Who should be vaccinated first - An analysis
A simulation of the impact of different vaccination strategies on Corona pandemic lethality.
The question we ask ourselves
It is obvious that it is rather questionable to start with vaccination at the mayor’s office. However, the question of which strategy performs better or worse compared to others is more intriguing, although significantly more complex and difficult to answer. The following analysis presents a data-based evaluation of different strategies and is an approach to those current questions about the approach to date.
The basics of our models
In the sense of a clean calculation of possible trajectories, we reduce the number of people living in Austria (8.9 million) by those persons who were already infected with the coronavirus. Thus, we settle at about 8.5 million inhabitants of Austria (see assumptions).
To further build our models, based on one of the strategies defined in the next chapter, the vaccine doses(58K) available per week are divided. Subsequently, we simulate who has been infected with the Corona virus in one week. At this point, we do not venture a prediction about the evolution of the number of cases, so we make a blanket assumption of 1,500 new infections per day, or 10,500 new infections per week. This number of individuals is drawn at random from the population.
Skip to the conclusion
Different vaccination strategies have different efficacy, but with sometimes serious differences.
The simulation suggests that the current strategy performs well, but could be improved by prioritizing according to risk factors already in the first vaccination phase. It is difficult to give a definitive answer to the question of the best strategy, but based on the simulation, a prioritization by age, cardiovascular disease, and diabetes can be recommended, which performs best compared to the other strategies.
The impact of vaccination has a visible impact on the number of deaths from Covid-19 after only a few weeks. By early March, the number of people saved by vaccination already exceeds the number of deaths and has a significant impact on the pandemic, even though a conservative estimate of the number of vaccine doses available was used.
A mortality probability is calculated for the infected persons, depending on age, sex and existing risk factors, with vaccinated persons being assigned a mortality probability of 0. Subsequently, based on the mortality probability, it is simulated how many of the infected persons would have died in the respective week in connection with the virus (see Appendix). The simulator also calculates the number of deaths without vaccination, which allows an estimate of the efficiency of the strategy.
After one simulation run (one week), the infected individuals are removed from the data set and the process is repeated. Clearly, those vaccinated in week 1 remain vaccinated in week 2 and again have a probability of death of 0 in case of infection in week 2.
Possible vaccination strategies
In the following, we present the different vaccination strategies whose efficiency we put to the test here:
this simulation gives the number of deaths when no vaccination is available or available doses are not vaccinated.
the vaccine doses are randomly selected in the population Each person has the same probability of being vaccinated regardless of age, sex, and other factors. This strategy serves as a reference value for the results.
Austria’s vaccination strategy depends solely on age in the first quarter. The above risk factors are only included at later time points, so the simulation of this strategy prioritizes only by age. Within an age group, individuals are vaccinated in random order.
Prioritization by hypertension
Because hypertension is the most prevalent risk factor in the population, the effects of this strategy were tested grouping by this factor (and age) alone.
This more complex strategy incorporates multiple factors into prioritization. First, it sorts by known age groups; within age groups, individuals with cardiovascular disease If individuals also have diabetes, vaccination begins with these individuals. This strategy is obvious because it combines the obvious risk factor of age with the factors with the highest probability of death.
This strategy again uses multiple risk factors but does not include age. To test whether the three factors adequately represent age and thus represent an effective strategy.
This strategy again incorporates age, but not as the most important Individuals with hypertension are vaccinated first; only within this group are older individuals prioritized. Additionally, cancers are included.
The strategies can be divided into three different groups based on the graph.
The strategies with the highest number of casualties are those without vaccination, random vaccination, and prioritization purely by hypertension. If vaccinations are randomly distributed in the population, the number of deaths is only minimally reduced. Prioritization by blood pressure performs better than the other two strategies, but is far from optimal distribution and does not have the desired effect.
The strategy with three included risk factors, but without age, performs significantly better and shows above all a decrease in the number of deaths the more vaccine doses are available. Nevertheless, it can be seen that the inclusion of age results in a significant increase in efficiency.
The strategy that chooses age as a secondary prioritization factor performs slightly worse than the strategy that prioritizes only by age (state of Austria). This suggests that an optimal strategy should prioritize by age first. The Austrian state strategy was nevertheless beaten by the composite strategy by age, cardiovascular disease, and diabetes. According to this analysis, prioritization by age makes sense, but should be combined with evaluation of other factors.
Number of people rescued
Now we turn the perspective around. In this section, we take a closer look at the number of people saved. This is the difference between those who died without vaccination and those who died despite the vaccination schedule.
Diese Grafik ist das Spiegelbild der vorherigen Grafik. Klarerweise werden keine Personen gerettet, wenn niemand geimpft wird. Die zufällige Impfverteilung rettet im Laufe der Zeit eine geringe Anzahl an Personen. Die übrigen Strategien weisen in der Simulation bereits nach wenigen Wochen eine hohe Anzahl geretteter Personen auf. An dieser Stelle sei erwähnt, dass in der Grafik keineswegs kumulierte Werte der Geretteten visualisiert werden, sondern jeweils die in einer einzelnen Woche geretteten Personen. Diese Anzahl steigt unter allen Strategien von Woche zu Woche an.
Forecast of the further course for Austrian strategy
In this section, the strategy adopted for the state of Austria was extended and simulated for a longer period (52 weeks). The calculation does not include additional vaccine quotas that may be available in the future, but assumes the current number of vaccines per week. The following graph visualizes the number of people saved, as well as the number of people who died with or without vaccination.
This graph shows that already between the end of February and the beginning of March the number of people saved exceeds the number of people who actually died. The simulation indicates noticeable effects of vaccination from this point on. The number of new infections is again assumed to be constant from week to week at 1,500. Thus, the impact of potential policy measures taken (exit restrictions) or mutations that may be more contagious or dangerous to humans than originally assumed are not considered. Especially with regard to the available vaccine doses, the simulation is thus a very conservative estimate, which outputs encouraging findings.
Verschiedene Impfstrategien sind unterschiedlich wirkungsvoll, jedoch mit teils gravierenden Unterschieden.
Die durchgeführte Simulation legt den Schluss nahe, dass die derzeit verfolgte Strategie gut abschneidet, jedoch verbessert werden könnte, indem bereits in der ersten Impfphase ebenso nach Risikofaktoren gereiht werden würde. Eine endgültige Antwort auf die Frage nach der besten Strategie zu geben ist schwierig, jedoch kann basierend auf der Simulation eine Priorisierung nach Alter, Herz-Kreislauf-Erkrankungen und Diabetes empfohlen werden, welche im Vergleich zu den anderen Strategien am besten abschneidet.
Die Auswirkungen der Impfung haben bereits nach wenigen Wochen sichtbaren Einfluss auf die Anzahl der Todesfälle durch eine Erkrankung an Covid-19. Anfang März übersteigt die Anzahl der durch die Impfungen geretteten Personen bereits jene der Verstorbenen und hat damit deutlichen Einfluss auf den Pandemieverlauf und das obwohl von einer konservativen Schätzung der Anzahl der vorhandenen Impfdosen ausgegangen wurde.
General conditions and assumptions
- Based on the data from the Corona dashboard of AGES , a dataset was created with all people living in Austria, classified by gender and age group. This dataset comprises about 8.9 million entries (as of January 2020, people living in Austria).
- In addition to age, 5 risk factors leading to an increased probability of death in case of corona infection were included: Cardiovascular disease, diabetes, cancer, chronic respiratory disease, and hypertension. These factors were taken from 
- Using available data, the risk factors were distributed among the different age groups Where possible, the age distribution of the risk factors was addressed (e.g., the proportional incidence of cancer is significantly higher with age). In this way, a data set was created that should represent all persons living in Austria.  – 
- Each person is assigned a probability of death in case of infection based on their age and sex. These values are taken from the AGES-Corona dashboard. For those individuals who have been assigned one or more risk factors, the probability of death increases (calculation in the appendix).
- The simulated period is the first quarter of 2021 (12 weeks). Based on the vaccination dashboard data , approximately 1.4 million vaccine doses are scheduled for this period. Since each person must be vaccinated twice, we assume 700,000 available vaccinations, which are divided based on weekly deliveries of 58,000 per week. 
: AGES Covid19-Dashboard; https://covid19-dashboard.ages.at/dashboard_Tod.html (zuletzt abgerufen am 25.01.2021)
: Impfdashboard des Ministeriums für Soziales, Gesundheit, Pflege und Konsumentenschutz; https://info.gesundheitsministerium.at/ (zuletzt abgerufen am 25.01.2021)
: Case fatality rate of COVID-19 by preexisting health conditions by Our world in data; https://ourworldindata.org/mortality-risk-covid#case-fatality-rate-of-covid-19-by-preexisting-health-conditions (zuletzt abgerufen am 25.01.2021)
: Krebsdiagnosen im Lebensverlauf, Zentrum für Krebsregisterdaten; https://www.krebsdaten.de/Krebs/DE/Content/Publikationen/Kurzbeitraege/Archiv2018/2018_4_Thema_des_Monats_lebensverlauf.html (zuletzt abgerufen am 25.01.2021)
: Statistik Austria: Krebserkrankungen; http://www.statistik.at/web_de/statistiken/menschen_und_gesellschaft/gesundheit/krebserkrankungen/index.html (zuletzt abgerufen am 25.01.2021)
: Diabetes in Deutschland – Zahlen und Fakten, diabinfo; Diabetes in Deutschland – Zahlen und Fakten; https://www.diabinfo.de/zahlen-und-fakten.html (zuletzt abgerufen am 25.01.2021)
: Lebenszeitprävalenz von Asthma bronchiale in Deutschland nach Alter und Geschlecht im Jahr 2011; https://de.statista.com/statistik/daten/studie/260261/umfrage/lebenszeitpraevalenz-von-asthma-bronchiale-in-deutschland-nach-alter/ (zuletzt abgerufen am 25.01.2021)
: Bluthochdruck: Häufigkeit; BlutdruckDaten; https://www.blutdruckdaten.de/lexikon/bluthochdruck-haeufigkeit.html (zuletzt abgerufen am 25.01.2021)
: Dr. Michael Matlik: Prävalenz von Herz-Kreislauf-Erkrankungen in Deutschland; https://www.spitta-medizin.de/news/sport/sportmedizin/story/praevalenz-von-herz-kreislauf-erkrankungen-in-deutschland__239.html (zuletzt abgerufen am 25.01.2021)
: Worldometer Coronavirus; https://www.worldometers.info/coronavirus/country/austria/ (zuletzt abgerufen am 25.01.2021)
I. Calculation of mortality probability
All individuals in the dataset are assigned a probability of death in the event of coronavirus infection based on age group and sex. In the example of a man between 75 and 84 years of age, this is 13.7% according to . If this man also has other risk factors, the probability of death increases in percentage.
Example: The man also suffers from diabetes. The probability of death is then
0,137 * (1+ 0,073) =0.147
The value of 7.3% is taken from . If the man also suffers from cardiovascular disease, the probability of death in the simulation is calculated as follows:
0,137 * (1+0,073+0,105) = 0,161
Calculating the probability of death in this way is clearly an assumption. However, consistently plausible results of simulated mortality rates between 1.5 and 2% among infected individuals were obtained in this manner. This corresponds approximately to the mortality in Austria. (1.9% as of 01/25/21; ).
II. simulation of deceased persons
All infected persons are assigned a probability of death as previously described. A second probability is calculated, which differs from the first only in that it is reset to 0 for vaccinated individuals; for all other infected individuals, the two probabilities are identical.
A random number generator outputs a number between 0 and 1 for all infected individuals. This number is representative of the severity of the disease progression. If the random number is below the (first) calculated probability of death, the person is considered to have died. If the number is only below the first probability, but not below the second (i.e., person vaccinated), the person counts as deceased without vaccination, but not as deceased with vaccination. This person was “saved” by the vaccination.
If you are interested, we will be happy to provide the code behind the simulations. For questions, comments, and criticisms, we are available at firstname.lastname@example.org.