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.
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Mannion, R., Ruskin, H.J. & Pandey, R.B. A monte carlo approach to population dynamics of cells in a HIV immune response model. Theory Biosci. 119, 145–155 (2000). https://doi.org/10.1007/s12064-000-0011-7
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DOI: https://doi.org/10.1007/s12064-000-0011-7