Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models

The dynamics of HIV-1 infection consist of three distinct phases starting with primary infection, then latency and finally AIDS or drug therapy. In this paper we model the dynamics of primary infection and the beginning of latency. We show that allowing for time delays in the model better predicts viral load data when compared to models with no time delays. We also find that our model of primary infection predicts the turnover rates for productively infected T cells and viral totals to be much longer than compared to data from patients receiving anti-viral drug therapy. Hence the dynamics of the infection can change dramatically from one stage to the next. However, we also show that with the data available the results are highly sensitive to the chosen model. We compare the results using analysis and Monte Carlo techniques for three different models and show how each predicts rather dramatic differences between the fitted parameters. We show, using a χ2 test, that these differences between models are statistically significant and using a jackknifing method, we find the confidence intervals for the parameters. These differences in parameter estimations lead to widely varying conclusions about HIV pathogenesis. For instance, we find in our model with time delays the existence of a Hopf bifurcation that leads to sustained oscillations and that these oscillations could simulate the rapid turnover between viral strains and the appropriate CTL response necessary to control the virus, similar to that of a predator–prey type system.