Published time: 30 March 2020
Authors: Sebastian Alexander Muller, Michael Balmer, Andreas Neumann, Kai Nagel
Keywords: COVID-19, immunity, model, infection
We use human mobility models, for which we are experts, and attach a virus infection dynamics to it, for which we are not experts but have taken it from the literature, including recent publications. This results in a virus spreading dynamics model. The results should be verified, but because of the current time pressure, we publish them in their current state. Recommendations for improvement are welcome. We come to the following conclusions:
1. Complete lockdown works. About 10 days after lockdown, the infection dynamics dies down. This assumes that lockdown is complete, which can be guaranteed in the simulation, but not in reality. Still, it gives strong support to the argument that it is never too late for complete lockdown.
2. As a rule of thumb, we would suggest complete lockdown no later than once 10% of hospital capacities available for COVID-19 are in use, and possibly much earlier. This is based on the following insights:
a. Even after lockdown, the infection dynamics continue at home, leading to another tripling of the cases before the dynamics are slowed.
b. There will be many critical cases coming from people who were infected before lockdown. Because of the exponential growth dynamics, their number will be large.
c. Researchers with more detailed disease progression models should improve upon these statements.
3. Our simulations say that complete removal of infections at child care, primary schools, workplaces, and during leisure activities will not be enough to sufficiently slow down the infection dynamics. It would have been better, but still not sufficient, if initiated earlier.
4. Infections in public transport play an important role. In the simulations shown later, removing infections in the public transport system reduces the infection speed and the height of the peak by approximately 20%. Evidently, this depends on the infection parameters, which are not well known. — This does not point to reducing public transport capacities as a reaction to the reduced demand, but rather use it for lower densities of passengers and thus reduced infection rates.
5. In our simulations, removal of infections at child care, primary schools, workplaces, leisure activities, and in public transport may barely have been sufficient to control the infection dynamics if implemented early on. Now according to our simulations, it is too late for this, and (even) harsher measures will have to be initiated until possibly a return to such a restrictive, but still somewhat functional regime will again be possible.
Evidently, all of these results have to be taken with care. They are based on preliminary infection parameters taken from the literature, used inside a model that has more transport/movement details than all others that we are aware of but still not enough to describe all aspects of reality and suffer from having to write computer code under time pressure. Optimally, they should be confirmed independently. Short of that, given current knowledge we believe that they provide justification for “complete lockdown” at the latest when about 10% of available hospital capacities for COVID-19 are in use (and possibly earlier; we are no experts in hospital capabilities).
What was not investigated in detail in our simulations was contact tracing, i.e. tracking down the infection chains and moving all people along infection chains into quarantine. The case of Singapore has so far shown that this may be successful. Preliminary simulation of that tactic shows that it is difficult to implement for COVID-19 since the incubation time is rather long, people are contagious before they feel sick, or maybe never feel sufficiently sick at all. We will investigate in future work if and how contact tracing can be used together with a restrictive, but not totally locked down the regime.
When opening up after lockdown, it would be important to know the true fraction of people who are already immune, since that would slow down the infection dynamics by itself. For Wuhan, the currently available numbers report that only about 0.1% of the population was infected, which would be very far away from “herd immunity”. However, there have been and still may be many unknown infections.
Mobility traces and spreading of COVID-19