A Monte Carlo approach to population dynamics of cells in a HIV immune response model

Using a direct Monte Carlo simulation, population growth of helper T-cells (N-H) and viral cells (N-V) is studied for an immune response model with an enhanced spatial inter-cellular interaction relevant to HIV as a function of viral mutation. In the absence of cellular mobility (P-mob = 0), the hel per T-cells grow nonmonotonically before reaching saturation and the viral population grows monotonically before reaching a constant equilibrium. Cell ular mobility (P-mob = 1) enhances the viral growth and reduces the stimula tive T-cell growth. Below a mutation threshold (P-c), the steady-state dens ity of helper T-cell (rho(H)) is larger than that of the Virus (rho(V)); th e density difference Delta rho(o)(= rho(V) - rho(H)) remains a constant at P-mob = 1 while -Delta rho(o) --> 0 as P-mut --> P-c at P-mob = 0. Above th e mutation threshold, the difference Delta rho(o) in cell density, grows wi th Delta P = P-mut - P-c monotonically: Delta rho(o) proportional to (Delta P)(beta) with beta similar or equal to 0.574 +/- 0.016 in absence of mobil ity, while Delta rho(o) similar or equal to 6(Delta P) with P-mob = 1.