Growth patterns and scaling laws governing AIDS epidemic in Brazilian cities

TL;DR

This study analyzes the growth and distribution patterns of AIDS cases across Brazilian cities over 33 years, revealing logistic growth, power-law decay, and allometric relationships that inform epidemic modeling and control strategies.

Contribution

It provides a comprehensive quantitative analysis of AIDS epidemic dynamics in Brazil, highlighting growth laws, distribution patterns, and the impact of city size on infection spread.

Findings

AIDS cases exhibit logistic growth with initial exponential phase.

Reproduction number decays as a power law over time.

Distribution of cases among cities follows a power law.

Abstract

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.