Mathematical Modelling of the Immune System and Disease

Associated People:

Daniel Coombs (University of British Columbia)

Jessica M. Conway (University of British Columbia)

Associated Sites:
PIMS University of British Columbia
Associated PIMS Programs:

IGTC in Mathematical Biology

While on successful drug treatment, routine testing does not usually detect virus in the blood of an HIV patient. However, more sensitive techniques can detect extremely low levels of virus. Occasionally, routine blood tests show “viral blips”: short periods of elevated, detectable viral load. In work with postdoctoral fellow Jessica Conway, we explored the hypothesis that residual low-level viral load can be largely explained by re-activation of cells that were infected before the initiation of treatment, and that viral blips can be viewed as occasional statistical events. We proposed a stochastic mathematical model of latently-infected cells, activated cells, and virus. The model is designed to capture random fluctuations of the system as well as the average behaviour. We used our model to estimate the time it takes for all the latently-infected cells to be eradicated. Eradication of these cells is considered a major hurdle in eliminating infection. We predicted a wide range of eradication times, highlighting the importance of further intensive studies of latently-infected cells. We also estimated the frequency and duration of viral blips in treated patients, finding qualitative agreement with clinical studies. By refining our models in future work, we hope to find guidelines that can be used in practise to distinguish between clinically insignificant statistical blips, and instances of drug failure.

Some UBC students made a video about some of this work.
HIV fluctuating dynamics"