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Diagnostic testing followed by isolation of identified cases with subsequenttracing and quarantine of close contacts - often referred to astest-trace-isolate-and-quarantine (TTIQ) strategy - is one of the cornerstonemeasures of infectious disease control. The COVID-19 pandemic has highlightedthat an appropriate response to outbreaks requires us to be aware about theeffectiveness of such containment strategies. This can be evaluated usingmathematical models. We present a delay differential equation model of TTIQinterventions for infectious disease control. Our model incorporates a detailedmechanistic description of the state-dependent dynamics induced by limited TTIQcapacities. In addition, we account for transmission during the early phase ofSARS-CoV-2 infection, including presymptomatic transmission, which may beparticularly adverse to a TTIQ based control. Numerical experiments, inspiredby the early spread of COVID-19 in Germany, reveal the effectiveness of TTIQ ina scenario where immunity within the population is low and pharmaceuticalinterventions are absent - representative of a typical situation during the(re-)emergence of infectious diseases for which therapeutic drugs or vaccinesare not yet available. Stability and sensitivity analyses emphasize factors,partially related to the specific disease, which impede or enhance the successof TTIQ. Studying the diminishing effectiveness of TTIQ along simulations of anepidemic wave we highlight consequences for intervention strategies.

A mechanistic model to assess the effectiveness of test-trace-isolate-and-quarantine under limited capacities