This CellML version of the model has been checked in COR and PCEnv. The units are consistent and the original source code was used to fix the CellML model such that it now runs to recreate the published results. The original paper contains three different mathematical models and this particular CellML model represents the first model of self-renewing memory CD4+ T cell homeostasis in the absence of HIV infection.

Model Structure

ABSTRACT: BACKGROUND: The asymptomatic phase of HIV infection is characterised by a slow decline of peripheral blood CD4(+) T cells. Why this decline is slow is not understood. One potential explanation is that the low average rate of homeostatic proliferation or immune activation dictates the pace of a "runaway" decline of memory CD4(+) T cells, in which activation drives infection, higher viral loads, more recruitment of cells into an activated state, and further infection events. We explore this hypothesis using mathematical models. METHODS AND FINDINGS: Using simple mathematical models of the dynamics of T cell homeostasis and proliferation, we find that this mechanism fails to explain the time scale of CD4(+) memory T cell loss. Instead it predicts the rapid attainment of a stable set point, so other mechanisms must be invoked to explain the slow decline in CD4(+) cells. CONCLUSIONS: A runaway cycle in which elevated CD4(+) T cell activation and proliferation drive HIV production and vice versa cannot explain the pace of depletion during chronic HIV infection. We summarize some alternative mechanisms by which the CD4(+) memory T cell homeostatic set point might slowly diminish. While none are mutually exclusive, the phenomenon of viral rebound, in which interruption of antiretroviral therapy causes a rapid return to pretreatment viral load and T cell counts, supports the model of virus adaptation as a major force driving depletion.

The original paper reference is cited below:

Understanding the slow depletion of memory CD4+ T cells in HIV infection, Andrew Yates, Jaroslav Stark, Nigel Klein, Rustom Antia, and Robin Callard, 2007, PLoS Medicine, volume 4, issue 5, 948-955. PubMed ID: 17518516