3 research outputs found
A model of partial differential equations for HIV propagation in lymph nodes
Texto completo versión postprint de autor.-- PACS numbers: 02.30.Ks,02.30.Hq,87.18.Hf,87.19.XxA 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.This work was partially supported
by the following Brazilian funding agencies: CAPES,
FAPESB/PRONEX, CNPq and National Institute for
Science and Technology/Complex Systems.Peer reviewe
A model of partial differential equations for HIV propagation in lymph nodes
Texto completo versión postprint de autor.-- PACS numbers: 02.30.Ks,02.30.Hq,87.18.Hf,87.19.XxA 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.This work was partially supported
by the following Brazilian funding agencies: CAPES,
FAPESB/PRONEX, CNPq and National Institute for
Science and Technology/Complex Systems.Peer reviewe