Effects of viral mutation on cellular dynamics in a Monte Carlo simulation of HIV immune response model in three dimensions

The cellular dynamics of HIV interaction with the immune system is explored in three-dimensions using a direct Monte Carlo simulation. Viral mutation with probability, P-mut, is considered with immobile and mobile cells. With immobile cells, the viral population becomes larger than that of the helper cells beyond a latency period T-crit and above a mutation threshold P-crit. That is at P-mut greater than or equal to P-crit, T-crit proportional to (P-mut - P-crit)(-gamma), with gamma similar or equal to 0.73 in three dimensions and gamma similar or equal to 0.88 in 2-D. Very little difference in P-crit is observed between two and three dimensions. With mobile cells, no power-law is observed for the period of latency, but the difference in P-crit between two and three dimensions is increased. The time-dependency of the density difference between Viral and Helper cell populations (rho(V) - rho(H)) is explored and follows the basic pattern of an immune response to infection. This is markedly more defined than in the 2-D case, where no clear pattern emerges.