Mathematical modelling could reduce infection rates

Photo by Waldemar Brandt on UnsplashA quick scan of the cell phone display and the long-awaited entrance to a movie theater, a concert, a handball hall, or even a store that offers something other than groceries, medications, and other everyday necessities opens up. Is this what an important step on the long road out of the Covid 19 lockdown looks like?

Virologist Bernhard Fleckenstein of the University of Erlangen can very well imagine it: "An app on a cell phone shows the negative result of a Covid 19 antigen test from the same day, allowing entry," says the founding president of the Society for Virology, explaining a viable path out of the lockdown.

Even the third wave of the pandemic, carried by the B.1.1.7 variant first detected in the United Kingdom and already rolling in, could be broken in this way, says Kai Nagel of the Technical University of Berlin: "Used broadly, rapid tests should very much reduce infection numbers, according to our model calculations."

The mobility researcher and his team have been simulating the lives of 1.5 million people in Berlin on the computer since the beginning of the pandemic. Just like in the real city, these model figures rush to bus stops and subway stations, are on their way to work or to a concert by bike or in a car, sit alone or with others at home and in the classroom. If the researchers bring into this computer world, say, a model person infected with the "British" variant, they can observe how the virtual pathogen spreads and whether it displaces the previous virus types.

"This B.1.1.7 variant is considerably more infectious and should therefore prevail," says Bernhard Fleckenstein. "We are therefore in a dangerous situation." Kai Nagel's model calculations say much the same thing. In these simulations, the team led by the TUB researcher has infected model figures transmit the virus to other people with an assumed probability and adjusts this assumption to the Covid-19 data of the Robert Koch Institute (RKI) until the computer simulation of the recent past delivers almost the same infection and hospital numbers as the RKI actually reports. Then, at the end of February 2021, the models showed that, as early as the beginning of March, infections with the B.1.1.7 variant were first expected to catch up with those of the conventional viruses and overtake them soon thereafter. And the RKI promptly reported that in the last week of February, the British variant had accounted for 46 percent of infections, with a continuing strong upward trend.

Does this make relaxations completely counter-intuitive? What would happen if schools continue to open? Or are even other services possible in addition to hairdressers? If Kai Nagel simulates such slight openings, the infection curves would show a steep upward trend as early as mid-March. The third wave would then come with full force and would reach significantly higher values than the second wave in December 2020, both in terms of infected persons and patients admitted to hospitals.

Even if researchers maintain the measures in place until recently, with closed hair salons and garden centers without any relaxation in their simulations, a powerful third wave is developing. However, as temperatures rise starting in April, people are likely to move more and more activities outdoors. This would reduce the probability of transmission. In this case, the simulations suggest that third-wave infection numbers would remain a bit below December 2020 levels.

In addition, because many of the people who are particularly susceptible to Covid-19 are likely to have already been vaccinated in the spring, the number of patients in clinics should be much lower than in the winter second wave, according to the model.

In the models, the third wave flattens even more if measures were tightened further, reciprocal visits banned entirely, and workplaces largely paralyzed. But "such very harsh restrictions would have a small additional effect relative to their severity," explains Kai Nagel. An option, as the results of the meeting of prime ministers and the federal government on Wednesday also show, is not tightening at the moment anyway. Many people are longing for relaxation, schools should not close again, culture, gastronomy, tourism and retail need perspectives.

However, the model calculations show that this also exists with the highly infectious B.1.1.7. For this, it is necessary to know with some degree of certainty what contribution the various areas of our lives and the measures taken in each case to contain the pandemic have on the incidence of infection.

Researchers determine the development of an epidemic with the reproduction number R. If it is at one, a hundred infected people on average infect another hundred people and the epidemic stagnates. If the R value is above that, the number of infections rises faster and faster until the event gets out of control.

"According to our simulations, private households alone already contribute 0.5 're-infection points' to the R value for the British variant," Nagel says. That means that with an R of 1, about half of all infections happen there - which is almost impossible to change. This makes the other, more influenceable factors, which together otherwise bring the R far beyond 2, all the more important.

A big chunk here is the working environment, which contributes another 0.3 re-infection points to the R value in the British variant without protective measures. By contrast, if people work as much as possible in home offices or single-person offices - and consistently wear FFP-2 protective masks in areas where such single-person jobs are not possible - this contribution drops dramatically to 0.03 points. "So in multi-person offices, FFP2 masks should be worn, similar to what is already done in supermarkets," Nagel says. However, the models assume that the masks also provide good protection in practice - which a recent study by Stiftung Warentest does not necessarily confirm.

That leaves the quick tests. If all employees are tested before starting work, only 0.02 re-infection points should be added to the R-value. This would require 6.3 million rapid tests every week in Berlin alone.

If daycare centers, schools and universities run similarly to the way they did before the pandemic, the education sector contributes 0.3 points to the R-value according to the models. If students and teachers wear FFP2 masks during class and if alternate teaching is consistently enforced, this value drops below 0.01 points. A rapid test for all students and teachers before each day of instruction has a similar effect. This would require Berlin to provide 2.4 million tests each week.

Retailers contribute 0.1 reinfection points without protection requirements. Good and properly worn FFP2 masks reduce this value to less than 0.01. "Indoor catering is particularly problematic because, after all, no mask can be worn when eating and drinking, and people often speak relatively loudly there," Nagel explains. Normally, therefore, the contribution of restaurants, bistros, bars and the like is quite high. But even if only half as many guests are catered for as in pre-pandemic times, it still drops to 0.13. By contrast, things look considerably better for the catering trade in the outdoor area, which contributes 0.05 points to the R-value.

If, as now, a very infectious variant is rampant and a similar number of people ride buses and trains as before the pandemic, public transport also contributes about 0.2 points. If, on the other hand, the occupancy rate is as low as it is now and all passengers wear FFP2 masks, the value drops to 0.02. Museums and string concerts also contribute less than 0.01 points if visitors wear FFP2 masks. In contrast, the situation is unclear in theaters and at choral performances or wind orchestras - even with thinned-out attendance.

Another problem area from the point of view of infection control is the private sphere: according to the simulations, indoor celebrations alone without protective measures can contribute 0.25 points to the R-value, similarly visiting friends and relatives outside one's own household and other private meetings. In contrast, if everyone wears FFP2 masks even when visiting private homes, this contribution drops to 0.03. Rapid tests before each meeting even lower this value to 0.01.

"That's exactly how we've been doing it for a few weeks now," explains Bernhard Fleckenstein, who, as a doctor, can already buy such rapid tests at the pharmacy. During family visits, everyone is tested in advance and can then come together without worries if the result is negative. "Other visitors only come over our doorstep with an FFP2 mask." Following this - certainly idealized and hardly completely feasible - model, in the future every individual could protect the people they meet and, of course, themselves at home and during visits.

The situation is different in the public sector, however: "There we need a system with clear rules that must be defined by politicians," says Fleckenstein. For example, rapid tests could be carried out in pharmacies and private companies free of charge or for a personal contribution similar to the prescription fee for patients with health insurance. A certificate via app or printout could then enable entry into areas that were previously inaccessible in the lockdown, similar to a vaccination certificate, for example. If it works, the return to normality could begin step by step.



Photo by Waldemar Brandt on Unsplash

 


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