On cell resistance and immune response time lag in a model for the HIV infection

Recently, a cellular automata model has been introduced (Phys. Rev. Lett. 87 (2001) 168102) to describe the spread of the HIV infection among target cells in lymphoid tissues. The model reproduces qualitatively the entire course of the infection displaying, in particular, the two time scales that characterize its dynamics. In this work, we investigate the robustness of the model against changes in three of its parameters. Two of them are related to the resistance of the cells to get infected. The other one describes the time interval necessary to mount specific immune responses. We have observed that an increase of the cell resistance, at any stage of the infection, leads to a reduction of the latency period, i.e., of the time interval between the primary infection and the onset of AIDS. However, during the early stages of the infection, when the cell resistance increase is combined with an increase in the initial concentration of infected cells, the original behavior is recovered. Therefore we find a long and a short latency regime (eight and one year long, respectively) depending on the value of the cell resistance. We have obtained, on the other hand, that changes on the parameter that describes the immune system time lag affects the time interval during which the primary infection occurs. Using different extended versions of the model, we also discuss how the two-time scale dynamics is affected when we include inhomogeneities on the cells properties, as for instance, on the cell resistance or on the time interval to mount specific immune responses.