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This paper aims to discuss how the public budget and the model of basic attention in public health could affect the infant mortality rates in a certain territory. The research was carried out in the Southern Coastal Territory of Bahia, in the State of Bahia, Northeast Region of Brazil. It is a quantitative and descriptive investigation, based on secondary data referring to the period from 2006 to 2015, collected between 2017 and 2018 in official Brazilian public data banks. It was verified that, although the average rate of infant mortality fell gradually from 2006 in the territory, it is still higher than the national average within the investigated period. In 2006, the average rate of the territory was 35.53% and decreased to 18.56% in 2015. However, throughout the period the average rate remained higher than the Brazilian average, which is 18%. Infant mortality rates have a strong relationship with social, economic, and environmental factors. In the case investigated, they are associated with the fragmentation and fragility of public health service networks in the municipalities of the region. [ABSTRACT FROM AUTHOR]