ODE to Monte Carlo: Simulating a Dynamical System for HIV Progression

Lindi Wahl, University of Western Ontario
(with Jane Heffernan)

Abstract

Non-linear ODEs have been widely used to study the progression of HIV in an infected individual. These deterministic systems are unable to model variability in the infection timecourse or the outcome of the infection. ODE models also pre-suppose constant transition probabilities between states, for example, that the probability of cell death is independent of the age of the cell. Finally, incorporating physiological detail, such as the numerous classes of immune cells, can become unwieldy in these approaches. Although some of these drawbacks could be elegantly addressed using stochastic, partial or integral differential equations, we chose instead to develop a Monte Carlo simulation at the level of individual cells and virions. This simulation allows us to mimic the ODE system, quantifying variability, and can easily be extended to include other biological details. I will describe our approach and discuss some interesting predictions; for example we are able to quantify the probability that an initial exposure to HIV does not result in an infection, but is cleared due to stochastic fluctuations when the infected cell population is small.