Compartments and Phases

  • Facts

Mr. Node stumbled on a simulation of a virus explanation of how a pandemic works. It is provided by the Washington Post. It reminded him of his own models to simulate the behaviors of complex adaptive situations. He had a model available for to establish where the initial curves stop being exponential. In Fig.1 he shows the dynamics of COVID-19 deaths as observed (in alphabetic order) in France (F), the Netherlands (NL), China (PRC), the UK, the USA and the world.

The fourth graph has the most detail. It also shows the model’s curve (algorithm 0). All four graphs show the same data. Only the scales of the y-values are different. They show the curves for F, NL, PRC, UK, USA and the world from the week in which their first casualties are registered until week 23 of the pandemic (May 29, 2020).

Mr. Node reads the graphs as follows.

  • Globally (black): contamination begins in week 1, the first victim is in week 4 and the curve flattens in week 9, however, exponential growth picks up again in week 10 and becomes more or less steeply linear by week 15 (9-1=8);
  • The PRC (darkish): contamination begins in week 1, the first victim is in week 4 and the curve flattens in week 9 (9-1=8);
  • In France (F, brown): first contaminations and first victims are in week 9 and the curve (really) flattens in week 15 (15-9=6);
  • In the UK and in the USA (resp. red and grey): the curves begin in week 9, the first victims are in week 11 and the curves turn into steep linear growth in week 16 and remain there (16-9=7)
  • In the NL (orange) contamination begins in week 10, the first victim is in week 11 and the curve begins to flatten in week 13 (13-10=3);

We are on the lookout for segmenting the dynamics of the complex situations we are studying. We do this by grouping individuals (e.g., born, susceptive, infective, resistent, deceased) in compartments and by grouping models in sequential mechanisms (functional phases). The current question concerns choosing the first compartment-phase domains, globally and for the PRC, F, the USA, the UK and NL.

The PRC took 9 weeks from the first contamination until it had flattened the curve. Really flattened it. It had to face several hurdles: the virus was new, it broke out at a political inconvenient time (postponing the party’s congress) and also at a social inconvenient time (resulting lock-downs during preparations of the spring or new year’s festival). Several things were supportive to the success. One is the experience with the Sars epidemic and the lessons learned. Another is the collectivist social-constitutional system. It allows for substantial public support for behavioral rules that protect others. And for the toleration of serious enforcement of such rules.

France began reclaiming control 6 weeks after its first victim. Of course it had an advantage: the seriousness of the pandemic and how it could be addressed had been shown at Wuhan, Italy and Spain. But like in Italy and Spain, the carnival festival and its customs helped spread the virus. A serious president ordaining serious lock-downs to a receptive population helped France to really flatten the curve in May.

The USA and the UK began claiming control 7 weeks after the first contaminations were identified in their jurisdictions. The numbers show that there indeed are no longer exponential curves. Yet their numbers of infected keep growing at a high pace. Both jurisdictions have leaders that initially downplayed the pandemic’s gravity which may contribute to the slow pace of reclaiming control over the pandemic in these countries.

For modeling purposes these considerations suggest that control over the pandemic is a complex affair, knowing how it works qua contamination mechanisms is not enough, and neither is knowledge about how rules on individual autonomy prevent rules on social distancing to be heeded. Nor is knowledge on how the economy transforms under the new conditions enough. We will need to consider all four perspectives concurrently.

And — since today (May 30, 2020) began with a rebellion sweeping through the USA which may trigger Trump to further jeopardize current global leadership — be prepared for further systemic risks to be faced when additional triggers for critical transitions in our social systems emerge.