The COVID-19 trajectories worldwide have shown several surprising features which are outside the purview of classical epidemiological models. These include (a) almost constant and low daily case rates over extended periods of time, (b) sudden waves emerging from the above solution despite no or minimal change in the level of non-pharmaceutical interventions (NPI), and (c) reduction or flattening of case counts following relaxation of NPI. To explain these phenomena, we add contact tracing to our recently developed cluster seeding and transmission (CST) model. We find no fewer than four effects which make prediction of epidemic trajectories uncertain. These are (a) cryptogenic instability, where a small increase in population-averaged contact rate causes a large increase in cases, (b) critical mass effect, where a wave manifests after weeks of quiescence with no change in parameter values, (c) knife-edge effect, where a small change in parameter across a critical value causes a huge change in the response of the system, and (d) hysteresis effect, where the timing and not just the strength of a particular NPI determines the subsequent behaviour. Despite these effects however, some non-obvious conclusions regarding NPI appear to be robust. In particular, (a) narrowing the circle of one's social interactions can be as effective a measure as reducing interactions altogether, and (b) a good contact tracing program can effectively substitute for much more invasive measures. Finally, we propose the contact tracing capacity ratio - a metric of the load to which the tracers are subject - as a reliable early warning indicator of an imminent epidemic wave.
THE MAHALANOBIS DISTANCE BETWEEN THE HURST COEFFICIENT AND THE ALPHA-STABLE PARAMETER: AN EARLY WARNING INDICATOR OF CRISES