Figure 1.
New cases of AIDS in Brazil reported in 2012.
The radius of the circles are proportional to the logarithm of the absolute frequency yi,t. The histograms along the axis represent the dependence of the distribution of the AIDS cases on the geographic position (latitude and longitude) of the cities. Besides reflecting in a great extent the population distribution, this figure also provides a general information concerning the spatial spreading of the epidemics over the country.
Figure 2.
Time evolution of the epidemics.
(a) Growth of within the period 1980–2012 for 5138 Brazilian cities. The dashed blue line is Equation (1) with the parameters
,
,
and
. The continuous red line is Equation (1) with the parameters
,
,
and
. (b) Growth of the corresponding accumulated number of cases
shown in log-lin scale. The inset represents the first points of the curve of
, corresponding to the period 1980–1985. The solid line is a fit in this region, given by
with
. (c) Decay of the actual reproduction number
for the whole period shown at log-log scale. The solid line is a linear fit (in log-log scale) giving a power law exponent
. The green points correspond to the numerical solution of the continuous equation
with
for the Gompertz model, connecting the fit of Equation (1) to the patterns of the data.
Figure 3.
PDF of the absolute frequency among cities.
(a) Log-log plot of the probability density function, P(yi,t), where yi,t corresponds to the number of AIDS cases diagnosed in 2012 on 2891 Brazilian cities. The solid line has slope 1.87 and was obtained by a maximum likelihood fit to the data. (b) Temporal evolution of the power law exponent αt for the period 1986–2012. The error bars correspond to 99% bootstrapped confidence intervals.
Figure 4.
Allometric relationship between the epidemics and population of the cities.
yi,t as a function of the population of the city (pi,t) shown at log-log scale for fixed years: (a) 2000; and (b) 2010. The solid lines are linear fits performed for cities with 3000 or more inhabitants. The solid lines have slopes (a) 1.37 and (b) 1.31.
Figure 5.
Moments of the yi,t in Brazilian cities in the period 1989–2012.
The total of 5138 cities are split in 4 groups: 〈yi,t〉<2 (Group I), 2≤〈yi,t〉≤10 (Group II), 10<〈yi,t〉≤84 (Group III), and 〈yi,t〉>84 (Group IV).