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Latin America is experiencing severe impacts of the SARS-CoV-2 pandemic, but poverty and weak public health institutions hamper gathering the kind of refined data needed to inform classical SEIR models of epidemics. We present an alternative approach that draws on advances in statistical ecology and conservation biology to enhance the value of sparse data in projecting and ameliorating epidemics. Our approach, leading to what we call a Stochastic Epidemic Gompertz model, with few parameters can flexibly incorporate heterogeneity in transmission within populations and across time. We demonstrate that poverty has a large impact on the course of the pandemic, across fourteen Latin American countries, and show how our approach provides flexible, time-varying projections of disease risk that can be used to refine public health strategies., Comment: 22 pages, 5 figures, Supplementary Material not uploaded