Wodarz, Hamer, 2007

Model Structure

CD4+ T helper cells represent a major target for the replication of human immunodeficiency virus (HIV). Conversely, CD4+ T cells are also an essential component of the immune response to HIV. A considerable proportion of the HIV-specific CD4+ T cells become infected with the virus which, in turn, has important implications for understanding the dynamics between HIV and the immune response. Infection of HIV-specific CD4+ T cells can have several outcomes for the dynamics between the virus and the immune system, including:

  • enhanced viral spread through the division of infected CD4+ T cells; and also

  • impaired effector responses, such as CD8+ cytotoxic T lymphocytes (CTL), through the compromised ability of the CD4+ T cells to deliver help.

Mathematical models of the kinetics of HIV infection and replication have improved our understanding of the relationship between HIV and immune responses. In their mathematical model(s), described here in CellML, Wodarz and Hamer (2007) characterise the infection dynamics in HIV-specific CD4+ T cells. Their aim was to demonstrate the the potential consequences of autocatalytic virus spread and describe the different roles of CD4+ T cells during HIV infection.

The original publication contains four different mathematical models:

  • The first is a simple model of autocatalytic virus spread via the division of infected CD4+ T cells. This simple model forms the core of the subsequent, more complex models, and allows some basic analytical insights into the properties of autocatalytic virus spread.

  • The second model builds on this core model by including a description of the infectious spread of the virus amongst CD4+ T cells.

  • The third model adds further complexity by incorporating alternative target cells which are do not react against HIV, such as T cells with other specificities and antigen presenting cells.

  • Finally, the forth model describes CD8+ CTL dynamics during HIV infection, and considers the effects of both cell proliferation and death.

The CellML model presented here represents the first model of autocatalytic virus spread. The other three models have also been coded in CellML and can be downloaded as version 1 variants 1, 2 and 3 of the model.

The complete original paper reference is cited below:

Infection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus?, Dominik Wodarz and Dean H. Hamer, 2007, Mathematical Biosciences (Full text and PDF versions of the article are available to journal subscribers on the Mathematical Biosciences website.) PubMed ID: 17379260