Epidemic explosion despite careful testing?

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little figures carefully handling a covid test bar
Photo: Marco Federmann / Pixabay.

Scientists at the Institute of Science and Technology Austria (IST Austria) and at the Center for Advancing Electronics Dresden (cfaed / Technische Universität Dresden) show that little differences in behavior decide between success and complete failure of epidemic control. In their study, the scientists were able to show that limits in testing and contact tracing are responsible for this sudden change in the epidemic outcome. Testing followed up by contact tracing is extremely efficient in slowing down epidemics, however once their limit is exceeded the epidemic accelerates resulting in a faster than exponential spread. The study was published in the journal Nature Communications.

Physicist Prof. Björn Hof at IST Austria, whose group specializes in fluids and turbulent flows, has unexpectedly gone deep into pandemic research with his team, and in collaboration with Prof. Marc Timme, Professor of Network Dynamics at cfaed / TU Dresden. When early last year Hof had to cancel his planned visit to Wuhan, China, due to the SARS-CoV-2 pandemic, his focus abruptly shifted to epidemic spreading. "My group normally investigates turbulent flows in pipes and channels," he explains. “Over the last 10 years we have shown that the onset of turbulence is described by statistical models that are equally used to describe forest fires and epidemics.” Given this experience, programming an epidemic model was a straightforward exercise for Burak Budanur, the group’s theorist and computational expert.

The epidemic curve does not flatten, it collapses

Standard epidemic models suggest that the level of mitigation has a continuous effect on the height of the epidemic peak. “The expectation is that the curve flattens in proportion to the level of social distancing”, says Davide Scarselli, main author of the paper. However, when he first simulated epidemics taking limits in testing and contact tracing into account, the picture was a very different one. The maximum of infected people initially decreased as expected but then suddenly collapsed to almost zero as the mitigation level reached a certain threshold. In one limit, approximately half of the people got infected during the epidemic. In the other one only three percent caught the disease. Surprisingly, it was impossible to obtain a result in between these two outcomes: Either there is an outbreak of considerable size, or there is almost none whatsoever.

"This also means that a small increase in infection parameters after a very weak propagation can suddenly lead to an explosion in case numbers once the testing capacities are exhausted," says Prof. Marc Timme. Timme, an expert on self-organizing nonlinear dynamics of networked systems, joined the team after it was initially unclear what influence the structure of the transmission networks might have.

Failure yields faster than exponential growth

Testing of known contacts (not testing per se) is one of the most powerful ways to slow down an epidemic. However, the number of cases that can be traced every day is limited and so is the number of tests that can be administered. As the researchers found out that exceeding these limits at one point during the epidemic has far-reaching consequences. “If this happens”, says Timme, “the disease begins to spread faster in the unchecked areas and this unavoidably causes a super-exponential increase in infections.” Already, exponential growth is immense. It means doubling infections every few days. Super-exponential though signifies that even the rate of doubling becomes faster and faster.

As long as this acceleration can be avoided, epidemic curves collapse to a comparably low case level. Interestingly, it matters relatively little whether contact tracing is protected by a small or a large safety margin. The numbers remain comparatively low. If on the other hand the limit is only surpassed by a single case the super-exponential growth causes the total case numbers to jump to a tenfold level.

Marginal differences and disproportionate effects

“Like most nations, Austria didn´t react early against the second wave. Once not all contacts could be traced anymore during last September, it wasn’t difficult to predict that case numbers would soon surge at a faster than exponential rate”, says Scarselli. While over the last year it has become apparent that an early and decisive response is essential when facing exponential growth, the team’s study shows that test limits make timing even more crucial.
More recently, the team has looked into optimal strategies, where lockdowns are used as a preventive tool rather than an emergency brake. A manuscript that outlines the optimal strategy, which minimizes both, the number of infected people and the required lockdown time, is currently in progress.


Discontinuous epidemic transition due to limited testing.
Autoren: Davide Scarselli, Nazmi Burak Budanur, Marc Timme & Björn Hof
Nature Communications, 2021
DOI: 10.1038/s41467-021-22725-9
Link: https://www.nature.com/articles/s41467-021-22725-9

Press inquiries:

IST Austria, Hof Group - Nonlinear Dynamics and Turbulence

Prof. Björn Hof
Phone: +43 2243 9000 5801
E-mail: bjoern.hof@ist.ac.at

TU Dresden, Center for Advancing Electronics Dresden:

Prof. Marc Timme, Chair of Network Dynamics
Phone: +49 351 463 43972
E-mail: marc.timme@tu-dresden.de

Matthias Hahndorf
Science Communications
Phone: +49 351 463 42847
E-mail: matthias.hahndorf@tu-dresden.de

About the Chair of Network Dynamics
The Chair of Network Dynamics headed by Prof. Marc Timme was created in 2017. The aim of this TU Dresden Strategic Professorship affiliated with both the former Cluster of Excellence “Center for Advancing Electronics Dresden” (cfaed) and the Institute for Theoretical Physics is to connect insights from Applied Mathematics and Theoretical Physics with applications in Biology and Engineering. It is the first chair of network dynamics of this cross-disciplinary kind in Central Europe. Since networks are almost everywhere around us the research team aims for a unifying understanding of the fundamental mechanisms underlying the collective dynamics of large, nonlinear interconnected systems by combining first principles theory with data-driven analysis and modelling. A substantial part of their work focuses on investigating emergent phenomena and developing conceptually new perspectives on complex systems as well as the theoretical computational tools necessary to understand these systems. This fundamental understanding forms the basis to predict, and eventually control, the dynamics of complex networked systems across disciplines.
More information: www.cfaed.tu-dresden.de/cfnd-about

About cfaed
cfaed is a research cluster at TU Dresden (TUD). As an interdisciplinary research center for perspectives of electronics it is located at the TUD as a central scientific unit, but also integrates nine non-university research institutions in Saxony as well as TU Chemnitz as cooperating institutes. With its vision, the cluster aims to shape the future of electronics and initiate revolutionary new applications, such as electronics that do not require boot time, are capable of THz imaging, or support complex biosensor technology. These innovations make conceivable performance improvements and applications that would not be possible with the continuation of today's silicon chip-based technology. In order to achieve its goals, cfaed combines the thirst for knowledge of the natural sciences with the innovative power of engineering.

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