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Safe Policy Design for Controlling Epidemic Spreading under Heterogeneous Testing Capabilities

This paper studies a model that captures epidemic spreading in a population with heterogeneous testing capabilities. The detection of the disease is faster in a subpopulation because of access to better testing capabilities, whereas another subpopulation relies on standard testing to confirm positive cases once individual have manifested symptoms. This model is a particular case of a recently proposed vectorized SIR model, for which we characterize various invariance properties and the stability properties of its set of equilibria. We leverage these analytical results to design social distancing policies that guarantee that the impact of the pandemic satisfies certain specifications, namely, that the total capacity of the healthcare system does not get overburdened and that the total number of infections throughout the pandemic remains below a thresh-old. Simulations illustrate the extent to which higher testing capabilities allow for more lenient social distancing policies.