Abstract
Goal: Because a fast vaccination rollout against coronavirus disease 2019 (COVID-19) is critical to restore daily life and avoid virus mutations, it is tempting to have a relaxed vaccination-administration management system. However, a rigorous management system can support the enforcement of preventive measures, and in turn, reduce incidence and deaths. Here, we model a trustable and reliable management system based on blockchain for vaccine distribution by extending the Susceptible-Exposed-Infected-Recovery (SEIR) model. The model includes prevention measures such as mask-wearing, social distancing, vaccination rate, and vaccination efficiency. It also considers negative social behavior, such as violations of social distance and attempts of using illegitimate vaccination proofs. By evaluating the model, we show that the proposed system can reduce up to 2.5 million cases and half a million deaths in the most demanding scenarios.
Keywords: Blockchain, COVID-19, SARS-CoV-2, SEIR model, vaccination model, vaccination passport
I. Introduction
With the ongoing coronavirus disease 2019 (COVID-19) pandemic, the world has been waiting for vaccines against the disease to counter its negative health and economic impacts that have affected everyone. COVID-19 is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is highly contagious and has been fatal for millions of people [1]–[5]. COVID-19 is transmitted through droplets of nasal secretion and saliva that are expelled when a person coughs, heavily breaths, talks, or even normally breathes. Detection of saliva is difficult as multiple of its components may need to be detected. Therefore, face-covering is considered a pivotal prevention measure as it provides a high degree of protection to both the wearer and the surrounding people. However, it is not 100% protective. Therefore, there is hope that vaccinations will mitigate or even stop the spreading of this disease [6].
Recently, the rollout of COVID-19 vaccines, while exercising social distancing and wearing face masks, is giving hope to the global population of restoring normal life. As more of the world population is now getting vaccinated, the management of the rollout and verification of vaccination records require not only accurate bookkeeping but also ubiquitous and secure access while maintaining user privacy. Accurate and accessible vaccination records are critical to provide an effective vaccination rollout and to support the execution of preventive measures, such as social distancing [2], [7].
COVID-19 vaccines from different manufacturers are being administered to the world population [8]–[10] aiming to vaccinate people rapidly and thus to leverage restoring normalcy, minimize health and economic damage, and reduce virus mutation opportunity [11]. The speedy distribution has to be carefully managed to avoid suboptimal benefits. However, the desirable synchronization and coordination of electronic vaccination records may be difficult to achieve in such a large vaccine distribution as it requires compatibility and administrative agreements among vaccination sites and upper administrators. Furthermore, the lack of secure processes to record vaccination events may make it difficult to enforce prevention measures at the rollout time and in the future. Vaccine verification could help to quickly restore daily social activities and traveling, as it may allow us to identify the susceptible and the potential source of infection. This verification requires reliable vaccination records that are secure, private, and accessible.
Blockchain has been proposed as a technology that can satisfy the security and reliability of vaccination records [12]–[16]. Beyond the technological advantages, a management system leveraged by blockchain may encourage people to get vaccinated and ultimately reduce the number of COVID-19 cases and deaths. In such approach, electronic immunization records are tied to verifiable blockchain transactions. Despite many recent proposals of blockchain-based vaccination certification approaches to store verifiable vaccination records, their impact on limiting or stopping the incidence of COVID-19 is still unknown.
To address this issue, we model the incidence and vaccination rollout by extending two Susceptible-Exposed-Infected-Recovered (SEIR) models. The SEIR-Vaccination (SEIR-V) model includes a vaccinated compartment using a conventional vaccination rollout campaign, and the SEIR-Vaccination-Blockchain (SEIR-VB) model uses blockchain to perform vaccination verification. With SEIR-VB, a policy of social distancing can be encouraged by enabling vaccination verification as a passport to activities that may require reduced social distancing. This paper shows that blockchain not only facilitates the management of vaccinations but also decreases the incidence of COVID-19 cases and deaths as compared to a system without blockchain.
II. Materials and Methods
Developed as a secure ledger in digital cryptocurrencies [17], blockchain is an immutable distributed ledger technology that records verifiable transactional data [18]. Its immutability feature makes it applicable to a variety of healthcare systems [19]–[21]. A blockchain ledger consists of a cryptographically secured chain of chronologically ordered blocks of transactions. This ledger is distributed across multiple peers to ensure data availability and resiliency against failures and attacks [22].
Bansal et al. [14] proposed to use blockchain as a repository of test results and vaccination records as verifiable immunization certificates. Hasan et at. [16] proposed a blockchain-based solution to securely store digital medical passports with immunity certificates for COVID-19. Eisenstadt et al. [15] developed a prototype of a decentralized blockchain-based mobile application to store portable COVID-19 vaccination certificates. Such certificates may be used to verify the susceptibility of a person to contract COVID-19 and of being a source of infection.
Blockchain can also be used as a decentralized tracking information system. For example, Marbouh et at. [23] proposed a blockchain that leverages smart contracts to transparently and reliably consolidate statistical data on COVID-19 incidence. Nguyen et at. [24] presented a conceptual architecture that combines blockchain and artificial intelligence to monitor and track the COVID-19 outbreak in real-time.
Blockchain can find its main application in detecting events that actually occurred, such as a vaccination, vaccine production, or social distancing neglects. Tseng et al. [25] and Yong et al. [26] proposed a blockchain system to verify the legitimacy of drugs and vaccines, respectively. Blockchain has been also proposed to monitor the efficacy of administered vaccines and dosages and to detect possible secondary effects [24]. However, these works have not addressed the question that justifies its adoption during the COVID-19 vaccination rollout, as how helpful blockchain would be in such a campaign by preventing cases and deaths. We address this question in this paper through the following models.
A. Extended SEIR Models
The SEIR model is used to evaluate the spreading of an infectious disease over time [27]. It categorizes individuals of a population into different compartments. The susceptible compartment is the group of individuals without immunity to the infection. The exposed compartment is the group of individuals who have been in close contact with infected individuals, and the recovered compartment is the group of the individuals who have recovered from the disease and developed immunity.
The prevention measures that reduce the number of COVID-19 cases considered in the extended SEIR models are mask wearing and social distancing. Vaccination against COVID-19 is a measure considered in the model to reduce cases and to convert a susceptible individual into an immune individual. This conversion depends on the vaccine efficacy, the vaccination rate, and the time for individuals to develop immunity. The willingness of individuals to get vaccinated also affects the immunity rate. Particularly, the models consider symptomatic and asymptomatic COVID-19 infections. The models also consider individuals’ behaviors that affect the efficacy of these measures, such as neglecting social distancing and falsely claiming wellness and vaccination.
Both SEIR-V and SEIR-VB models are described by (1) to (7), which determine the daily number of individuals in the respective compartments. The daily rate of change in the number of susceptible individuals, given by (1), is the sum of unvaccinated individuals that get exposed to both symptomatic and asymptomatic infected individuals, based on the contagious rate (
); the susceptible individuals that get vaccinated based on both the vaccination rate (
), and the likelihood of vaccine willingness (
); and the vaccinated individuals that remain susceptible based on the vaccine efficacy (
). The contagious rate 
is defined as the ratio between the basic reproduction number (
), which is defined by the average number of secondary cases that an infected individual infects, and the infection period [28].
Table I describes the variables used in the models. 
and 
represent the susceptible and infected individuals in the SEIR-V (
=
) and SEIR-VB (
=
) models, respectively (8). The daily number of exposed individuals, given in (2), accounts for the newly exposed individuals; the exposed and unvaccinated individuals who may start to develop symptoms after the incubation period (
days); and the fraction of the total exposed individuals that are vaccinated and recover as determined by the vaccine efficacy. The daily number of infected individuals includes symptomatic and asymptomatic cases, and both having a similar viral load [29]. A case fatality rate (
) is defined as the ratio of the number of deaths to the total number of cases.
TABLE I. Parameters Used in the Evaluation of Cases and Deaths of the SEIR-V and SEIR-VB Models.
The daily number of infected symptomatic individuals in (3) accounts for the exposed and unvaccinated individuals who get COVID-19 symptoms with a probability of symptomatic infection 
; the cases that recover after the infection period of 
days; the asymptomatic individuals that develop COVID-19 symptoms with probability 
after 
days; and the critical cases that unfortunately become deaths after the critical infection period of 
days. The daily number of asymptomatic individuals in (4) accounts for the portion of exposed and unvaccinated individuals who become asymptomatic; the cases that develop infection; and the cases that remain asymptomatic and develop immunity with or without vaccination after 
days or 
days, respectively.
The daily number of recovered individuals, determined by (5), is the accumulated number of the recovered cases and the vaccinated individuals per day. A portion of the vaccinated individuals develop immunity. The portion is defined by the vaccine efficiency. The daily number of immune individuals in (6) is a function of both the recently vaccinated individuals and the vaccinated individuals that develop immunity. The daily number of deaths in (7) is the accumulated number of critical cases that result in deaths.
 |
Then, the 
and 
for the SEIR-V and SEIR-VB models are:
 |
The different compartments of the SEIR-V and SEIR-VB models follow the tree diagram shown in Fig. 1. False vaccination claims might occur with probability 
. Infected individuals are aware of infection with probability 
and may conceal the infection with probability 
. The percentage of the mask-wearing population and the protection efficacy of mask wearing are denoted by 
and 
, respectively.
Fig. 1.
Tree diagram of the factors that determine the highly susceptible, infected, and contagious individuals and the sequence of states of an individual used in the proposed SEIR extended models. The diagram shows the considered states in this paper.
Individuals with an active immunization proof (i.e., a proof showing the period that immunization is active) are allowed to socialize and participate in regular activities. Individuals without the proof may be allowed to socialize with restrictions with probability 
. Table I lists the notations used in this paper. 
and 
for an immunization system without blockchain are denoted as 
as in (9) and 
as in (10), and for a system with blockchain, as 
as in (11) and 
as in (12), respectively. See the code of these models in [30].
III. Results
The numerical evaluations of SEIR-V and SEIR-VB show the difference in the number of cases and deaths for a period of 120 days using parameters as reported in the literature (Table I also shows the default values). Both SEIR-V and SEIR-VB are applied to a population of 330 million individuals (e.g., USA population), as an example. As initial conditions, the population considers 2% infected cases [31], which includes symptomatic and asymptomatic cases, and the rest as susceptible. These models were developed during 2020 and 2021.
The evaluation considers the following parameters: A reproduction number of 2.5 [32]; a case fatality rate of 2/100 [33]; an average infection, incubation, and critical infection periods of 9, 5, and 19 days, respectively [34]–[37]; a probability of infection awareness of 2/100 [38]; a vaccine efficacy of 95% [39], [40]; the start of the vaccination rollout on day 1; a daily vaccination rate of 5/1000 [41]; a vaccine willingness of 80% [42], [43]; and an immunity period of 14 days after vaccination [44], [45].
The models assume that individuals with a vaccination proof socialize without restrictions, while those without a proof may socialize with a 10% restriction. Immunity may be claimed arbitrarily by any individual. Infected individuals may conceal the infection with 3/10 probability [46], and neglect prevention rules. The probability of asymptomatic infection is set to 6/10, from which 3/10 may become symptomatic after 14 days [47]–[49]. Both the daily and total reduced number of cases and deaths are analyzed considering different percentages of the population that wear masks. The mask-wearing efficacy is set to 80% [50], [51]. Table I shows the default parameters used in the evaluation of the SEIR-V and SEIR-VB models.
A. Reduced Cases and Deaths by Blockchain
Fig. 2 shows the reduced number of cases and deaths by using the blockchain management system. Fig. 2(a) shows the reduced prevalence of COVID-19 cases through enforcing prevention measures, such as managing access to places that require a reduced social distancing by verification of vaccination certificates. Fig. 2(b) shows the reduced total number of deaths. The figures show that during the first 20 days of the vaccination rollout, the blockchain management system would decrease the number of cases by more than 2.5 million with 50% of the population wearing masks and about 500,000 cases with 90% of the population wearing masks. Fig. 2(b) shows that the blockchain system can reduce the number of deaths by about 46,000 with 50% of the population wearing masks and about 4,200 deaths with 90% of the population wearing masks.
Fig. 2.
Reduced (a) prevalence; (b) cumulative reduced number of deaths; and total reduced number of deaths using a blockchain-based immunization system for a period of 120 days, as a function of (c) probability of infection awareness; (d) probability of concealing infection; (e) probability of unsafe socializing; (f) vaccine efficacy; and (g) daily vaccination rates. Prevalence and number of deaths are more effectively reduced as conditions worsens. It is in such cases that blockchain is more impactful.
B. Impact by People Behavior and Vaccine Features
We classify the variables into two groups: prevention measures that decrease the incidence, such as vaccination efficacy, vaccination rate, and social distancing, and negative social behavior that increases the incidence, such as infected individuals who are aware or unaware of their infections and unvaccinated individuals claiming being vaccinated, all ignoring social distancing.
Fig. 2(c) shows that the number of deaths decreases as individuals become aware of their infection and quarantine themselves. These results show that the adoption of blockchain could reduce more than 30,000 deaths for 70% of infection awareness with 50% of the population wearing masks. The difference in the number of deaths increases as the percentage of the wearing-mask population decreases because blockchain enables the detection of high-risk individuals as more individuals are exposed. The blockchain system may reduce about 3,000 deaths with 90% of the population wearing masks and 100% of infection awareness.
C. Impact of Individual's Behavior
Fig. 2(d) shows that the blockchain system may reduce about 27,000 deaths with 10% of the infected individuals concealing their infection and 50% of the population wearing masks. On the other hand, this system may decrease about 3,000 deaths with 90% of the population wearing masks. The blockchain system also shows benefits against false vaccination claims. Fig. 2(e) shows that the blockchain system may reduce about 70,000 deaths for a 90% false vaccination claim rate with 50% of the population wearing masks and about 6,700 deaths with 90% of the population wearing masks. Its smallest impact is a reduction of about 2,700 deaths for a 10% rate of false vaccination claims with 90% of the population wearing masks.
The blockchain management system also reduces the number of cases and deaths when individuals neglect social distancing. It reduces about 60,000 deaths when each individual practices unsafe social distancing with 50% of the population wearing masks, as shown in Fig. 2(f). The smallest impact can be seen by a reduction of about 5,000 deaths with 90% of the population wearing masks.
D. Impact of Vaccine Features
Fig. 2(g) shows that a 100% effective vaccine alone would be insufficient to avoid as many deaths as the combination of vaccination, mask wearing, and social distancing would. The blockchain system combined with a 100% effective vaccine would reduce more than 40,000 deaths with 50% of the population wearing masks and about 4,000 deaths with 90% of the population wearing masks. A lower efficacy vaccine may increase the number of deaths and that may increase the role importance of the blockchain system.
Fig. 2(h) shows that at a daily vaccination rate of 1% of the population, the blockchain system would reduce 3,700 and 35,000 deaths with 90 and 50% of the population wearing masks, respectively. Table II shows that the blockchain system can reduce the number of cases as the contagion level increases. For example, the proposed system may reduce 15 and 47 million cases under no social distancing but with 50% of the population wearing masks and a low vaccination rate of 0.1%, for virus reproduction numbers of 2.5 and 3.5, respectively. Also, the blockchain system could reduce 1.3 and 1.9 million cases for a high vaccination rate of 0.5%, with 50% of the population wearing masks, and individuals socializing with 90% restrictions with reproduction numbers of 2.5 and 3.5, respectively.
TABLE II. Cases and Deaths for Different Virus Reproduction Numbers, Probability of Unsafe Socializing, and Vaccination Rates. Cases and Deaths Can Be Decreased by Using Both Blockchain and Prevention Measures Despite Large Reproduction Numbers.
Basic Reproduction Number ( )
|
Probability of unsafe Socializing ( )
|
(Reduced number of cases, Reduced number of deaths) in thousands | |||||
Daily Vaccination Rate ( ) (%)
| |||||||
| Low (0.10) | High (0.50) | ||||||
Percentage of the Population Wearing Masks ( ) (%)
| |||||||
| Low (10) | Medium (50) | High (90) | Low (10) | Medium (50) | High (90) | ||
| 2.5 | 0.10 | (4549.04, | (1392.31, | (258.99, | (3904.62, | (1256.25, | (238.22, |
| 24.82) | 7.68) | 1.43) | 21.15) | 6.85) | 1.30) | ||
| 0.50 | (28 327.80, | (3851.26, | (524.70, | (19 614.47, | (3288.74, | (478.83, | |
| 142.88) | 20.99) | 2.90) | 101.49) | 17.81) | 2.61) | ||
| 1.00 | (204 776.90, | (15 566.14, | (963.47, | (149 254.40, | (11 295.44, | (863.80, | |
| 1028.72) | 80.30) | 5.31) | 742.90) | 59.25) | 4.71) | ||
| 3.0 | 0.10 | (6245.50, | (1745.62, | (313.37, | (5235.33, | (1565.76, | (287.97, |
| 33.85) | 9.61) | 1.73) | 28.26) | 8.53) | 1.57) | ||
| 0.50 | (52 525.99, | (5330.80, | (644.18, | (34 066.27, | (4443.70, | (586.27, | |
| 256.35) | 28.87) | 3.56) | 172.10) | 23.97) | 3.20) | ||
| 1.00 | (243 863.00, | (27 648.09, | (1221.79, | (199 461.10, | (18 734.58, | (1087.45, | |
| 1284.53) | 138.31) | 6.72) | 1029.78) | 96.38) | 5.92) | ||
| 3.5 | 0.10 | (8431.48, | (2131.15, | (368.64, | (6877.79, | (1899.43, | (338.44, |
| 45.32) | 11.72) | 2.04) | 36.96) | 10.34) | 1.85) | ||
| 0.50 | (89 492.53, | (7247.59, | (769.17, | (56 559.08, | (5878.57, | (698.05, | |
| 428.90) | 38.92) | 4.24) | 280.07) | 31.57) | 3.81)) | ||
| 1.00 | (255 965.10, | (47 324.80, | (1508.76, | (225 759.70, | (30 368.07, | (1332.48, | |
| 1389.28) | 230.20) | 8.29) | 1197.98) | 153.03) | 7.25) | ||
With the vaccination rollout, the number of individuals wearing masks may decrease but that could increase the number of cases and deaths. Table II shows that with a low daily vaccination rate of 0.1%, with 50% of the population wearing masks and no individuals keeping social distance, the system could reduce more than 80,000 deaths for a (virus) reproduction number of 2.5 and more than 230,000 deaths for a reproduction number of 3.5. On the other hand, at a daily vaccination rate of 0.5%, 90% of the population wearing masks, and individuals socializing with 90% restrictions, the system could still reduce 1,300 and 1,850 deaths for reproduction numbers of 2.5 and 3.5, respectively. Even though these numbers of deaths are small in comparison with the initial population, decreasing incidence and mortality is deemed significant.
IV. Discussion
Modeling and forecasting the incidence of infectious diseases such a COVID-19 is challenging because of the dynamics of the many involved parameters [52]. The parameters used in our evaluations are time invariant. However, as more people become vaccinated, mask wearing rates may decrease and evaluations of such scenario would be needed.
Using blockchain to track vaccinated individuals would support the enforcing of prevention measures. These evaluations consider a uniform enforcement of preventive rules across the whole population in the SEIR-VB model, but non-uniformity may be more realistic in a country and that may need to be considered. Enforcing the prevention measures in the world has been challenging. Therefore, the use of blockchain may face some resistance and a flexible approach may need to be developed. Also, the current rollout may target fast vaccination of the population to provide a fast health and economic relief. Such a case may include variable vaccination rates that may need to be analyzed in similar performance terms as done in this paper.
V. Conclusion
Blockchain provides a means to reliably record vaccinations and issues time-dependent certificates that can be used to enforce vaccination verification in a pandemic. We modeled and evaluated a vaccine distribution management system that reliably verifies whether an individual is vaccinated so that such individual can be allowed to participate in social activities of normal daily life, including reduced social distancing, traveling, or group gatherings.
The performance of the proposed blockchain system was evaluated by the reduced number of cases and deaths between the blockchain management system and a conventional system that uses no blockchain. The results indicate that the adoption of blockchain as an immunization control system could reduce the number of cases and deaths, as an important effect of performing preventive measures.
Contributor Information
Jorge Medina, Email: jmc237@njit.edu.
Roberto Cessa-Rojas, Email: rojas@njit.edu.
Vatcharapan Umpaichitra, Email: Vatcharapan.Umpaichitra@downstate.edu.
References
- [1].Velavan T. P. and Meyer C. G., “The COVID-19 epidemic,” Trop. Med. Int. Health, vol. 25, no. 3, p. 278, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [2].Wu D., Wu T., Liu Q., and Yang Z., “The SARS-CoV-2 outbreak: What we know,” Int. J. Infect. Dis., vol. 94, pp. 44–48, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [3].Pedersen S. F. et al. “SARS-CoV-2: A storm is raging,” J. Clin. Investigation, vol. 130, no. 5, pp. 2202–2205, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [4].Fathi-Kazerooni S., Rojas-Cessa R., Dong Z., and Umpaichitra V., “Time series analysis and correlation of subway turnstile usage and Covid-19 prevalence in New York city,” 2020, arXiv:2008.08156. [DOI] [PMC free article] [PubMed]
- [5].Fathi-Kazerooni S., Rojas-Cessa R., Dong Z., and Umpaichitra V., “Correlation of subway turnstile entries and Covid-19 incidence and deaths in New York city,” Infect. Dis. Model., vol. 6, pp. 183–194, 2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [6].Piraveenan M. et al. “Optimal governance and implementation of vaccination programs to contain the Covid-19 pandemic,” 2020, arXiv:2011.06455. [DOI] [PMC free article] [PubMed]
- [7].Krueger T. et al. “Risk of Covid-19 epidemic resurgence with the introduction of vaccination passes,” medRxiv. The Preprint Server for Health Sciences, 2021. [Google Scholar]
- [8].Vaccines J., “A randomized, double-blind, placebo-controlled phase 3 study to assess the efficacy and safety of Ad26.COV2.S for the prevention of SARS-CoV-2-Mediated COVID-19 in adults aged 18 years and older,” 2020. [Google Scholar]
- [9].Burki T. K., “The Russian vaccine for COVID-19,” Lancet Respir. Med., vol. 8, no. 11, pp. e85–e86, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [10].Knoll M. D. and Wonodi C., “Oxford-AstraZeneca COVID-19 vaccine efficacy,” Lancet, vol. 397, no. 10269, pp. 72–74, 2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [11].Priesemann V. et al. “An action plan for pan-European defence against new SARS-CoV-2 variants,” Lancet, vol. 397, no. 10273, pp. 469–470, 2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [12].McGhin T., Choo K.-K. R., Liu C. Z., and He D., “Blockchain in healthcare applications: Research challenges and opportunities,” J. Netw. Comput. Appl., vol. 135, pp. 62–75, 2019. [Google Scholar]
- [13].Ahmad R. W., Salah K., Jayaraman R., Yaqoob I., Ellahham S., and Omar M., “Blockchain and COVID-19 pandemic: Applications and challenges,” IEEE TechRxiv, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [14].Bansal A., Garg C., and Padappayil R. P., “Optimizing the implementation of COVID-19 ‘immunity certificates’ using blockchain,” J. Med. Syst., vol. 44, no. 9, pp. 1–2, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [15].Eisenstadt M., Ramachandran M., Chowdhury N., Third A., and Domingue J., “COVID-19 antibody test/vaccination certification: There's an app for that,” IEEE Open J. Eng. Med. Biol., vol. 1, pp. 148–155, 2020, doi: 10.1109/OJEMB.2020.2999214. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [16].Hasan H. R. et al. , “Blockchain-based solution for COVID-19 digital medical passports and immunity certificates,” IEEE Access, vol. 8, pp. 222093–222108, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [17].Nakamoto S., “Bitcoin: A peer-to-peer electronic cash system,” Manubot, Tech. Rep., 2019.
- [18].Crosby M. et al. “Blockchain technology: Beyond Bitcoin,” Appl. Innov., vol. 2, no. 6–10, p. 71, 2016. [Google Scholar]
- [19].Angraal S., Krumholz H. M., and Schulz W. L., “Blockchain technology: Applications in health care,” Circulation: Cardiovasc. Qual. Outcomes, vol. 10, no. 9, 2017, Art. no. e003800. [DOI] [PubMed] [Google Scholar]
- [20].Engelhardt M. A., “Hitching healthcare to the chain: An introduction to blockchain technology in the healthcare sector,” Technol. Innov. Manage. Rev., vol. 7, no. 10, 2017. [Google Scholar]
- [21].Linn L. A. and Koo M. B., “Blockchain for health data and its potential use in health IT and health care related research,” in Proc. ONC/NIST Use Blockchain Healthcare Res. Workshop, Gaithersburg, MD, USA: ONC/NIST, 2016, pp. 1–10. [Google Scholar]
- [22].Wang S., Ouyang L., Yuan Y., Ni X., Han X., and Wang F., “Blockchain-enabled smart contracts: Architecture, applications, and future trends,” IEEE Trans. Syst., Man, Cybern. Syst., vol. 49, no. 11, pp. 2266–2277, Nov. 2019. [Google Scholar]
- [23].Marbouh D. et al. , “Blockchain for COVID-19: Review, opportunities, and a trusted tracking system,” Arabian J. Sci. Eng., pp. 1–17, 2020. [DOI] [PMC free article] [PubMed]
- [24].Nguyen D., Ding M., Pathirana P. N., and Seneviratne A., “Blockchain and AI-based solutions to combat coronavirus (COVID-19)-like epidemics: A survey,” 2020, arXiv:2106.14631. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [25].J.-H. Tseng, Y.-C. Liao, Chong B., and S. W. Liao, “Governance on the drug supply chain via gcoin blockchain,” Int. J. Environ. Res. Public Health, vol. 15, no. 6, 2018, Art. no. 1055. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [26].Yong B., Shen J., Liu X., Li F., Chen H., and Zhou Q., “An intelligent blockchain-based system for safe vaccine supply and supervision,” Int. J. Inf. Manage., vol. 52, 2020, Art. no. 102024. [Google Scholar]
- [27].Li M. Y. and Muldowney J. S., “Global stability for the seir model in epidemiology,” Math. Biosci., vol. 125, no. 2, pp. 155–164, 1995. [DOI] [PubMed] [Google Scholar]
- [28].Delamater P. L., Street E. J., Leslie T. F., Yang Y. T., and Jacobsen K. H., “Complexity of the basic reproduction number (R0),” Emerg. Infect. Dis., vol. 25, no. 1, p. 1, 2019. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [29].Lee S. et al. “Clinical course and molecular viral shedding among asymptomatic and symptomatic patients with SARS-CoV-2 infection in a community treatment center in the Republic of Korea,” JAMA Intern. Med., vol. 180, no. 11, pp. 1447–1452, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [30].Medina J. and Rojas-Cessa R., “Model code of extended SEIR Models with vaccination rollout and blockchain,” 2021. [Online]. Available: https://tinyurl.com/ch9atdku
- [31].Sánchez-Romero M., Lego V. di, Prskawetz A., and Queiroz B. L., “An indirect method to monitor the fraction of people ever infected with covid-19: An application to the United States,” PLoS One, vol. 16, no. 1, 2021, Art. no. e0245845. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [32].Bartsch S. M. et al. “Vaccine efficacy needed for a COVID-19 coronavirus vaccine to prevent or stop an epidemic as the sole intervention,” Amer. J. Prev. Med., vol. 59, no. 4, pp. 493–503, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [33].He W., Yi G. Y., and Zhu Y., “Estimation of the basic reproduction number, average incubation time, asymptomatic infection rate, and case fatality rate for COVID-19: Meta-analysis and sensitivity analysis,” J. Med. Virol., vol. 92, no. 11, pp. 2543–2550, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [34].Cevik M., Tate M., Lloyd O., Maraolo A. E., Schafers J., and Ho A., “SARS-CoV-2, SARS-CoV, and MERS-CoV viral load dynamics, duration of viral shedding, and infectiousness: A systematic review and meta-analysis,” Lancet Microbe, 2020. [DOI] [PMC free article] [PubMed]
- [35].Walsh K. A. et al. “The duration of infectiousness of individuals infected with SARS-CoV-2,” J. Infection, 2020. [DOI] [PMC free article] [PubMed]
- [36].Lauer S. A. et al. , “The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: Estimation and application,” Ann. Intern. Med., vol. 172, no. 9, pp. 577–582, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [37].Zhou F. et al. “Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: A retrospective cohort study,” Lancet, vol. 395, no. 10229, pp. 1054–1062, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [38].Hellewell J. et al. “Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts,” Lancet Glob. Health, vol. 8, no. 4, pp. e488–e496, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [39].Mahase E., “Covid-19: Moderna vaccine is nearly 95% effective, trial involving high risk and elderly people shows,” Brit. Med. J. (Online), vol. 371, 2020. [Google Scholar]
- [40].Polack F. P. et al. “Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine,” New England J. Med., vol. 383, no. 27, pp. 2603–2615, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [41].“Coronavirus (covid-19) vaccinations,” Our World in Data, Apr. 6, 2021. [Online]. Available: https://ourworldindata.org/covid-vaccinations
- [42].Szilagyi P. G. et al. , “National trends in the US public's likelihood of getting a COVID-19 vaccine-April 1 to Dec. 8, 2020,” JAMA, vol. 325, no. 4, pp. 396–398, 2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [43].Reiter P. L., Pennell M. L., and Katz M. L., “Acceptability of a COVID-19 vaccine among adults in the United States: How many people would get vaccinated?” Vaccine, vol. 38, no. 42, pp. 6500–6507, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [44].Baden L. R. et al. “Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine,” New England J. Med., vol. 384, no. 5, pp. 403–416, 2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [45].Eua A. T. and Agnihothram S., “Emergency use authorization (EUA) for an unapproved product review memorandum identifying information”. [Google Scholar]
- [46].Levine T. R., Kim R. K., and Hamel L. M., “People lie for a reason: Three experiments documenting the principle of veracity,” Commun. Res. Rep., vol. 27, no. 4, pp. 271–285, 2010. [Google Scholar]
- [47].Johansson M. A. et al. , “SARS-CoV-2 transmission from people without COVID-19 symptoms,” JAMA Netw. Open, vol. 4, no. 1, pp. e2035057–e2035057, 2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [48].White E. M. et al. , “Asymptomatic and presymptomatic severe acute respiratory syndrome coronavirus 2 infection rates in a multistate sample of skilled nursing facilities,” JAMA Intern. Med., vol. 180, no. 12, pp. 1709–1711, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [49].Oran D. P. and Topol E. J., “Prevalence of asymptomatic SARS-CoV-2 infection: A narrative review,” Ann. Intern. Med., vol. 173, no. 5, pp. 362–367, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [50].Howard J. et al. “An evidence review of face masks against COVID-19,” Proc. Nat. Acad. Sci., vol. 118, no. 4, 2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [51].Wang Y. et al. “Reduction of secondary transmission of SARS-CoV-2 in households by face mask use, disinfection and social distancing: A cohort study in Beijing, China,” BMJ Glob. Health, vol. 5, no. 5, 2020, Art. no. e002794. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [52].Bertozzi A. L., Franco E., Mohler G., Short M. B., and Sledge D., “The challenges of modeling and forecasting the spread of COVID-19,” Proc. Nat. Acad. Sci., vol. 117, no. 29, pp. 16 732–16 738, 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]