Possible Future Scenarios

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How will COVID-19 spread in the coming days? Does it matter if we change our behaviour? And how long will all this take?

We developed a SIR model to sketch three different future scenarios (Figure 1), starting from the 16th of March 2020:
(I) If we continue as before, the growth rate remains at around 30% per day (red curve).
(II) If we partially restrict our contacts (orange curve) and only meet about half as many people, then the exponential growth will slow down and we gain some time.
(III) If we introduce much stricter measures for all people, then the curve may flatten out (green) - only few new cases occur.

Model details and the Python code are available on our github repository.

From the evolution of the total number of cases, it can be seen very clearly that a change in behaviour will only be visible in 7-10 days. Only on day 7 the curves start to show a difference from each other. This is because many people are already infected, but they have not yet been identified and tested. Due to this uncertainty, it is especially important to reduce the number of contacts for everyone. If we wait another 5 days, the number of cases will increase threefold, even in the best scenario (Fig. 1B)! This also means three times as many serious cases that require medical attention, hospitals, intensive care and respiratory equipment. This would significantly increase the number of deaths! To save these lives, we must act now.

Our model is based on standard susceptible-infected-recovered (SIR) assumptions: every infected person “I” can infect a susceptible person “S” with rate λ. The infected persons “I” recover (“R”) with rate μ.We estimate these parameters from the past case numbers using Bayesian Markov-Chain Monte-Carlo importance sampling. Of course, one could think of extending to model, e.g. to investigate how local segregation, or even stricter isolation of people at risk and specific age groups impacts the future disease spread. Yet, the standard SIR model provides very valuable forecasts for the next month.

In general, to reduce the number of newly infected people, the goal is that every infected person infects less than one new person. Only then, the spread will diminish.
To save lives, and to reduce the number of people in need of intensive care, it is of particular importance to avoid that people with high risk of complications get infected.

Figure 1, A: We modeled three different future scenarios for the development of confirmed COVID-19 cases in Germany: unchanged spread, mild restriction of contacts, or strict restriction of contacts. B: We also analyzed how a delayed restriction impacts case numbers: Strict restrictions starting on day zero, or five days later can make a substatial difference in case numbers. A delay of five days in implementing restrictions has a major impact on the expected case numbers. Model assumptions: The forecasts are based on the SIR model. A, red: The infection rate is unaltered. A, orange: The infection rate (which scales as a function of the number of contacts per person) is cut in half. A, green: The infection rate is reduced to 1/10th. Shaded areas indicate the variability in the prediction (95 % confidence interval). This forecast was created using the data up to 2020/03/15. We chose that date, because first policy changes, like closing of kindergarden and schools, started on that date. We now can compare the predicted effect with the true future development. The code (python) implementing the model and the detailed methods are available on github. Model and code can easily be adapted to other regions.

Figures: MPRG Priesemann, Max Planck Institute for Dynamics and Self-Organization
Published in: Science