Counter-intuitive COVID-19 Trajectories - Explanations, Early Warning Indicator and Mitigation Strategies

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 even after relaxation of NPI. To explain these phenomena, we add contact tracing to our recently developed cluster seeding and transmission (CST) model, which is predicated on heterogeneous rather than homogeneous mixing of people in society. With this addition, 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 can manifest after weeks of quiescence with no change in parameter values, (c) knife-edge effect, where a small change in parameter across a critical value can cause 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 evolution of the epidemic. Despite these effects however, it is a robust conclusion that a good contact tracing program can effectively substitute for much more invasive measures. We further find that the contact tracing capacity ratio - a metric of the stress to which the tracers are subject - can act as a reliable early warning indicator of an imminent epidemic wave. Extensive simulations demonstrate that whenever there is a drop in capacity ratio during a period of low daily infections, there is a very high probability of the case counts rising significantly in the immediate future. Author summaryClose to two years into the pandemic, the trajectories of COVID-19 in different places and at different times have shown wild variations and confounded modeling and forecasting efforts. Our new mathematical model can help to explain these variations. Some solutions of our model are non-standard but realistic. For example, we find an epidemic curve where daily cases remain on a plateau for a long time before suddenly exploding into a wave, despite interventions remaining constant throughout. We also find solutions showing that a specific intervention, for example capacity reduction at public gatherings, is very effective if implemented early on in a wave but useless if implemented a little later. Our proposed early warning indicator can be a game-changer for epidemic forecasting and model-based intervention strategies. Current forecasting algorithms have the weakest performance at the inflection points where there is an abrupt change in trend in the daily infection rates. The early warning indicator can give us advance notice of an approaching inflection point, and enable the authorities to take preventive measures before a wave actually arrives. Our results indicate that close communication between contact tracing personnel and public health authorities can achieve synergistic mitigation of the pandemic.