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We combine infectious disease transmission and the non-pharmaceuticalintervention (NPI) response to disease incidence into one closed modelconsisting of two coupled delay differential equations for the incidence rateand the time-dependent reproduction number. The model contains three freeparameters, the initial reproduction number, the intervention strength, and theresponse delay relative to the time of infection. The NPI response is modeledby assuming that the rate of change of the reproduction number is proportionalto the negative deviation of the incidence rate from an intervention threshold.This delay dynamical system exhibits damped oscillations in one part of theparameter space, and growing oscillations in another, and these are separatedby a surface where the solution is a strictly periodic nonlinear oscillation.For parameters relevant for the COVID-19 pandemic, the tipping transition fromdamped to growing oscillations occurs for response delays of the order of oneweek, and suggests that effective control and mitigation of successive epidemicwaves cannot be achieved unless NPIs are implemented in a precautionary manner,rather than merely as a response to the present incidence rate.

The tipping effect of delayed interventions on the evolution of COVID-19 incidence