  Brazil holds approximately 1/3 of population living infected with AIDS
(acquired immunodeficiency syndrome) in Central and South Americas, and it was
also the first developing country to implement a large-scale control and
intervention program against AIDS epidemic. In this scenario, we investigate
the temporal evolution and current status of the AIDS epidemic in Brazil.
Specifically, we analyze records of annual absolute frequency of cases for more
than 5000 cities for the first 33 years of the infection in Brazil. We found
that (i) the annual absolute frequencies exhibit a logistic-type growth with an
exponential regime in the first few years of the AIDS spreading; (ii) the
actual reproduction number decaying as a power law; (iii) the distribution of
the annual absolute frequencies among cities decays with a power law behavior;
(iv) the annual absolute frequencies and the number of inhabitants have an
allometric relationship; (v) the temporal evolution of the annual absolute
frequencies have different profile depending on the average annual absolute
frequencies in the cities. These findings yield a general quantitative
description of the AIDS infection dynamics in Brazil since the beginning. They
also provide clues about the effectiveness of treatment and control programs
against the infection, that has had a different impact depending on the number
of inhabitants of cities. In this framework, our results give insights into the
overall dynamics of AIDS epidemic, which may contribute to select empirically
accurate models.
