key: cord-0725984-t25pi4u0
authors: Lin, Yi‐Fan; Li, Yuwei; Duan, Qibin; Lei, Hao; Tian, Dechao; Xiao, Shenglan; Jiang, Yawen; Sun, Caijun; Du, Xiangjun; Shu, Yuelong; Zou, Huachun
title: Vaccination strategy for preventing the spread of SARS‐CoV‐2 in the limited supply condition: A mathematical modeling study
date: 2022-05-04
journal: J Med Virol
DOI: 10.1002/jmv.27783
sha: 2600a7d391ff493ffd5e6db289f6550e3d913f20
doc_id: 725984
cord_uid: t25pi4u0

To mitigate SARS‐CoV‐2 transmission, vaccines have been urgently approved. With their limited availability, it is critical to distribute the vaccines reasonably. We simulated the SARS‐CoV‐2 transmission for 365 days over four intervention periods: free transmission, structural mitigation, personal mitigation, and vaccination. Sensitivity analyses were performed to obtain robust results. We further evaluated two proposed vaccination allocations, including one‐dose‐high‐coverage and two‐doses‐low‐coverage, when the supply was low. 33.35% (infection rate, 2.68 in 10 million people) and 40.54% (2.36) of confirmed cases could be avoided as the nonpharmaceutical interventions (NPIs) adherence rate rose from 50% to 70%. As the vaccination coverage reached 60% and 80%, the total infections could be reduced by 32.72% and 41.19%, compared to the number without vaccination. When the durations of immunity were 90 and 120 days, the infection rates were 2.67 and 2.38. As the asymptomatic infection rate rose from 30% to 50%, the infection rate increased 0.92 (SD, 0.16) times. Conditioned on 70% adherence rate, with the same amount of limited available vaccines, the 20% and 40% vaccination coverage of one‐dose‐high‐coverage, the infection rates were 2.70 and 2.35; corresponding to the two‐doses‐low‐coverage with 10% and 20% vaccination coverage, the infection rates were 3.22 and 2.92. Our results indicated as the duration of immunity prolonged, the second wave of SARS‐CoV‐2 would be delayed and the scale would be declined. On average, the total infections in two‐doses‐low‐coverage was 1.48 times (SD, 0.24) as high as that in one‐dose‐high‐coverage. It is crucial to encourage people in order to improve vaccination coverage and establish immune barriers. Particularly when the supply is limited, a wiser strategy to prevent SARS‐CoV‐2 is equally distributing doses to the same number of individuals. Besides vaccination, NPIs are equally critical to the prevention of widespread of SARS‐CoV‐2.

The outbreak of COVID-19 caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to an unprecedented public health and economic crisis worldwide since December 2019. 1 To mitigate the spread, a variety of nonpharmaceutical interventions (NPIs) have been implemented, including screening and isolation, travel restriction, remote schooling and work distancing. [2] [3] [4] Although these efforts are beneficial to control the spread in a short term, globally, as of March 4, 2022 , there have been 440 807 756 confirmed cases of COVID-19, including 5 978 096 deaths, reported by the World Health Organization (WHO). 5 Additionally, in many countries, relaxation of NPIs has led to a resurgence of the epidemic as herd immunity has not been reached thus far. 6 A long-term solution, such as vaccines that protect from SARS-CoV-2 infection, remains urgently needed.

The competition for developing vaccines against SARS-CoV-2 started in early 2020 and more than 50 companies began development of the first vaccine. 7 At present, 14 vaccines have been approved for urgent use, including 3 nucleic acid vaccines (Curevac, Moderna, and BioNTech), 3 inactivated virus vaccines (Bharat, Sinovac, and Sinopharm), and 8 viral-vectored vaccines (Clover Biopharmaceutical, Serum institute, Novavax, Sanofi, AstraZeneca, Janssen, Gamaleya, and CanSino). 8 As of March 5, 2022, a total of 10 704 043 684 vaccine doses have been administered globally. 5 The benefits of an effective vaccine for individuals and their communities have resulted in widespread demand, so it is critical that decision-making on vaccine distribution is well-motivated, particularly in the initial phases when vaccine availability is limited. 7, [9] [10] [11] As the basis of regulatory approvals, the initial vaccine was released in early 2021, there are two main suggested approaches to vaccine prioritization: (i) directly vaccinate those at highest risk for severe outcomes and (ii) protect them indirectly by vaccinating those who do the most transmitting. 12, 13 Model-based investigations of the trade-offs between these strategies have found that the optimal balance between direct and indirect protection depends on both vaccine efficacy and supply, recommending direct vaccination of older adults for low-efficacy vaccines and for high-efficacy but supply-limited vaccines. 14 Rather than comparing prioritization strategies, others have compared hypothetical vaccines, showing that even those with lower efficacy for direct protection may be more valuable if they also provide better indirect protection by blocking transmission. 14 Prioritization of transmission-blocking vaccines can also be dynamically updated on the basis of the current state of the epidemic, shifting prioritization to avoid decreasing marginal returns. 15 However, the strategies of prioritizing and optimizing doses complement are highly dependent on different vaccine efficacy (VE) and durability of immunity. An optimal resource allocation will largely reduce the transmission economically.

To evaluate the vaccine allocation strategies, we built an age and occupation stratified SEIRS (susceptible, exposed, infectious, recovered, and susceptible) model. Since age has been shown to be an important correlate of susceptibility, seroprevalence, severity, and mortality, this model includes an age-dependent contact matrix, susceptibility to infection, and infection fatality rate (IFR), allowing us to estimate the cumulative incidence of SARS-CoV-2 infections by means of forward simulations of disease dynamics. [16] [17] [18] [19] [20] [21] [22] [23] 2 | METHODS An individual-based dynamic model, stratified by age and occupation, was built to simulate the transmission of SARS-CoV-2 based on the epidemical progression of susceptible-exposed-infectious-removedsusceptible (SEIRS) structure. This model includes NPIs aimed at mitigating the epidemic.

In the model simulation, each healthy individual (susceptible) has a chance of being infected with SARS-CoV-2 under the force transmission rate depending on the number of daily contacts and the probability of SARS-CoV-2 being transmitted from an infected to uninfected contact. Once infected, the individual enters the exposed period. At the end of the exposure period, an individual will become infectious, either symptomatic or asymptomatic. Most infectious individuals recover but some will die (with IFR). We assumed that the recovered individual would be re-infected after waned immunity, including natural immunity. Each individual was assigned a social contact parameter (locationspecific contact matrices, including home community, school, workplace, and other) by their occupation. This study assumed an individual has no age-dependence in transmissibility, and the likelihood of viral exposure varied by individuals depending on the number of infectious people in their social network. We considered age-stratified contact matrices from the BBC pandemic project in describing the average daily effective number of contacts that an individual has with others. 24 Age-stratified IFRs were collected from a model-based analysis under New York City during the 2020 spring pandemic wave. 25 

Each modeled individual was ascribed demographic characteristics (e.g., age and occupation) and epidemiological characteristics (e.g., exposed period, infectious period, symptomatic or asymptomatic status, recovery or death from infection). We incorporated asymptomatic infections into this model, although it remains unclear as to the asymptomatic rate and the extent asymptomatic patients contribute to viral transmission. [26] [27] [28] [29] All the detailed information is presented in the supplementary materials.

Although existing studies have been focusing on the antibody responses to SARS-CoV-2, it is still vague in the natural and vaccine acquired immunity. 8, 30 Therefore, we considered 90 and 120 days of acquired immunity priority before getting susceptible again in our simulation. [31] [32] [33] The transmission was dependent upon the period of exposure, period of infectiousness, and basic reproductive number (R 0 ). [34] [35] [36] [37] We also incorporated an asymptomatic rate denoting the probability of an infected case being asymptomatic and assumed a reduced rate of infection for asymptomatic cases. 24, 26, 35, 36, 38 After the infectious period, an individual has the chance to recover or die. 34,39

In this model, we mimicked the transmission in four assumed periods.

The first period is the free transmission period, during which no NPIs are implemented. The second period is the structural mitigation period, during which structural NPIs including isolation and quarantine are implemented. In this period, the infected individuals are isolated until they recover or die, and their close contacts are quarantined for 14 days. The accuracy rate of screening (sensitivity) was considered in this modeling. 40, 41 The third period is the personal mitigation period, during which personal NPIs including social distancing, mask-wearing, and hand washing are in place. The individuals begin to change their protection behavior depending on the government policy adherence rate. The assumed efficacy of mask-wearing and hand washing is introduced into this model. 42 The final period is the vaccination period.

In our study, we introduced VEs into our simulation to predict the effect of the vaccine, which is associated with the NPIs adherence rate. 8 Risk compensation was considered in our model. When the coverage rates reach the target value (≥50%), the adherence of personal NPIs becomes 50% lower among vaccinated people. In this situation, the theoretical immunity is elicited after all recommended doses of the vaccine are injected. We proposed two scenarios of vaccine-allocation strategies (assumed two injections) based on the limited vaccine supply. Scenario 1 (one-dose-high-coverage): distributing the two doses to two people, each person with one dose (lower VE); Scenario 2 (two-doses-low-coverage): distributing the two doses to one person, each person with two doses (higher VE). Among these scenarios, we assumed time varied supplies, increased by 0.5% per day.

We simulated 100 million individual-level transmission events by repeatedly generating contact distributions for a primary case and randomly generating infections among these contacts. This process was repeated a thousand times, and each simulation was to generate a set of epidemic trends including (1) daily newly confirmed cases and (2) daily total cumulative confirmed cases. Our primary sensitivity analyses were to the level of vaccination coverage (60% and 80%), the adherence rate of NPIs (50% and 70%), and the asymptomatic rate (30% and 50%). We further assumed the (natural and vaccinated) immunity waned after 90 and 120 days. Furthermore, our model suggested that with the increase in the asymptomatic infection rate, the prevention and control of SARS-CoV-2 was becoming more and more unfavorable. As the asymptomatic infection rate rose from 30% to 50%, the infection rate increased from 1.73 (95% CI, 1.59-1.87) to 3.31 (95% CI, 3.14-3.47), which was 0.92 (SD, 0.16) times higher. However, no matter how high the asymptomatic rate was, higher NPIs adherence and higher vaccination coverage can always prevent more SARS-CoV-2 infections (Figure 2 ). According to our simulation, relying on a 30% asymptomatic rate, 70% NPIs adherence rate, 80% vaccination coverage, and 180 days of immunity, the infection rate remained at 1.42% (total confirmed cases, 142 243; 95% CI, 134 598-152 471), which reduced the infections most.

The epidemiological impacts of the different dosing scenarios on mitigating the SARS-CoV-2 spread, when the vaccine supply was limited, are shown in Figure 3 .

Assuming the adherence rate of NPIs was 70%, supposing the same amount of vaccines were available, under scenario 2 (completely vaccinated), relying on an immunity duration of 90 days, the IFR and infection rate were 0.74 (SD, 0.01%) and 3.38% (SD, 0.83%), whereas the values were 0.72% (SD, 0.01%) and 2.76% (SD, 0.90%) when immunity waning after 120 days.

Considering scenario 1 (partially vaccinated), when the duration of immunity was 90 days, the IFR and infection rate were 0.74% (SD, 0.01%) and 2.69% (SD, 1.16%), whereas the values were 0.72% (SD, 0.01%) and 2.37% (SD, 1.12%) when immunity waning after 120 days (Table 1) . 

In this modeling, the findings showed that the vaccines and NPIs substantially contributed to the SARS-CoV-2 transmission control.

With higher vaccination coverage and NPIs adherence rate, more infections can be avoided. Compared to no vaccination, the number of infections can be reduced by 40% or 26% if the vaccination coverage reached 80% or 60%). Furthermore, when the adherence rate increases from 50% to 70%, 28% of infected cases can be further saved. To acquire the theoretical vaccine immunity, all recommended vaccine doses should be injected. However, when the vaccine (assumed more than two injections) supply was limited, the partially vaccinated strategy was superior to the completely vaccinated since it helped to reduce the infections by 67.57%. Finally, the transmission 

The proportion of total infected cases among the population. The infection rate of SARS-CoV-2 among 16 (2 4 ) different hypotheses. The primary sensitivity analyses were on the level of vaccination coverage (60% and 80%), the adherence of NPIs (50% and 70%), the asymptomatic rate (30% and 50%), and the assumed (natural and vaccinated) waned immunity after 90 and 120 days. 44 The reason for the strong infectivity of SARS-CoV-2 variants is that it can escape the neutralizing antibodies produced by the immune system, and the more lethal variants could substantially decrease the net benefit of vaccination. [45] [46] [47] [48] [49] [50] [51] [52] Therefore, the current issues on whether a third dose of enhanced vaccine is needed and when to vaccinate it has also become a topic of public concern. 53-55 Moreover, how to cope with the evolution of the SARS-CoV-2 and develop a vaccine with a "broad-spectrum effect" in avoiding virus escape is an important problem that researchers need to urgently solve. 56, 57 The variants reduced the VE to varying degrees, but the vaccine is still protective. 58, 59 Whichever vaccine appears, rational allocation of resources is very important. The current vaccination modeling research is mainly focusing on two directions. First, to minimize the deaths, Bubar et al. 12 recommended older adults enjoy a vaccine priority due to its higher fatality rate. Second, to mitigate the spread, Yang et al. 13 suggested several essential workers could be prioritized for F I G U R E 3 Daily SARS-CoV-2 incidence rate among the population. Focusing on 70% NPIs adherence rate and considering the same amounts of limited vaccine supplies. The daily incidence rates with different asymptomatic rates and durations of immunity are represented as black and red curves, respectively. The panels in the left and right columns represent different scenarios. vaccination to maintain essential services in the early phase of a vaccination program due to its higher contacts. In our model, we

propose an interesting idea that when the vaccines are lacking in the early stage, to maximize the coverage, the total number of doses to be vaccinated should be equally distributed to the same amount of people even if it reduces the VE so that individuals can quickly establish an immune barrier.

All kinds of NPIs have been introduced in mitigating the transmission of SARS-CoV-2. The major NPIs, including isolation and quarantine, social distancing, mask, and hand washing, are recommended by WHO. 60 Isolating confirmed cases stops the offspring generating and effectively blocks the transmission of SARS-CoV-2, and the contact tracing helps to minimize the potential transmission from second cases. 61 Proper use and disposal of masks is also essential to avoid increasing risk of transmission. 68, 69 Our study also has several limitations. First, in this modeling, we did not consider the time-varied antibody responses and viral load dynamics. 70 [75] [76] [77] [78] [79] [80] In conclusion, although the world has taken many different NPIs (58000-31620005). All funding parties did not have any role in the design of the study or in the explanation of the data.

The authors declare no conflicts of interest.

The data that support the findings of this study are available from the corresponding open accessed websites.

Yawen Jiang http://orcid.org/0000-0002-0498-0662

Huachun Zou http://orcid.org/0000-0002-8161-7576

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