a general stability condition for models with age structure. We then use numerical methods to study solutions of our model focusing on the analysis of primary HIV infection. We show that the time to reach peak viral levels in the blood depends not only on initial conditions but also on the way in which viral production ramps up. If viral production ramps up slowly, we find that the time to peak viral load is delayed compared to results obtained using the standard (constant viral production) model of HIV infection. We find that data on viral load changing over time is insufficient to identify the functions specifying the dependence of the viral production rate or infected cell death rate on infected cell age. These functions must be determined through new quantitative experiments.

Highlights

  • We develop an age-structured model for HIV-1 infection dynamics that tracks the length of time a T cell has been infected

  • We developed a model of HIV-1 infection that accounts for variations in the death rate of productively infected T cells and viral production that are due to the age of the cellular infection

  • T ≥ 0 to be the time since a person has become infected with HIV-1 and a time or age of infection, a, which keeps track of the time between a T cell becoming infected and its ultimate death

Read more

Summary

Introduction

We develop an age-structured model for HIV-1 infection dynamics that tracks the length of time a T cell has been infected. In the standard ordinary differential equation model of HIV-1 infection presented in [6, 7, 24] a transcritical bifurcation occurs at c = πkT0/δ, where π is the constant virion production rate and T0 = s/d. The age class amax includes all cells whose age of infection was greater than or equal to amax and was chosen such that the viral production rate in the last class satisfies P (amax) = (1 − 10−6)Pmax.

Results
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call