COVID-19 vaccines offer hope to ending the COVID-19 pandemic while restoring social activities 1,2. However, for most countries in the world, only a limited supply of vaccines are available daily, at least at the initial stage 3,4. How to allocate the limited daily supply of COVID-19 vaccines to minimizing the impact of the epidemic? This question has been all over the news since the approval of the first COVID-19 vaccines.
With limited COVID-19 vaccines supplied daily, a competition arises between the vaccination campaign and the epidemic. On the one hand, the vaccination provides protection for people by building up the immunity to the viruses. On the other hand, the epidemic continues to grow, driven by vulnerable people who are not yet vaccinated. It is only the when the immunity accumulation ``runs’’ more fast than the epidemic that the targets of vaccination programs (e.g. reducing the number of infections, hospitalization and deaths) can be achieved. To speed up the immunity accumulation in the population, strategic allocation strategies of vaccines are needed.
Among all the possible allocation strategies, there must exist some allocation strategies that can achieve the minimal value of the program targets (e.g., minimizing the number of deaths). Therefore, using the optimization methods to find such allocation strategies is desirable. But solving such a problem could be difficult. The static optimization model, which allocates a constant proportion of vaccines into each age group over time, is much easier to solve. However, the static optimal allocation strategies for single objectives (e.g., minimizing the number of death) can sacrifice other untargeted objective (e.g., infections) substantially, possibly due to the failure to account for the evolving of the epidemiological situation.
Compared to the static optimization, the dynamic optimization allows the allocation decision updated daily, and therefore can account for changes in age-specific risks (e.g., of infection, hospitalization) over time. But solving the dynamic optimization model is more challenging, due to the large size of compartments and the nonlinearity of the disease transmission dynamics.
We explore a two-step optimization method, and importantly, use it to investigate how the dynamic optimal allocation of minimizing one objective (e.g., deaths) perform on the secondary objectives (e.g., infections), compared to the dynamic optimal allocation of directly minimizing the secondary objectives (e.g., infections)?
Calibrating the model with COVID-19 data in China, we show that the dynamic (time-varying) optimal prioritization strategies for single objectives could perform well on the secondary objectives. In other words, the time-varying optimal prioritization strategy of minimizing infections could also reduce the number of deaths, into values close to that under the optimal prioritization strategy of minimizing deaths directly. The results are highly practical relevant, supporting that the relevance of both direct protection and indirect protection5, vaccinating the groups at high risks directly and vaccinating the groups that have high transmissions but may not high risks, in defining the vaccination age groups.
In order to gauge the potential gain of implementing these optimal prioritizations strategies in practice, we further compare them with a uniform adaptable vaccination (the random mass vaccination), where vaccines are allocated proportionally to the (daily updated) size of the unvaccinated susceptible population of each age group. The benefits are large in many contexts and are stable across differential scenarios, e.g., the differential efficacy of COVID-19 vaccines.
Nevertheless, in some contexts, the random mass vaccinations could be comparable to the optimal prioritization strategies. One example is the setting with too low daily supplies, where even the optimization approaches cannot help too much because they “can‘t make bricks without straw”. Another example is the setting, on the other extreme, with very high daily supplies, where even the random mass vaccination can perform very well with adequate daily supplies!
The insights above are from the scenario where we fix the speed of the epidemic and vary across the daily supplies, or the speed of immunity accumulation process. We can also do this in the opposite way, namely, fixing the speed of immunity accumulation process and see how the benefits change with the speed of the epidemic. As expected, when the speed of the epidemic is very fast or very slow, the random mass vaccination could be comparable to the optimal prioritisation strategies.
Moreover, if the vaccination campaign runs earlier than the starting of epidemic (e.g., more than 60 days in China), the random mass vaccination could perform comparable to the optimal prioritization strategies. This is because these different strategies, albeit utilizing distinct priority orders, could have enough people at hight risks vaccinated before the epidemic onset. On the other extreme, if the vaccination campaign starts too late (e.g., more than 30 days in China), the random vaccination program can also achieve close values of objectives as the optimal prioritisation strategies.
We illustrate the changes of benefits in varying scenarios. You will find that the jujube kernel shapes with very thin heads and tails (like Figure 1 below) in our paper.
- Burgess, R. A. et al. The COVID-19 vaccines rush: participatory community engagement matters more than ever. The Lancet 397, 8–10 (2020).
- Gallagher, M. E. et al. Indirect benefits are a crucial consideration when evaluating SARS-CoV-2 vaccine candidates. Nature Medicine 27, 4–5 (2020).
- Coronavirus vaccines: expect delays Q1 global forecast 2021. https://img.lalr.co/cms/2021/01/28193636/report-q1-global-forecast-2021-1.pdf (2021).
- Wouters, O. J. et al. Challenges in ensuring global access to COVID-19 vaccines: production, affordability, allocation, and deployment. Lancet vol. 397 1023–1034 (2021).
- Lipsitch, M. & Dean, N. E. Understanding COVID-19 vaccine efficacy. Science 370, (2020).