  Diagnostic testing followed by isolation of identified cases with subsequent
tracing and quarantine of close contacts - often referred to as
test-trace-isolate-and-quarantine (TTIQ) strategy - is one of the cornerstone
measures of infectious disease control. The COVID-19 pandemic has highlighted
that an appropriate response to outbreaks requires us to be aware about the
effectiveness of such containment strategies. This can be evaluated using
mathematical models. We present a delay differential equation model of TTIQ
interventions for infectious disease control. Our model incorporates a detailed
mechanistic description of the state-dependent dynamics induced by limited TTIQ
capacities. In addition, we account for transmission during the early phase of
SARS-CoV-2 infection, including presymptomatic transmission, which may be
particularly adverse to a TTIQ based control. Numerical experiments, inspired
by the early spread of COVID-19 in Germany, reveal the effectiveness of TTIQ in
a scenario where immunity within the population is low and pharmaceutical
interventions are absent - representative of a typical situation during the
(re-)emergence of infectious diseases for which therapeutic drugs or vaccines
are not yet available. Stability and sensitivity analyses emphasize factors,
partially related to the specific disease, which impede or enhance the success
of TTIQ. Studying the diminishing effectiveness of TTIQ along simulations of an
epidemic wave we highlight consequences for intervention strategies.
