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Decisions on public health measures to contain a pandemic are often based on parameters such as expected disease burden and additional mortality due to the pandemic. Both pandemics and nonpharmaceutical interventions to fight pandemics, however, produce economic, social, and medical costs. The costs are, for example, caused by changes in access to healthcare, social distancing, and restrictions on economic activity. These factors indirectly influence health outcomes in the short- and long-term perspective. In a narrative review based on targeted literature searches, we develop a comprehensive perspective on the concepts available as well as the challenges of estimating the overall disease burden and the direct and indirect effects of Covid-19 interventions from both epidemiological and economic perspectives, particularly during the early part of a pandemic. We review the literature and discuss relevant components that need to be included when estimating the direct and indirect effects of the Covid-19 pandemic. The review presents data sources and different forms of death counts, and discusses empirical findings on direct and indirect effects of the pandemic and interventions on disease burden as well as the distribution of health risks.