A monte carlo approach to population dynamics of cells in a HIV immune response model

Summary 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 helper T-cells grow nonmonotonically before reaching saturation and the viral population grows monotonically before reaching a constant equilibrium. Cellular mobility (P _mob=1) enhances the viral growth and reduces the stimulative T-cell growth. Below a mutation threshold (P _c), the steady-state density of helper T-cell (p _H) is larger than that of the Virus (p _v); the density difference Δp _o(=pV−pH) remains a constant at P _mob=1 while −Δp _o→0 as P _mut→P _c at P _mob=0. Above the mutation threshold, the difference Δp _o in cell density, grows with ΔP=P _mut−P _c monotonically: ΔP _o ∞ (ΔP)^β ≃ with β≈0.574±0.016 in absence of mobility, while Δp _o≈6(ΔP) with P _mob=1.