Optimal vaccine allocation for COVID-19 in the Netherlands: A data-driven prioritization

Abstract

For the control of COVID-19, vaccination programmes provide a long-term solution. The amount of available vaccines is often limited, and thus it is crucial to determine the allocation strategy. While mathematical modelling approaches have been used to find an optimal distribution of vaccines, there is an excessively large number of possible allocation schemes to be simulated. Here, we propose an algorithm to find a near-optimal allocation scheme given an intervention objective such as minimization of new infections, hospitalizations, or deaths, where multiple vaccines are available. The proposed principle for allocating vaccines is to target subgroups with the largest reduction in the outcome of interest. We use an approximation method to reconstruct the age-specific transmission intensity (the next generation matrix), and express the expected impact of vaccinating each subgroup in terms of the observed incidence of infection and force of infection. The proposed approach is firstly evaluated with a simulated epidemic and then applied to the epidemiological data on COVID-19 in the Netherlands. Our results reveal how the optimal allocation depends on the objective of infection control. In the case of COVID-19, if we wish to minimize deaths, the optimal allocation strategy is not efficient for minimizing other outcomes, such as infections. In simulated epidemics, an allocation strategy optimized for an outcome outperforms other strategies such as the allocation from young to old, from old to young, and at random. Our simulations clarify that the current policy in the Netherlands (i.e., allocation from old to young) was concordant with the allocation scheme that minimizes deaths. The proposed method provides an optimal allocation scheme, given routine surveillance data that reflect ongoing transmissions. This approach to allocation is useful for providing plausible simulation scenarios for complex models, which give a more robust basis to determine intervention strategies.

Fig 1. Simulated epidemic and evaluation of the impact of vaccination by allocation strategy.

The epidemic is simulated by an age-structured SIR model. R₀ and generation time were set as 1.2 and 5 days, respectively. The population was stratified by 10-year age bin, and a contact matrix of the Netherlands in June 2020 was used for the simulation [32]. Panel (A) illustrates the total incidence of infection in the population, and age-specific incidences (B) and the force of infection (C) reflect heterogeneous contacts between age-groups. The impact of vaccination on the number of infections (D), hospitalizations (E), and deaths (F) was compared under five different strategies; no vaccination (red), allocation from old to young groups (yellow), young to old groups (purple), at random (blue), and optimized allocation (green). In panel (D), curves of the optimized allocation and the young-to-old allocation are overlapped. In panel (E) and (F), curves of the optimized allocation and the old-to-young allocation are overlapped. For simplicity, the vaccination coverage was set as 40%, and the effect of vaccines was in place at day 50 (from the initial time point of the simulation), resulting in the immediate depletion of susceptible and infected individuals on that day.

Fig 2. The order of vaccine allocation by age and by prioritization strategy for a stockpile that suffices to vaccinate 80% of the population.

From the top row, the objective is the minimization of infections, hospitalizations, and deaths respectively. From the left column, the proportion of vaccinated among age <20, 21–30, 31–40, 41–50, 51–60, 60+ are plotted over allocated vaccines. Note that the X-axis shows the percentage of allocated vaccines.

Fig 3. Performance of allocation schemes on different objectives for a stockpile that suffices to vaccinate 80% of the population.

The breakdown of the stock is Pfizer (46%), AstraZeneca (22%), Moderna (8%), and Janssen (24%). The Y-axis shows the percentage reduction in the number of infections (A), hospitalizations (B), and deaths (C), and the X-axis is the percentage of allocated vaccines. Red, light blue, and dark blue plots indicate the allocation strategies to minimize the number of infections, hospitalizations, and deaths respectively. The starting point of effective reproduction number (i.e., the reference point without any vaccination) was set as 1.2.