Effect of mutation on helper T-cells and viral population: A computer simulation model for HIV

Summary A Monte Carlo simulation is proposed to study the dynamics of helper T-cells (N _H) and viral (N _V) populations in an immune response model relevant to HIV. Cellular states are binary variables and the interactions are described by logical expressions. Viral population shows a nonmonotonic growth before reaching a constant value while helper T-cells grow to a constant after a relaxation/reaction time. Initially, the population of helper cells grows with time with a power-law, N _H ∼t ^β, before reaching the steady-state; the growth exponent β increases systematically (β ≈ 1 – 2) with the mutation rate (P _mut≈0.1–0.4). The critical recovery time (t _c) increases exponentially with the viral mutation, t _c≈Ae ^αP _mut , with α=4.52±0.29 in low mutation regime and α=15.21±1.41 in high mutation regime. The equilibrium population of helper T-cell declines slowly with P _mut and collapses at ∼ 0.40; the viral population exhibits a reverse trend, i.e., a slow increase before the burst around the same mutation regime.