On the dynamics of certain models describing the HIV infection

Dayse H. Pastore, Jorge P. Zubelli

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This article concerns some global stability aspects of a class of models introduced by Nowak and Bangham that describe in a fairly successful way the initial phases of the HIV dynamics in the human body as well as some generalizations that take into account mutations. We survey recent results implying that the biologically meaningful positive solutions to such models are all bounded and do not display periodic orbits. For the mutationless cases the dynamics is characterized in terms of certain dimensionless quantities, the so-called basic reproductive rate and the basic defense rate. As a consequence, we infer that the finite dimensional models under consideration cannot account, without further modifications, for the third phase of the HIV infection. We conclude by suggesting a modification that according to our numerical simulations may describe the collapse of the infected patient.

Original languageBritish English
Title of host publicationDynamics, Games and Science I
Subtitle of host publicationDYNA 2008, in Honor of Mauricio Peixoto and David Rand
EditorsDavid A. Rand, Mauricio Matos Peixoto, Alberto Adrego Pinto
PublisherSpringer Verlag
Number of pages18
ISBN (Electronic)9783642114557
StatePublished - 2011
EventInternational conference on dynamical systems and game theory, DYNA 2008 - Braga, Portugal
Duration: 8 Sep 200812 Sep 2008

Publication series

NameSpringer Proceedings in Mathematics
ISSN (Print)2190-5614
ISSN (Electronic)2190-5622


ConferenceInternational conference on dynamical systems and game theory, DYNA 2008


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