#### Title

A Monte Carlo Approach to Population Dynamics of Cells in a HIV Immune Response Model

#### Document Type

Article

#### Publication Date

7-1-2000

#### Department

Physics and Astronomy

#### Abstract

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 (rho(H)) is larger than that of the Virus (rho(V)); the 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 the mutation threshold, the difference Delta rho(o) in cell density, grows with 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 mobility, while Delta rho(o) similar or equal to 6(Delta P) with P-mob = 1.

#### Publication Title

Theory in Biosciences

#### Volume

119

#### Issue

2

#### First Page

145

#### Last Page

155

#### Recommended Citation

Mannion, R.,
Ruskin, H. J.,
Pandey, R. B.
(2000). A Monte Carlo Approach to Population Dynamics of Cells in a HIV Immune Response Model. *Theory in Biosciences, 119*(2), 145-155.

Available at: https://aquila.usm.edu/fac_pubs/4175