Quantifying Covid19-Vaccine Location Strategies For Germany

Abstract

Background: Vaccines are an important tool to limit the health and economic damage of the Covid-19 pandemic. Several vaccine candidate already provided promising effectiveness data, but it is crucial for an effective vaccination campaign that people are willing and able to get vaccinated as soon as possible. Taking Germany as an example, we provide insights of using a mathematical approach for the planning and location of vaccination sites to optimally administer vaccines against Covid-19. Methods: We used mathematical programming for computing an optimal selection of vaccination sites out of a given set (i.e., university hospitals, health department related locations and general practices). Different patient-to-facility assignments and doctor-to-facility assignments and different constraints on the number of vaccinees per site or maximum travel time are used. Results: In order to minimize the barriers for people to get vaccinated, i.e., limit the one-way travel journey (airline distance) by around 35 km for 75% of the population (with a maximum of 70 km), around 80 well-positioned facilities can be enough. If only the 38 university hospitals are being used, the 75% distance increases to around 50 km (with a maximum of 145 km). Using all 400 health departments or all 56,000 general practices can decrease the journey length significantly, but comes at the price of more required staff and possibly wastage of only partially used vaccine containers. Conclusions: In the case of free assignments, the number of required physicians can in most scenarios be limited to 2 000, which is also the minimum with our assumptions. However, when travel distances for the patients are to be minimized, capacities of the facilities must be respected, or administrative assignments are prespecified, an increased number of physicians is unavoidable.

Vaccine Allocation and Distribution: A Review with a Focus on Quantitative Methodologies and Application to Equity, Hesitancy, and COVID-19 Pandemic

“…The model, which is based on a constraint satisfaction programming framework, can efficiently distribute the available vaccines adjusting different parameters (such as the distribution of population, total population, total number of available vaccines, the number and capacity of distribution centers). Leithaeuser et al [91] formulated a model to optimally select vaccination sites in Germany within a given set (such as university hospitals). The authors considered different patient-to-facility and doctor-to-facility assignments as well as various constraints connected to the number of vaccines per site or maximum travel.…”

Pharmacy-based immunization: a systematic review

“…These models might be easily adapted to PBI needs. Leithäuser et al ( 77 ) used mathematical modeling techniques to optimally select the locations of vaccination centers among a given set, and to assign patients to the centers. The objective consisted of minimizing patients' travel distance and the number of required facilities and physicians.…”

A decision support system for the optimal allocation and distribution of COVID-19 vaccines using analytic hierarchy process (AHP) and integer programming (IP) model

“…The second criteria, Density, refers to the population density of the community, or the number of residents residing in the community. Lastly, Distance is considered in the aim of providing convenience to the individuals who are to be vaccinated [33,34].…”