Identifiability Problems of Time-delay HIV Models

In vivo modelling of the pathogenesis of HIV-1 in plasma captures the interplay of the virus and CD4 cells in the cell-free viral spread process. Modelling is also done for both in vitro cell-to-cell and cell-to-free viral spread of HIV-1 and its kinetics in tissue cultures. Upon infection with HIV-1, there is a short intracellular “eclipse phase” or “latency”, during which the cell is infected but has not yet begun producing virus. One approach to account for the “eclipse phase” or “latency” is to introduce an intracellular delay in the models. This paper focuses on the identifiability of the parameters in the most popular HIV models with time delay, in vivo and in vitro. The identifiability of such parameters as the time-delay parameter; the effective reproductive rate of healthy cells; death rate of infected cells; average life time of productively infected cells; viral burst size; etc, is studied by the linear algebraic method based on differential 1-form. Medical interpretation for the identifiability results is given, and it provides guidelines in data collection for the identification of these parameters.