Background and Objective: Mathematical models are widely used to perform experiments in silico and predict how diseases evolve over time under different scenarios. It is estimated that the COVID-19 pandemic will still have long-term effects in increasing poverty and social inequalities, compromising the achievement of the Sustainable Development Goals (SDGs) for diseases such as Tuberculosis (TB) and HIV/AIDS. Our aim is to estimate the future impact of different economic crisis scenarios on AIDS and TB incidence and mortality, and the mitigating effect of alternative policy responses to reduce poverty by 2030 in Brazil. Methods: We developed two compartmental models of HIV/AIDS and TB transmission dynamics, integrating economic and epidemiological aspects. The annual poverty rate in Brazil was included in the formulation of the models main parameters, based on the National Household Sample Survey. We project three poverty scenarios (no mitigation, one-year mitigation, and long-term mitigation). Using a genetic algorithm, the model parameters were estimated to fit the AIDS and TB incidence and death rates from 2003 to 2019. Results: The models suggest that the implementation of social protection policies could mitigate lasting increases in poverty, avoiding a 13% (CI: 4% - 31%) increase in incidence and 21% (CI: 12% - 34%) in mortality from HIV/AIDS, and 16% (CI: 10% - 25%) in incidence and 22% (CI: 15% - 31%) in mortality from TB. Also, more than 140 (CI: 87 - 240) thousand cases and 22 (CI: 15 - 32) thousand deaths from HIV/AIDS and TB could be prevented by 2030. Conclusions: Understanding complex phenomena such as the pandemic effects of COVID-19 on socioeconomic and health outcomes requires the integration of multidisciplinary models. Here, we show the importance of implementing social protection policies to avoid a large increase in morbidity and mortality from HIV/AIDS and TB during the post-pandemic period.