Robustness of a Cellular Automata Model for the HIV Infection

TL;DR

This study assesses the robustness of a cellular automata model for HIV spread, showing that its core dynamics are stable across different lattice symmetries and dimensions, and insensitive to many parameter variations.

Contribution

It provides a comprehensive analysis of the model's robustness, confirming its qualitative consistency with observed HIV infection dynamics across various conditions.

Findings

Three-phase dynamics are stable across lattice symmetries.

Qualitative behavior persists despite changes in dimensionality.

Power-law behavior observed in infection variables over parameter ranges.

Abstract

An investigation was conducted to study the robustness of the results obtained from the cellular automata model which describes the spread of the HIV infection within lymphoid tissues [R. M. Zorzenon dos Santos and S. Coutinho, Phys. Rev. Lett. 87, 168102 (2001)]. The analysis focussed on the dynamic behavior of the model when defined in lattices with different symmetries and dimensionalities. The results illustrated that the three-phase dynamics of the planar models suffered minor changes in relation to lattice symmetry variations and, while differences were observed regarding dimensionality changes, qualitative behavior was preserved. A further investigation was conducted into primary infection and sensitiveness of the latency period to variations of the model's stochastic parameters over wide ranging values. The variables characterizing primary infection and the latency period exhibited power-law behavior when the stochastic parameters varied over a few orders of magnitude. The power-law exponents were approximately the same when lattice symmetry varied, but there was a significant variation when dimensionality changed from two to three. The dynamics of the three-dimensional model was also shown to be insensitive to variations of the deterministic parameters related to cell resistance to the infection, and the necessary time lag to mount the specific immune response to HIV variants. The robustness of the model demonstrated in this work reinforce that its basic hypothesis are consistent with the three-stage dynamic of the HIV infection observed in patients.