Journal of Computational and Applied Mathematics
The stochastic nature of early HIV infection is described in a series of models, each of which captures aspects of the dance of HIV during the early stages of infection. It is to this highly variable target that the immune response must respond. The adaptability of the various components of the immune response is an important aspect of the system's operation, as the nature of the pathogens that the response will be required to respond to and the order in which those responses must be made cannot be known beforehand. As HIV infection has direct influence over cells responsible for the immune response, the dance predicts that the immune response will be also in a variable state of readiness and capability for this task of adaptation. The description of the stochastic dance of HIV here will use the tools of stochastic models, and for the most part, simulation. The justification for this approach is that the early stages and the development of HIV diversity require that the model to be able to describe both individual sample path and patient-to-patient variability. In addition, as early viral dynamics are best described using branching processes, the explosive growth of these models both predicts high variability and rapid response of HIV to changes in system parameters.
In this paper, a basic viral growth model based on a time dependent continuous-time branching process is used to describe the growth of HIV infected cells in the macrophage and lymphocyte populations. Immigration from the reservoir population is added to the basic model to describe the incubation time distribution. This distribution is deduced directly from the modeling assumptions and the model of viral growth. A system of two branching processes, one in the infected macrophage population and one in the infected lymphocyte population is used to provide a description of the relationship between the development of HIV diversity as it relates to tropism (host cell preference). The role of the immune response to HIV and HIV infected cells is used to describe the movement of the infection from a few infected macrophages to a disease of infected CD4+" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.4px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative; CD4+ T lymphocytes.