Consequences of COVID-19 Simulations

+++ updated evaluation on facebook, for example on the development of newly infected +++

Corona presents us all with great challenges. At the same time there are many questions: How can we defeat the virus? When can we relax the measures? How far can we relax them? Will face masks help? In answering these questions, it helps to have a fundamental understanding of the spread of the virus. To this end, simulations are presented and discussed here.Based on a publication of the Robert Koch Institute in Berlin, an Excel tool has been created that simulates the spread of the epidemic in Germany as described there. The model was extended to include age groups, so that age-dependent effects can also be described. In addition, time-dependent infectivity was taken into account.

The Excel tool (without macros) can be downloaded here. The simulation cannot exactly describe the COVID-19 epidemic, but resembles some major properties of the virus infection. The use and the results are explained in a video. Here is the link. There also exists a video with a short summary of the results. Here the PDF of the slides shown in the video are made available. You are welcome to test with the COVID-19-Simulator how the virus spreads and what consequences result.

Some results explained in the video are:

  • Reducing the spread only so far that the intensive care beds in hospitals are not overloaded always leads to a significant infection of society and many deaths. The same applies to the demand for some extension of the time span in which a doubling of infections takes place (mathematical note see end of page). Such a way of dealing with the epidemic is ethically unacceptable.
  • The goal can therefore only be a successive reduction of new infections, as this is the only way to limit the number of deaths. It is essential that the effective reproduction number remains as much below 1 as possible. Reproduction number is the number of people infected by an infected person with the measures taken to prevent the virus from spreading. The basic reproduction number R0 is the value without countermeasures, the effective reproduction number, which ultimately matters, is the corresponding value with the measures. An approximation for the reproduction number is the ratio of the number of new infections on one day between the current value and the one exactly one week ago.
  • The difference between merely slowing down the spread and actually reducing new infections is only a slight intensification of the countermeasures. It is therefore incomprehensible why we do not increase the countermeasures by this small amount in order to eradicate the virus in the medium term.
  • The effective reproduction number comprises the number of contacts of a person and the probability that the infection will be passed on during the contact. Both can and must be reduced in order to reduce the effective reproduction number to a maximum of 1 at first, in order to reduce the still high numbers of new infections as quickly as possible. The more we make an effort, the fewer deaths will occur and the faster we will have overcome the crisis.
  • The reproduction number is the average value over the entire society. Since such small differences in this value decide between success and failure, this means that each individual contribution to reduction is essential. So everyone must contribute to reducing the effective reproduction number to the maximum.
  • Only after a significant reduction of new infections can the countermeasures be reduced, while the effective reproduction number must still be kept below 1 by maintaining sufficient countermeasures. This phase must be maintained presumably for many months.
  • In order to keep the effective reproduction number low, it is also possible to use home-made masks. Studies show that even single-layer fabric masks retain quite large proportions of the viruses. An increase to 2 or 3 layers can further improve the effectiveness. More layers will presumably make no sense, because the amount of leakage airflow next to the nose, for example, will then be increased and thus the effectiveness will decrease again. This also means that fabric masks not only protect the others but also the wearer. The discussion about the 'safety' of masks is wrong. Not even professional FFP3 masks provide 100% safety. The masks also reduce the probability of infection for the wearer, which is often doubted at present. For the containment of the epidemic it is not at all decisive that each individual is 100% protected, but only that the probability of an infection in the whole society is reduced, because this is decisive for the effective reproduction number. Of course, wearing masks must not lead to a looser approach to other measures. The rules of distance, the so-called social distancing, must therefore be maintained. Professional masks should be reserved for hospitals.
  • The argument often heard in comments in the media that by wearing a simple masks one does not protect oneself but only the others shows the absurdity of some of the discussions, since if all would wear masks - along the identical arguments - nobody would get infected, which is apparently a significant benefit also for the wearers. 
  • As long as the effective reproductive number in a country remains well below 1, infected persons imported from other countries will only lead to a manageable increase in the number of deaths among their own population. In the vicinity of so-called hot spots or from particularly affected regions of the world, however, entry restrictions make sense in order to reduce the effective reproduction number locally. Depending on the situation, the restrictions can also consist of quarantine measures.
  • Since the lockdown will cost economic power, the renewable-energy transition to fight climate change will be more difficult, because we need economic power for the investments that are to be made. This can possibly be partly compensated for, if we learn to reassess the balance between individual freedoms, individual obligations and the consequences for society as a whole as a result of the COVID-19 pandemic. This way, we can understand that due to the threatening overall social consequences of individual decisions and actions, quite concrete individual obligations will result.

Finally: Stay informed and healthy!


Basic model:

Heiden, M., Buchholz, U.: Modellierung von Beispielszenarien der SARS-CoV-2-Epidemie 2020 in Deutschland.

Age-dependence of mortality:

The Epidemiological Characteristics of an Outbreak of 2019 Novel Coronavirus Diseases (COVID-19) - China, 2020. Zijian Feng et al., Chinese Center for Disease Control and Prevention, CCDC Weekly 2020, 2(8), 113-122.

Ruan: Likelihood of survival of coronavirus disease 2019. The Lances, Infectious Diseases, March 30, 2020.

Time-dependence of infectivity:

He, X. et al., 2020: Temporal dynamics in viral shedding and transmissibility of COVID-19.

Efficiency of face masks:

Davies, K.-A. Thompson, K. Giri, G. Kafatos, J. Walker, A. Bennett. Testing the Efficacy of Homemade Masks: Would They Protect in an Influenza Pandemic? Disaster Medicine and Public Health Preparedness, 7(4), August 2013, 413-418.

Further information on face masks, guidelines, practical studies:

Mathematical note on time for doubling the number of infected:

The number regarded in these considerations is the accumulated number of infected (A. Kekulé, Coronavirus - Wege aus dem Lockdown, Die Zeit, 26.03.2020). How wrong this argument is becomes obvious, if the case of a reproduction number of 1 is regarded, which is exactly the limit between exponential spreading of an epidemic and successful control of the propagation of the virus. For a reproduction number of 1 the daily number of infected is a constant, say 1000 as an example. Then the accumulated number of infected on successive days will be 1000, 2000, 3000, 4000, 5000, 6000, etc. The first time for doubling is between day 1 and 2, that is one day. The next doubling occurs between day 2 and 4, i.e. 2 days, the next between 4 and 8, i.e. 4 days. It is realized that without any principal change in the spreading of the virus the time for doubling the number of infected increases automatically. In addition, the doubling time can only be meaningfully applied if the epidemic spreads exponentially with unrestrained growth. As soon as countermeasures are taken, the sum of infected persons, which corresponds to the integral of newly infected persons, no longer provides a meaningful measure. Also, the doubling time does not work properly if the number of newly infected people decreases - which is actually the goal of the countermeasures. Thus this doubling time cannot be a good guideline for evaluating the spreading of the epidemic. It is especially much less meaningful than the reproduction number, which clearly characterizes the situation and allows to distinguish between exponential spreading (R > 1) and successful control of the virus (R < 1). The reproduction number can be approximated by evaluating the ratio of the number of new infections on one day between the current value and the one before a specified time. If the time span of this evaluation corresponds to the mean time for a generation of infection transmission, the serial interval, the reproduction number is found quite accurately in this way. For COVID-19, this time is of the order of one week, so that an evaluation between two data with one week's interval currently seems to be very useful. Evaluating these data with the goal to realize, if the counter measures work, a certain 'smearing out' across the transition has to be expected due to the wide distribution e.g. of incubation time and other variables.