A model of partial differential equations for HIV propagation in lymph nodes

Abstract

A system of partial differential equations is used to model the dissemination of the Human Immunodeficiency Virus (HIV) in CD4+T cells within lymph nodes. Besides diffusion terms, the model also includes a time-delay dependence to describe the time lag required by the immunologic system to provide defenses to new virus strains. The resulting dynamics strongly depends on the properties of the invariant sets of the model, consisting of three fixed points related to the time independent and spatial homogeneous tissue configurations in healthy and infected states. A region in the parameter space is considered, for which the time dependence of the space averaged model variables follows the clinical pattern reported for infected patients: a short scale primary infection, followed by a long latency period of almost complete recovery and third phase characterized by damped oscillations around a value with large HIV counting. Depending on the value of the diffusion coefficient, the latency time increases with respect to that one obtained for the space homogeneous version of the model. It is found that same initial conditions lead to quite different spatial patterns, which depend strongly on the latency interval.