We parametrize public policies in the context of the COVID-19 pandemic to evaluate the effectiveness of policies through sensitivity-based methods in order to offer insights into understanding the contributions to critical measures in retrospective. The study utilizes a group-specific SEIR model with a tracing and isolation strategy and vaccination programs. Public policies are applied to minimize death tolls, mitigate the social and economic effects caused by infections and avoid the overburden of the health system. We propose derivative-based sensitivity analysis to evaluate the priorities of different strategies. As apposed to purely scenario-based approaches, the proposed method only uses qualitative properties of the underlying mathematical model. Combined with compartment models the strategy permits to assess the relative significance of policies under the typically large uncertainties. The study carries out experiments under past situations with Delta and Omicron variants in Germany. These experiments confirm a positive influence of tracing apps as earlier observed in simulation-based case studies as well as the importance of booster programs, especially for the elderly. Insights and methods gained from this study may provide support for decision-making processes in future public health crises and can be advanced to assessing criticality of measures for other societal challenges.
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