Vaccine inequity provides little benefit to HICs
Figure 2 presents the time series of the prevalence (the fraction of infectious individuals in the population at each time step) and the cumulative mortality rate (the fraction of the cumulative count of deceased individuals in the population at each time step) under different global vaccine allocation strategies. Countries are classified as HICs or LMICs. Specifically, HICs include all high-income countries defined by the World Bank, plus China and Russia, because of their capability for mass production of COVID-19 vaccines. Under equitable global vaccine allocation strategies, available vaccine supplies will be equally allocated to all countries on the basis of the prioritization criteria, regardless of their wealth. Four prioritization criteria are considered: the population size, prevalence, mortality rate, and incidence (please refer to the Methods for the details). In inequitable global vaccine allocation strategies, however, at least a portion χ of daily available vaccines are purchased by HICs, and the remaining vaccines are allocated to LMICs (for both, the prioritization criteria are adopted).
Fig. 2: Impacts of equitable and inequitable vaccine allocation strategies on epidemic dynamics. a–f, Time series of the prevalence (a–c) and the cumulative mortality rate (d–f) in HICs under different global vaccine allocation strategies. g–l, Time series of the prevalence (g–i) and the cumulative mortality rate (j–l) in LMICs under different global vaccine allocation strategies. Three prioritization criteria for allocation are adopted: the population size (left), prevalence (middle) and mortality rate (right). The dashed lines in each panel indicate the time when the pandemic ends if the corresponding prioritization criterion is adopted (time exceeding five years is not presented). The dashed line and the solid line referring to the same global vaccine allocation strategy are represented by the same colour. The transmissibility and severity of each strain and the vaccine efficacy against each strain are shown in Supplementary Fig. 2. Parameter values: M = 5, μ 1 = 5.6 × 10−3, θ = 0.2 and λ = 5 × 102 (λ is the decrease rate of the probability of emergence of new and more dangerous strains). Source data Full size image
We assume that (1) all current active cases are caused by strain 1 (calibrated by the epidemic data as of 15 June 2021), (2) the cumulative global vaccine supply will first increase exponentially until the maximum daily production capacity is reached in six months and then grow gradually at the maximum daily production capacity until the end of the pandemic, and (3) the cumulative global vaccine supply could fully vaccinate half of the world population in six months. Assumptions 2 and 3 are based on the prediction by Airfinity37, a health intelligence and analytics company. The results based on the prioritization criterion of incidence are similar to those based on prevalence and are shown in Supplementary Fig. 3.
We find that, in the first year, inequitable vaccine allocation strategies lead to a faster decline in incidence in HICs and a slower decline in LMICs, compared with the declines under equitable vaccine allocation strategies. The delay in vaccinations in LMICs not only leads to more infections in LMICs but also extends the duration of the pandemic globally. Under inequitable vaccine allocation strategies, we observe a rebound of cases in LMICs after the first year. Despite the short-term benefits, HICs are also vulnerable to reinfection, as the prevalence in HICs is shown to climb again in the subsequent waves (Supplementary Fig. 4). The onset of new waves of the disease in HICs is mainly caused by the higher probability of emerging new strains in LMICs. In the first four years, LMICs account for the majority of cases (Supplementary Fig. 5). Since each infection represents a chance of viral mutation, the probability of emerging new strains in LMICs is much higher than that in HICs. Importantly, a larger share of the global vaccine supply in inequitable allocation strategies (larger χ) results in little difference in mortality in HICs but results in a noticeable increase in LMICs. We observe similar results with various viral mutation parameters (Supplementary Figs. 6–14). Note that if an extremely transmissible strain evolves, vaccine inequity provides no benefits to HICs at all (for example, Supplementary Fig. 6).
Prioritization criteria for global vaccine allocation
We compare the impacts of four prioritization criteria for global vaccine allocation. Although the four criteria lead to similar pandemic durations under equitable vaccine allocation strategies, there is a slight increase in prevalence and mortality worldwide when countries with larger population sizes are prioritized (Supplementary Fig. 15). Similarly, under inequitable vaccine allocation strategies, prioritizing countries with larger population sizes leads to earlier onset of new waves. However, it is worth noting that in the scenarios where an extremely transmissible strain emerges (for example, M = 6 and θ = 0.26, where θ is the increase in transmissibility of each new strain, in Supplementary Fig. 16), prioritizing countries with larger population sizes can reduce the overall prevalence in the long run. There is a notable trade-off between protecting the infected countries first and building up immunity in the larger, more susceptible populations. Our results indicate that the transmissibility of the virus plays the key role here. In most cases, we should prioritize vaccination in countries with higher incidence, prevalence or mortality by trying to contain the virus within these countries; however, in the rare case where the new strain is extremely transmissible, vaccination should be prioritized in densely populated countries to prepare for the global outbreak of the new strain (Supplementary Figs. 15–17).
Vaccine inequity leads to the emergence of new strains
We further investigate the fractions of new cases resulting from different strains under equitable and inequitable vaccine allocation strategies (Fig. 3). As an example, we present the results based on the prioritization criterion of population size. We find that equitable vaccine allocation strategies substantially curb the spread of new strains. Due to viral mutations, new strains with higher transmissibility take over the world and are responsible for the majority of new cases in both HICs and LMICs. A slight increase in the incidence of the previous strains elevates the risk of outbreak of new strains. In addition, a larger share of the global vaccine supply for HICs (larger χ) results in earlier peaks for all emerged strains. Except for strain 1, the fraction of new cases produced by other strains in LMICs is much higher than that in HICs (Supplementary Figs. 18 and 19). These results further highlight that the short-term benefits to HICs under inequitable vaccine allocation are limited and come at the sacrifice of running a much higher risk of new strains’ outbreaks, eventually leading to unnecessary deaths in not only LMICs but also HICs. Note that, although equitable vaccine allocation strategies result in fewer infections and deaths globally, this may not always be the optimal decision for HICs. If the virus reaches its peak fitness sooner and stops mutating into more transmissible strains, HICs continue to benefit slightly more from vaccine inequity in the short term. However, the local epidemic cannot be fully ended due to continuous imported cases. This particular scenario is in line with a recent game-theoretical analysis9. However, we illustrate in the following that HICs can further improve their benefits by donating excess vaccines to LMICs when the local epidemic in HICs is under control.
Fig. 3: Emergence of new strains under equitable and inequitable vaccine allocation strategies. a–c, Area plots of the fraction of daily new cases produced by different strains. d–f, The ratio between the number of new cases produced by different strains and the world population. The plots are based on the equitable (left), inequitable and χ = 0.8 (middle), and inequitable and χ = 0.9 (right) vaccine allocation strategies. All results are based on the prioritization criterion of population size. The inset in d is a zoomed-in version of d. Parameter values: M = 5, μ 1 = 5.6 × 10−3, θ = 0.2 and λ = 5 × 102. Source data Full size image
Vaccine donation is a practical pathway to vaccine equity
We assume that an HIC adopts an allow-donation vaccine allocation strategy as follows: it will denote a certain portion (denoted by δ) of its vaccine supplies to international facilities, such as COVAX, as long as the prevalence in its population is less than a certain threshold (denoted by I thre ). These vaccines will be equitably allocated to all LMICs on the basis of the prioritization criteria. We explore different allow-donation vaccine allocation strategies (that is, different combinations of δ and I thre ) to examine their impact on epidemic dynamics in Fig. 4. Here we focus on the scenario where χ = 0.8 and countries with larger population sizes are prioritized for vaccination (the prioritization criterion currently adopted by COVAX). Countries benefiting from donations are those with a lower mortality through adopting the allow-donation vaccine allocation strategies.
Fig. 4: Impacts of different allow-donation vaccine allocation strategies on epidemic dynamics. a,c, Fraction of HICs (a) and LMICs (c) benefiting from donations. b,d, Average lives saved by vaccine donations as the share of the national population in HICs (r H , b) and LMICs (r L , d). Please refer to the Methods for the details of r H and r L . e, Fraction of HICs donating vaccines. f, Total number of donated vaccines. g,h, Prevalence in HICs (g) and LMICs (h) under different vaccine allocation strategies. The dashed lines indicate the time when the pandemic ends. Countries with larger population sizes are prioritized for vaccination. Parameter values: M = 5, μ 1 = 5.6 × 10−3, θ = 0.2 and λ = 5 × 102. Source data Full size image
Unsurprisingly, almost all LMICs benefit from vaccine donations regardless of when and how many vaccines are donated by HICs (Fig. 4c). More vaccines donated by HICs result in a larger reduction in the cumulative mortality in LMICs (Fig. 4d). The reduction in cumulative mortality in LMICs is more sensitive to the number of vaccines donated by HICs than to when HICs start donations. A small increase in vaccine donations results in a larger decrease in cumulative mortality in LMICs. Such decreases become significant only when the portion of vaccines denoted by HICs reaches a certain level (around 46%). For HICs, donating more vaccines brings higher benefits before a certain portion (80%) is reached (as shown in Fig. 4a,b). These results indicate that vaccine donations by HICs could protect both HICs and LMICs. It is in HICs’ rational self-interests to share vaccines with LMICs before vaccinating their entire population. The results with various viral mutation parameters (Supplementary Figs. 20–24) are consistent with those in Fig. 4.
Figure 4e–h illustrates the impacts of three representative allow-donation vaccine allocation strategies on epidemic dynamics. The values δ = 0.1 and I thre = 8 × 10−5 represent a scenario where HICs donate a small portion of vaccines to LMICs although the fraction of infected cases in their own countries is relatively high. The values δ = 0.9 and I thre = 2 × 10−5 represent a scenario where HICs donate a large portion of vaccines to LMICs only when the fraction of infected cases in their own countries is low. The values δ = 0.5 and I thre = 5 × 10−5 represent a scenario where HICs donate a moderate portion of vaccines to LMICs only when the fraction of infected cases in their own countries is relatively low. For the first year, the difference in the fraction of HICs donating vaccines is small under the three allow-donation vaccine allocation strategies (Fig. 4e). The difference in the count of vaccines donated to LMICs (Fig. 4f) is more obvious, which explains why the reduction in cumulative mortality in LMICs is more sensitive to the number of vaccines donated by HICs than to when HICs start donations. Among the three strategies, the one where δ = 0.5 and I thre = 5 × 10−5 leads to the best pandemic outcome, where the pandemic ends the earliest (only second to the fully equitable vaccine allocation strategy, which is hard to achieve). Compared with the scenario where δ = 0.9 and I thre = 2 × 10−5, the new wave that appears in HICs two years later has a much smaller size than that in the scenario where δ = 0.1 and I thre = 8 × 10−5. This indicates that HICs should donate a small portion of vaccines to LMICs even when the number of infected cases is high locally, rather than waiting for the local epidemic to be fully controlled.
Donating vaccines only to neighbours has limited effects
We further investigate the effects of vaccine donations if HICs donate vaccines to only their neighbouring LMICs (in the hope of reducing the risk of infected cases arriving from neighbouring LMICs) in Fig. 5. We consider three vaccine donation scenarios benefiting both HICs and LMICs based on the results in Fig. 4: δ = 0.46 and I thre = 8 × 10−5, δ = 0.6 and I thre = 6 × 10−5, and δ = 0.8 and I thre = 4 × 10−5. ‘Neighbours’ of a country are defined on the basis of the global mobility network derived from the real-world air traffic data from the Official Aviation Guide (https://www.oag.com/). A node represents a country or region. The existence of an edge between two countries or regions represents the existence of direct flights between them. We define four kinds of neighbours of a node: 1-hop, 2-hop, 3-hop and 4-hop neighbours. Here, k-hop neighbours of a target node refer to nodes that are at most k hops away from the target node38. Thus, 1-hop neighbours (generally called neighbouring countries) are countries that are reachable via direct flights; 4-hop neighbours contain all LMICs. Graphic illustrations of k-hop neighbours of a target country are provided in Fig. 5a–d. As Fig. 5h–j indicates, there is little difference in the cumulative mortality in LMICs under the 2-hop, 3-hop and 4-hop scenarios. However, if HICs donate vaccines to only their 1-hop (immediate) neighbours, there may be a noticeable increase in the cumulative mortality in LMICs (Fig. 5h). Although there is little difference in the cumulative mortality in HICs under different scenarios (Fig. 5e–g), donating vaccines to a larger proportion of LMICs rather than only neighbouring LMICs can lead to an earlier end of the pandemic.