Fraunhofer ITWM vs. Corona: With Mathematics against the Crisis

Fraunhofer ITWM Optimizes Location Planning for Vaccination Centers

Press Release / December 09, 2020

A first vaccine against the SARS-Cov-2-virus is expected to be available soon. But many questions are still open: How many vaccine doses are available? Who should be vaccinated first? Where should people be vaccinated? How many doctors are needed for vaccination? Researchers of the Fraunhofer Institute for Industrial Mathematics ITWM have now examined the last two questions together with the Robert Koch Institute (RKI) and the Technical University of Kaiserslautern (TUK).

In their publication, they consider different location scenarios and evaluate among other things the number of doctors needed, the distance of the population to the vaccination centers and the number of locations.

Vaccine Readiness and Availability Essential

Vaccines are the tool to contain the spread of the SARS-CoV-2-virus in the longer term and thus limit the health and economic damage of the pandemic. Before the end of this year, the first vaccines with promising efficacy could be approved and administered soon. For a successful vaccination campaign, however, it is also crucial that everyone is ready to be vaccinated and can be vaccinated as quickly as possible.

Therefore, health authorities need to make preparations already to ensure that the available vaccine capacity is used optimally from the outset. The Standing Commission on Immunization (STIKO) has already issued guidelines as to which groups of people should be vaccinated first in view of scarce resources. »Our focus, however, is on the logistical decision where the vaccine is to be administered and how much medical personnel is needed at which location«, says Dr. Neele Leithäuser from the Fraunhofer ITWM, who is optimizing the location planning for vaccination centers together with her colleague Johanna Schneider.

Optimization Problem With Many Variables

When choosing possible vaccination centers, many aspects have to be considered, such as the cooling of vaccine doses, the availability of medical staff or the possibility of implementing necessary hygiene concepts. A further crucial factor is the necessary travel time of humans from their residence to the vaccination center, since according to a current COSMO study the vaccination readiness decreases clearly with rising travel time. Due to the various criteria, several location scenarios with different numbers of vaccination centers were discussed in the study by TUK, RKI and ITWM.

Johanna Schneider explains for Germany: »Vaccinations were examined with family doctors, in health authorities, in university hospitals and at freely selected locations. Our analysis methods can also be easily transferred to other location scenarios.«

Distribution of the Vaccination Centers — © Fraunhofer ITWM
Distribution of the vaccination centers, depending on the scenario; the communities are colored according to the distance to the corresponding vaccination center. The size of the markers for vaccination centers depends on the number of patients to be vaccinated. (a) Free allocation to practices: 2000 general practitioners, 2000 locations (b) Assignment to the responsible health authority: 2193 doctors, 375 locations (c) Assignment to the nearest university hospital: 2017 doctors, 38 locations (d) Free choice of location, allocation to the next location: 2000 physicians, 81 locations

Compromise Scenario Health Authorities

A vaccination at the family doctor, as it is usual with other vaccinations, would be the most comfortable solution for the vaccinated persons due to the very short travel time. In view of the expected scarcity of the vaccine, the vaccination prioritization of endangered groups of persons as well as the short shelf life of opened vaccination containers, such a scenario holds however the danger of waste. In addition, the necessary cooling infrastructure cannot be implemented in the practices depending on the requirements.

The very well-equipped university hospitals meet the technical requirements - however, there are only 38 university hospitals in Germany. This leads to a significantly longer travel time and thus to a reduced willingness to get vaccinated. In addition, the centralization of vaccination requires a mature hygiene concept, but the proposed vaccination prioritization is easier to adhere to.

A compromise scenario is the 400 health authorities, which could at least be equipped with less specialized cooling technology. The study also shows, however, that 81 well-positioned vaccination centers are sufficient to ensure that 75 percent of the population can be vaccinated within 35 km beeline.

RKI, TUK and ITWM Evaluate Together

Together with the RKI and the TU Kaiserslautern, the researchers at the ITWM have discussed various vaccination scenarios and mathematical models. For selected scenarios, optimal locations were identified at the TU Kaiserslautern using mathematical programming and different allocations of the population to the individual vaccination sites were calculated. Various criteria were taken into account in the optimization, such as the travel time of the vaccinated persons, the workload of the doctors or the capacity limits of the vaccination centers. The individual scenarios were analyzed in detail at the ITWM and presented in graphical and tabular form for further discussion in appropriate decision-making bodies. The figure shows an example of an analysis of the distance of vaccinated patients to vaccination centers for various scenarios.

Project HealthFaCT

The location planning is embedded in the HealthFaCT joint project funded by the Federal Ministry of Education and Research (BMBF), which aims to optimize outpatient medical care in rural areas. »In the main project phase, we developed a model for the location optimization of emergency doctors, which we have now adapted to the optimization of vaccination centers«, says Prof. Dr. Sven Krumke, Dean of the Department of Mathematics at the Technical University of Kaiserslautern.

Press Release

Fraunhofer ITWM vs. Corona: With Mathematics against the Crisis

Fraunhofer ITWM Optimizes Location Planning for Vaccination Centers

Vaccine Readiness and Availability Essential

Optimization Problem With Many Variables

Further Information

Compromise Scenario Health Authorities

RKI, TUK and ITWM Evaluate Together

Contact Press / Media

Dr. Neele Leithäuser

Contact Press / Media

M.Sc. Johanna Münch

Contact Press / Media

Ilka Blauth