Notations and definitions:
Throughout the paper we analyzed the data using different normalizations, notations and definitions. Table 1, defines all notations used.
Overall pattern of the virus spread in Israel
Between March 2020 and January 2021, Israel faced three COVID-19 waves with a significantly higher number of cases in the second and the third waves. During each wave, following an increase in the number of new cases, the government introduced a lockdown to reduce the number of cases. One week into the third lockdown, Israel initialized its vaccination campaign.
As shown in Fig. 1a-b, the pattern of normalized positive cases in each age group (\({\widehat{P}}_{age})\) was similar during most of the pandemic - until the start of vaccinations. Notably, once the first selected population at risk began receiving vaccinations, there was an increase in new cases among the unvaccinated population (transition phase, Fig. 1b). When 48% of the population was either vaccinated or known recovered, a significant decrease in new cases was observed across all age groups (community-immunity phase, Fig. 1b). Such a decrease in the number of new cases was not demonstrated following the second national lockdown, where the reopening of the economy resulted in an increase in the number of new cases (also reported by Rossman et al) [4]. We believe that this phenomenon is the beginning of the community-immunity phase, and will show in following graphs that the change between the two phases can be predicted and partially understood.
The transition phase
To better understand the transition phase, we conducted an in-depth analysis of the young population. We calculated the positive impact factor of the young population relative to the entire population (\({\text{I}\text{m}\text{p}\text{a}\text{c}\text{t}}_{p-tot}\)) and susceptible population (\({\text{I}\text{m}\text{p}\text{a}\text{c}\text{t}}_{p-sus}\) ) (Fig. 1c). Prior to the national vaccination campaign, (left of the dashed red line), \({\text{I}\text{m}\text{p}\text{a}\text{c}\text{t}}_{p-tot}\) was oscillating around 0.6, indicating that the young population’s positive ratio was 60% compared to its ratio in the total population. Once vaccinations started (right of the dashed red line), this ratio increased, reaching a maximum of 1.3, thus suggesting a “shift” in the disease – from the entire population to the unvaccinated people. This increase may be explained by normalizing the positive cases by the percentage of the susceptible population (\({\text{I}\text{m}\text{p}\text{a}\text{c}\text{t}}_{p-sus})\) rather than that of the whole population. Once normalizing by the susceptible population, the increase in the positive impact factor did not exist, indicating that the susceptible population is younger when vaccinating the older population.
The driver of community-immunity
To understand the effect of vaccinations on the spread of the disease and to examine the effect in different regions of Israel, representing different demographics, we examined the effect of vaccinations in 250 cities across Israel. After initially plotting the normalized number of cases (\(\widehat{p}\)) for all cities, we revealed a crucial effect for the median age of the city’s population in determining the accurate value of community-immunity (Fig. 2a): cities with a younger population presented a decrease in the number of new cases at an earlier percentage of immunized population with approximately 20% difference in the threshold among them. Interestingly, the entire country, which has a median age of 30.5 years, reached the same decrease in the number of new cases at 50% immunization (similar to Fig. 1a-b). This decrease was correlated with median age alone and not with the population sector (Modiin Ellit, an Ultra-orthodox Jewish city, and Ar’ara, an Israeli Arab city, reached the decrease at a similar percentage), or socio-economic level (Bat Yam, a city belonging to the lower socioeconomic rank compared to Qesariya, a city belonging to the upper socioeconomic rank).
In addition, we evaluated the mean values of normalized accumulated cases in over 50 cities (E(\(\widehat{{A}_{c}}\left)\right)\) to raise the statistical confidence and lower the probability of other confounders. In order to achieve a large range of median ages we first sorted all cities by their median age, then pulled 50 cities at a time from the list with a stride of five from young to old cities (e.g. 0-50, 5-55, 10-60 etc.). For each batch of 50 cities we calculated E(\(\widehat{{A}_{c}}\left)\right(t)\), \({E(N}_{imun}\left)\right(t)\) and the median of the cities median age. The results presented in Fig. 2b-c match our previous observation (Fig. 2a), that a plateau occurs at higher percentages of immunization as the median age of the cities’ population increases (i.e., cities with younger populations reached the plateau at 50% immunization while cities with older populations reached it at 70%).
The results for Israel are different from the common belief that 60-75% of the population must be immune for herd immunity to be achieved (based on a theoretical R0 of 2.5-3) [5, 6]. This percentage relies on the assumption that all individuals in the susceptible community have the same probability of spreading the virus. However, we show that this is not true for Israel and most likely for other countries. The real R0 for each individual is affected by a combination of demographic, social, epidemiological factors, as well as many other parameters. A careful estimation suggest that the Reff was likely hovering around 1, throughout the study period.
Understanding the exact contribution of each parameter is not possible; therefore, we chose to estimate the overall R0 for each individual based on their age.
To that end, we examined the distribution of new cases and COVID-19 related hospitalizations incidence for different age groups. As shown in Fig. 3a, the incidence of new cases (\({P}_{age\text{\%}})\) in ages 15-35 (blue shaded area) were higher than their proportion in the population (\({N}_{age\text{\%}})\), indicating that these ages are the spreading “engine” of the virus. However, the high number of cases in this age group was not reflected in elevated numbers of hospitalizations (\({H}_{age\text{\%}})\) which remained higher in elderly patients. To describe the ratio between the incidence of these parameters in each age group and the group’s proportion in the general population, we used the definitions hospitalization impact factor (\({\text{I}\text{m}\text{p}\text{a}\text{c}\text{t}}_{H-tot})\) and positive impact factor (\({\text{I}\text{m}\text{p}\text{a}\text{c}\text{t}}_{p-tot})\), respectively (Fig. 3b). The red shaded area shows that the ages over 60 experienced more hospitalizations despite having a low positive impact factor. The hospitalization impact factor is important for avoiding the overload of hospitals and the positive impact factor can describe the effect of vaccinations on the spread of the disease across different ages. The findings of this analysis highlight the differences between age groups in terms of their contribution to both the transmission of the disease, and their contribution to the hospitalizations.
Realizing that each age group contributes differently to the spread of the pandemic highlighted the need to treat each vaccinated person in each city as an individual rather than assuming that everyone is an equal contributor to reaching community-immunity. We therefore chose to multiply each vaccinated or recovered person by the positive impact factor relevant for their age group. We demonstrated this hypothesis by implementing this technique on the data in Fig. 2b-c.
Figure 2d-e shows that the different median ages collapse to almost the same value of 60% immunizations needed for community-immunity. These findings demonstrate that most differences among the various cities were caused by the positive impact factor of each vaccinated person, implying that the observed difference among cities is mainly due to their different age structure.
Vaccination policy
In order to better understand the effect of the vaccination campaigns and rate on the overall positive cases and hospitalizations we compared different vaccination policies in a simulated environment. The positive and hospitalization impact factor present two opposing forces when trying to evaluate the best vaccination policy. On the one hand, vaccinating the age groups with the highest positive impact factors will reach community-immunity faster, on the other hand, vaccinating based on the hospitalization factors will result in immediate relief for the hospitals' burden. We simulated the pandemic without government intervention using a stochastic implementation of an extended susceptible-exposed-infectious-removed (SEIR+) modeling framework11. We formulized Israel’s contact network in a graph where links in the graph are based on family cells, social gatherings and community connections. We compare five different vaccination rates with four vaccination policies: (1) young to old: Prioritizing the younger population, (2) old to young: Prioritizing older population, (3) triangle: vaccinating the population over 60, then the younger population (16 to 35), then the remaining population, (4) all ages: vaccinations are equally distributed between all ages. To avoid stochastic influence, we repeated this process ten times with different seeds, and present the mean and variance of the results.
The final accumulated cases (after reaching community-immunity) of the four different policies are presented in Fig. 4a. As expected, prioritizing age groups with high positive impact factors results in a lower number of accumulated cases regardless of vaccination rate. The effect however, seems to degrade from 50% for fast vaccination rates to 10% for slow vaccination campaign.
The hospitalization factor (Fig. 4b), on the other hand, is much less predictive, as vaccinations affect the non-vaccinated population and change the probability of hospitalizations in the population. Fig. 4b presents two interesting results; Firstly, it seems that not prioritizing any age group is in most cases the best policy for reducing hospitalizations. Secondly, when the number of vaccinations per day is low and there is a prioritization to the younger population this might result in more hospitalizations than not vaccinating at all (when the number of vaccinations per day is low). This surprising result can be due to the transition phase described above which creates a “shift” in the disease spreading– from the entire population to the unvaccinated population. In this case, prioritizing the young population shifts the spreading to the elderly, which are more likely to be hospitalized. Therefore, although the number of positive cases is reduced, the probability of each positive case being hospitalized increases as the susceptible population is older.
Our simulation shows that prioritization and vaccination rate have an immense effect on the overall hospitalizations and number of cases. In Fig. 4-b, we show a difference of almost 40% between vaccination policies which maintains regardless to the vaccination rate. Despite the common belief that vaccinating the older population first will lead to a successful campaign, our model shows for most vaccination rates, that vaccinating everyone at the same pace (all ages) will achieve the best outcome. This strategy seems to work better than all other methods since it reduces the spreading population (by vaccinating people from the younger community) on the one hand, while lowering the number of potential hospitalizations (by vaccinating the older population) on the other. We note that our simulation is based on Israel’s impact factors and the graph represents the Israeli population, but the simulation is general and can be adapted to other countries easily.