An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells - Patrick W. Nelson; Michael A. Gilchrist; Daniel Coombs; James M. Hyman; Alan S. Perelson (Mathematical Biosciences and Engineering)
Mathematical models of HIV-1 infection can help interpretdrug treatment experiments and improve our understanding of the interplay between HIV-1and the immune system. We develop and analyze an age-structured model of HIV-1 infection thatallows for variations in the death rate of productively infected T cellsand the production rate of viral particles as a function of thelength of time a T cell has been infected. We show that this model is a generalization ofthe standard differential equation and of delay models previously used to describeHIV-1 infection, and provides a means for exploring fundamental issuesof viral production and death. We show that the model has uninfected andinfected steady states, linked by a transcritical bifurcation. We performa local stability analysis of the nontrivialequilibrium solution and provide a general stability condition for models withage structure. We then use numerical methods to study solutions of our model focusing on theanalysis of primary HIV infection. We show that the time to reach peak viral levels in theblood depends not only on initial conditions but also on the way in which viral productionramps up. If viral production ramps up slowly, we find that the time to peak viral loadis 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 insufficientto identify the functions specifying the dependence of theviral production rate or infected cell death rate on infected cell age. These functions mustbe determined through new quantitative experiments.