How a 2020 parameter turned our world upside down

A significant part of the COVID pandemic story is driven by one parameter in an epidemiological model. How can a single number dominate our lives in such a way, and how did and do we deal with this fact? A pandemic can be represented by, among other things, four different states and their transitions. At the beginning of the pandemic, most of the inhabitants of Switzerland are infectious (S), few are infected (I) or recovering after infection (R) or have died (D). The original SIR model was published in 1927. The model can be extended according to the Lego principle by adding further states such as new infections, vaccinations. These complex relationships are shown schematically in the figure.

Figure, left side: Simplified illustration of the balance equation of all states in a pandemic – S Susceptible, I Infected, R Recovered, D Death – and the transitions into the states. Right-hand side: Time course without state D. About 60% of the population is infected.

The parameter in the epidemiological model

This schematic sequence of a pandemic is expressed in equations. Each equation describes how one of the states changes over time. For us, this dynamic is relevant for the infectious S. Infectious people remain infectious or become infected through contact with infected people. The temporal change of S is equal – λ-I-S. If there are no infected persons, S does not change. If there are many infected, S decreases sharply, i.e. many infectious people become infected. The parameter λ, the effective contact rate, is the mysterious number mentioned. The contact rate is itself determined by the infectiousness of the virus and the frequency of contact between infectious persons and infected persons. If λ is large, it has the same influence on the infectious as many infected. Therefore, one goal in pandemic control is to keep this parameter small so that there is not an explosion of infected people. Measuring the average contact frequency of the Swiss population is a challenge that is not possible reliably without digital support. In addition to the parameter λ, which is central to controlling the pandemic, there are two other parameters in Figure 1. The ratio of the parameters λ and υ determines, for example in the SIR model, whether an epidemic will occur or not. How can we influence the dynamics of the infectious and infected so that the number of infected does not explode? On the one hand, this can be done through vaccination. This reduces the number of infectious people. On the other hand, our behaviour, such as hygiene measures, lockdown, compulsory home office, restrictions on private contacts, determines the contact rate. This controls λ. How was the parameter λ and the state S controlled in the pandemic?

Shock period

That COVID 19 could very likely have more in common with a pandemic like the Spanish flu than with SARS became clear to many Europeans with the pictures from Italy in February 2020. This unexpected situation posed several problems for policy-makers and institutions. Many decisions had to be made simultaneously in many areas without any empirical data. Since no precise data was available and thus the damage potential of the pandemic was unknown, all aspects of society were subordinated to the goal of containing the pandemic – down with the unknown parameter value λ by shock-like reduction of possible contacts. The shutdown was the result. Such decisions under uncertainty are determined by the courage, experience and wisdom of the decision-makers. The art here is not to become incapable of action in the simultaneously emerging flood of initial information, opinions and misinformation. This problem of being able to make evidence-based decisions accompanies the pandemic. Regardless of whether we know λand all the other epidemiological variables, the mathematical laws of pandemic dynamics set the pace for decisions: Decisions that are too late and weak always lead to a worsening of future conditions. In addition to a lack of medical knowledge, the digital foundations were also not available at this stage so that real-time data for parameter estimates and monitoring of the pandemic could be predicted. The lack of interoperability in the Swiss health system took its toll. For the rapid tests, for example, more than 2000 institutions have to provide data and more than 200 different IT systems have to be connected digitally. Could one have proceeded less resolutely and comprehensively? No, the epidemiological model could not be embedded in the overall context. American economists began to embed the epidemiological model in an economic model with the outbreak of the pandemic in January in order to better understand the connection between health and the economy. The best-known work by Eichenbaum, Rebelo and Trabandt was published as a preprint at the end of March 2020, when Switzerland was already in shutdown.[1]

Relaxation and second wave

After the shutdown, the situation eased. Knowledge about the virus increased steadily and construction sites in digitisation were remedied. Today, up-to-date figures on all kinds of health aspects are available on the FOPH website. Despite the maintenance of hygiene regulations, the compulsory use of masks and the introduction of contact tracing, Switzerland was hit by a second wave in late autumn, which exceeded the situation in spring. How is this possible? This is a consequence of the described model dynamics between infectious and infected persons. As long as there are enough contagious people and the parameter λ increases, there will always be outbreaks. The parameter λ can increase if a mutation is more contagious, as is the case with the British variant B117. In order to reduce the risks of mutations, the numbers of contagious cases must be kept as low as possible. The parameter λ can also increase if average contacts increase because behavioural rules are less well followed. Controlling the pandemic through behavioural constraints becomes increasingly difficult over time. The lack of perspective on a permanent opening phase wears down the population. For optimal control of the λ parameter to be possible in the long term in a liberal society, a credible perspective is needed. This must be implemented uniformly throughout Switzerland with a single strategy. If one does not want to live indefinitely in an alternation between shutdowns and openings, this is only possible with an inoculation.


Vaccination is the only measure that massively and rapidly reduces the number of people who can be infected. In the model, this is shown in the transfer function -λ-I-S from infectious to infected: Vaccination simultaneously reduces the parameter λ and S and thus infects fewer people. Therefore, rapid and unbureaucratic vaccination is the only strategy as long as no cure is available. If everyone is vaccinated in summer 2021, this means opening up to all vaccinated people, subject to hygiene measures, masks or rapid tests. Until everyone is vaccinated, the protection in the current third wave must be on the not yet vaccinated, and no longer on the risk groups. What are the prospects for the unvaccinated? The more people get vaccinated, the fewer restrictions on the non-vaccinated at home. Vaccination success has little to do with digitalisation. The different cantonal possibilities to register digitally, the embarrassment with the electronic vaccination card and the lack of clarity about the vaccination card are digitalisation issues. However, these are not decisive for the success of vaccination. What is important is to vaccinate quickly and unbureaucratically. The opening hours of the vaccination centres from 8 a.m. to 5 p.m. on weekdays are not a signal of perceived urgency. In the UK, the USA and Israel, vaccination is being carried out at full speed. The successes are already evident after one quarter. The handling of the AstraZeneca vaccine also shows the importance of decision-makers’ willingness to take risks for success. The data for approval of the vaccine was patchy. In this situation, the UK decided to vaccinate more than 20 million doses to date. After 79 cases of blood clots were reported with 19 deaths, two-thirds of them in younger women, the British decided to offer an alternative to those under 29. In Switzerland, the approval has been pending with Swissmedic for months, although the benefit-harm analysis is positive for AstraZeneca. For example, in the UK, the vaccine prevented 200 admissions to intensive care units for every 500,000 people aged 60-69. This was offset by the potential for serious harm from the vaccine. 2] This aspect of the risk assumption will have to play an essential role in the subsequent reappraisal of the pandemic.


  • 1] Martin S. Eichenbaum, Sergio Rebelo and Mathias Trabandt, The Macroeconomics of Epidemics, NBER Working Paper Series, 2021.
  • 2] Medicines and Healthcare products Regulatory Agency (MHRA) , March, 2021 and Wynton Center for Risk and Evidence Communication, March, 2021
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AUTHOR: Paolo Vanini

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