Determining The Age Priority in Universal Vaccination Using Economic Evidence: Case From US Based On Dynamic Transmission Model

Background: Currently, increasing regions have realized that universal vaccination are necessary to prevent COVID-19. However many of them are facing problems associated with insucient supply or chaotic allocation of vaccines. This study selected the United States population as an example and explored prioritization strategies of COVID-19 vaccination for different age groups to achieve the highest economic eciency. Methods: We built a dynamic transmission model to predict the incidence of SARS-CoV-2 infections under the prioritization strategies of vaccination for different ages within a 180-day simulation period. Quality-adjusted life year (QALY) was selected as the outcome. Medical costs included direct medical cost and vaccine cost based on a healthcare system perspective. Data on SARS-CoV-2 epidemiology, vaccine ecacy, and medical costs were derived from publicly available databases and previously published literature. Different COVID-19 vaccines were included in scenario analysis. The robustness of the study results was evaluated by one-way sensitivity analysis and probabilistic sensitivity analysis. Results: COVID-19 vaccination is economical compared with no vaccination. Priority vaccination for adults aged 25–59 years saves $31,664.2 million and that for adults over 60 years old saves $30,082.9 million in medical costs compared with no vaccine intervention. Additionally, priority vaccination for adults aged 25–59 years vs. over 60 years old saves $1,581.3 million. In contrast, priority vaccination for adults aged over 60 years vs. 25–59 years old gains 0.001 QALYs and costs $4.7 per capita, with an incremental cost-effectiveness ratio of $4,829.3/QALY, and it is economical when taking gross domestic product per capita of the United States in 2020 as the willingness-to-pay threshold. The results of sensitivity analysis indicate that the base-case results are robust. Conclusions: From a healthcare system perspective, it is most economical to prioritize adults aged over 60 years for COVID-19 vaccination in the United States, thereby achieving effective resource allocation and saving the government costs.


Objectives
A dynamic transmission model was used to explore different prioritization orders of vaccination against COVID-19 (priority vaccination for different age groups or no vaccination) for all people in the United States based on an economic perspective, without considering changes in population due to international migration. This research has been registered on PROSPERO and the registration number is CRD42021240072.

Study perspective
We selected a healthcare system perspective and considered the direct bene ts COVID-19 patients get through the health resource consumption caused by vaccination.

Participants
The study included healthy people who had never suffered from COVID-19 throughout the United States. The participants were divided into four age groups: 0-19 years, 20-24 years, 25-59 years, and over 60 years.

Intervention and control
The study compared the economy of vaccination prioritization for different age groups and no vaccination.
Program 1: Priority is given to vaccination for young people at 25-59 years old, followed by over 60 years, then 20-24 years, and nally 0-19 years. A second dose of vaccine is administered after all age groups have received one dose.
Program 2: Priority is given to vaccination for people over 60 years old, followed by 25-59 years, then 20-24 years, and nally 0-19 years. A second dose of vaccine is administered after all age groups have received one dose.

Program 3: No vaccine is administered for intervention.
The vaccine used in the study is BNT162b2 mRNA manufactured by P zer. A total of two doses are required. After the rst dose is administered, the second dose should be administered 21 days later.

Outcomes
COVID-19 incidence rate was used as a proxy indicator of vaccine e cacy. Additionally, incremental cost-effectiveness ratio (ICER) and net bene t were used as economic decision-making indicators.
2.6 Model design 2.6.1 Dynamic transmission model structure The United States population was divided into 10 major health states, and some health states were sub-divided according to age. In the dynamic transmission model, healthy people are infected via contact with people who have been infected with the virus but have not developed the disease, or with exposed people who have developed the disease. Over time, the infection progresses from latent to active, and the infected people choose to receive treatment or not. Although vaccination can reduce the infection risk, the vaccine's protection rate is not 100%. There is still a risk of being infected after vaccination, and vaccinated people remain susceptible in a strict sense. The speci c model structure is shown in Figure 1.
Simulation period The study period was set to 6 months for four reasons. (1) Future changes in national policies and individual behaviors across various countries are likely to in uence disease progression. Simulation over a too long period of time may result in large differences compared with the real situation of the disease. Taking 6 months as the study period can reduce the uncertainty of the model and improve its authenticity to a certain degree. (2) The supply of vaccines is limited. Although the United States government promises that every American can be vaccinated, a 180-day study period reduces parameter uncertainty by taking into account the actual situation of vaccine production and transportation, vaccination in batches by the day as a unit, and a lack of strong evidence supporting the effective protection period and sequelae of vaccine. (3) Acute infectious diseases are typically characterized by a short duration, with little in uence on the cost-effectiveness. Model simulation for too long a period of time therefore results in greater uncertainty. (4) According to existing clinical evidence [23], the immune period for SARS-CoV-2 of people who have recovered after infection is approximately 6 months. If the study period is set to a year, then it is necessary to consider the case of removed people, namely recovered people who have again become susceptible to infection, as well those who have died naturally, which greatly increases the model's complexity and distortion.
Cycle period The simulation involved 180 one-day cycles. The transfer rate between health states was calculated using a differential equation composed of the number of infected people and the infection rate. The choice of the cycle period was mainly based on the strong infectivity of COVID-19, with relatively large changes during disease progression. If using a longer cycle period, the estimation of indirect protection would be distorted to a greater degree. COVID-19 is an acute infectious disease with rapid development and multiple routes of infection. COVID-19 vaccines have been on the market for a short time  and there are limited data on COVID-19, making it almost impossible to acquire data from all the same samples. Therefore, we made the following  assumptions while keeping as close to the real situation as possible: (1) We assume there is no infection risk for hospitalized people.

Model Assumption
(2) Despite the possibility of infection in healthy people who have contacted the virus in nature, there is currently no strong evidence indicating that it is a major source of infection. Therefore, the possibility of infection in healthy people who have contacted the virus in nature or on virus-contaminated items was disregarded in this study.
(3) Although SARS-CoV-2 mutations have occurred, virus mutation per se is a complicated event occurring by chance, and the infection rate after mutation shows greater uncertainty. To ensure the study would be conducted smoothly, we assume that the virus continues to be infectious and will no longer evolve.
(4) We assume that people who have recovered from COVID-19 infection have 100% immunity in the study period.
(5) The cost of adverse reactions was not taken into account because there have been very few reports on adverse reactions to the COVID-19 vaccine, and considering the reported anaphylaxis in rare cases [24].
(6) No cost was considered for death. (7) We assuming that there is no age limit for vaccination; that is, all age groups can be vaccinated.
Furthermore, parameters such as mother-to-child transmission and births among the study population were not considered in the study because of insu cient evidence of transmission routes and the relatively short study period.

Model Parameters
The baseline values of demographic, epidemiological, vaccine, and economic parameters (Table 1) were determined through extensive searches of published literature and associated data in major databases (e.g., PubMed, Web of Science, and Cochrane Library), some authoritative websites (e.g., World Health Organization (WHO)), and United States Centers for Disease Control and Prevention (CDC). The calculations and sources of key parameters are introduced brie y in the following subsections. The utility of people in incubation period 0.96 0.92 1.00 beta [34] The utility of quarantined people 0.93 0.80 1.00 beta [33] The utility of exposed people 0.60 0.56 0.65 beta [35] The utility of people in hospital 0.7 0.67 0.74 beta [27] The utility of people in ICU 0.  [25,27]. The number of exposed people who are susceptible to infection was calculated as the number of con rmed cases minus quarantined people minus hospitalized people minus people recovered after infection. Both the total number of people hospitalized and the number of people hospitalized in the intensive care unit (ICU) were derived from statistical data on the CDC website [28, 29].

Epidemiological parameters
Because of the 1-day cycle period used in this study, we converted annual and monthly rates in the acquired data into daily rates (including natural mortality rate and in-hospital/out-of-hospital cure/mortality rate). Taking the annual rate as an example, the calculation of the daily rate is based on the following equation: where x is the annual rate and y is the daily rate.
Natural mortality rate was converted based on statistical data retrieved from the CDC website in 2018 and according to age [30]. Out-of-hospital mortality rate was derived from weekly reports of COVID-19 tracking data on the CDC website. In-hospital mortality rate came from the Morbidity and Mortality Weekly Report (MMWR) on the CDC website. In-hospital and out-of-hospital cure rates were obtained by subtracting the initial data of in-hospital and out-of-hospital mortality rates from 1 and then converted into a daily rate. Because the United States did not take effective quarantine measures in the early stage of the COVID-19 pandemic, we set the number of quarantined people to zero with a quarantine rate of zero. The number of contacts in different age groups of ordinary people was estimated based on the number of contacts in each age group before the outbreak of the pandemic in Wuhan, China [31]. The probability of transferring from incubation period to exposed period was calculated by dividing the cycle period by the duration of the incubation period, and the duration of the incubation period was extracted from Lauer's study [32]. The usage rate of the ICU was calculated by dividing the number of people hospitalized in the ICU by the total number of people hospitalized.

Health Utility
The health utility of healthy people was set to one, and the health utility of dead people was set to zero. Because no study has reported the health utility of people recovered after infection with SARS-CoV-2, we collected the data from an investigation of recovered in uenza patients in the United States [33]. The health utility of patients in the incubation period was derived from a study on in uenza pandemics [34], and the health utility of exposed people came from a study on in uenza patients [35]. Furthermore, the health utilities of patients hospitalized and those hospitalized in the ICU were derived from Kohli's research data [27].

Costs
Because of a lack of reports on the cost of quarantine for COVID-19 and our assumption of a quarantine rate of zero, we did not take into account the cost of quarantine in this study. The cost of hospital treatment, cost of ICU treatment, cost of vaccine, and cost of transportation management and vaccination were all derived from Kohli's research data and statistical data provided by the United States Centers for Medicare & Medicaid Services [27,36]. The cost of adverse reaction treatment and the incidence of adverse reactions were set to zero.

Willingness-to-pay
The willingness-to-pay threshold was set to one-time gross domestic product (GDP) per capita of the United States in 2020, and values were derived from data of the International Monetary Fund [37]. Daily discount rate was converted from the annual discount rate of 3% [27].

Economic evaluation indicators
To determine the economy of the intervention measures, we calculated the incremental cost-effectiveness ratio (ICER) and then compared it with the willingness-to-pay threshold. Additionally, we calculated the net bene t compared between different control programs, and the program with the larger net bene t was considered the most economical one (net bene t = bene t -cost). The bene t was de ned as direct medical costs saved by a reduction in the number of COVID-19 cases under the vaccination programs considering the cost of vaccine, as compared with the no-vaccination program.

Uncertainty analysis
One-way sensitivity analysis, probabilistic sensitivity analysis, and scenario analysis were carried out in this study.
One-way sensitivity analysis: We let 44 parameters including costs uctuate within a certain range. Based on the uctuation results, tornado diagrams were drawn to nd the major factors in uencing the results.
Probabilistic sensitivity analysis: We assumed that the 44 parameters with uncertainties follow a speci c probability distribution. Then, Monte Carlo simulations were carried out 10000 times. Based on the simulation results, a scatterplot and cost-effectiveness acceptability curve were drawn. The economy of the three intervention programs was determined with different willingness-to-pay thresholds. Assuming that the costs follow a Gamma distribution, the utility values have a Beta distribution, the demographic parameters t a Gamma distribution, and the epidemiological parameters t a Beta distribution. years can reduce the number of people infected, this program saves $1,581.3 million in medical costs compared with priority vaccination for adults aged over 60 years old. Therefore, in the case of the COVID-19 pandemic, any prioritization strategy of vaccination can save medical costs compared with no vaccine intervention. However, which program is more preferable still needs to be veri ed by further analysis and research. Details are summarized in Table 2.  Table 1. Based on a healthcare system perspective, any vaccination program compared with no intervention results in lower costs and positive economic outcomes, and is thus a very economical measure. Within the simulation period, priority vaccination for adults aged over 60 years costs more than priority vaccination for people aged 25-59 years, while producing better health outcomes. The former program is therefore more economical, when taking onetime GDP per capita of the United States (2020) as the willingness-to-pay threshold. Considering the two vaccination strategies, priority vaccination for adults aged over 60 years gains 0.001 QALYs per capita while costing $4.7 per capita more than priority vaccination for adults aged 25-59 years in the simulation period, with an incremental cost-effectiveness ratio (ICER) of $4,829.3/QALY. Because the mortality rate of older people is higher than that of young people, the increase in QALYs is mostly due to a reduction in the infections of older people, which prevents the death of older people. In general, all vaccination strategies require additional expenditure for the cost of vaccines compared with no vaccination. However, vaccination still shows an absolute advantage over no vaccination with regard to the strong infectivity of COVID-19 and the high cost of treatment. Details are provided in Table 3.   Table 1. For the one-way sensitivity analysis, the ve most in uential factors are selected and included in tornado diagrams. The results show that although parameter variation affects ICER to a certain degree, the economic results mentioned above are still absolutely robust, and the superior program still holds an absolute dominant position. That is, the two vaccination programs are absolutely superior to no vaccine intervention.
Furthermore, priority vaccination for people aged over 60 years vs. 25-59 years old is still absolutely economical, when taking one-time GDP per capita of the United States as the willingness-to-pay threshold. However, Fig. 2 (a, b) shows that the protection rate of the vaccine is still a major factor in uencing the economic results. Although there is currently evidence for the vaccine's protection rate, its protection period still needs to be corroborated by stronger evidence to verify the economy of the vaccine.

Probabilistic sensitivity analysis
The distribution of parameters used for probabilistic sensitivity analysis is provided in Table 1. The results (Fig. 2(e)) show that there is no uncertainty in the economic results of vaccination compared with no intervention. All vaccination programs analyzed in this study are advantageous over no vaccination.
Priority vaccination for adults aged over 60 years vs. 25-59 years is more economical in the case of taking one-time GDP per capita of the United States as the willingness-to-pay threshold. Furthermore, the cost-effectiveness acceptability curve (Fig. 2(d)) shows that vaccination is absolutely acceptable compared with no vaccination. Furthermore, the 50% acceptable probability of giving priority to vaccinating adults aged over 60 years is less than the one-time GDP per capita of the United States.

Scenario analysis
People in the United States have mostly received the P zer vaccine [22], namely BNT162b2. Therefore, the scenario analysis is performed to explore changes in the number of infected people and ICER after receiving vaccines from different manufacturers. The speci c scenarios are as follows:  Table 4. Because the adverse reactions are mostly mild, the cost of treatment for adverse drug reactions in each scenario was not considered in the scenario analysis. Because of a lack of research related to the protection rate of a single vaccine dose for some vaccines, the single dose protection rate was set to 52%, which is the protection rate of a single dose of the P zer vaccine. Vaccination achieves a certain protective effect irrespective of the vaccines (Fig. 3). However, it is assumed that the virus will not mutate; the immigration and emigration of the population are not considered, and there will be a certain period of immunity after infection. Therefore, the number of newly infected people will decrease gradually after reaching a peak. Although the assumptions are necessary and do not have a large in uence on the economic results of the model, they do have great limitations. Nonetheless, we have to make these assumptions to explore the rational use of limited resources.
The results of scenario analysis are summarized in Tables 5 and 6. Despite the different types of vaccines administered, the economic results are relatively stable with the one-time GDP per capita of the United States in 2020 as the willingness-to-pay threshold. Vaccination is more economical than no vaccination, while priority vaccination for adults aged over 60 years is more economical than priority vaccination for adults aged 25-59 years. Table 6 compares the results between vaccines. BNT162b2 (P zer) is signi cantly superior to the other vaccines without considering the cost of treatment for adverse reactions.

Main ndings
This study presents two main ndings. First, there is a great possibility that vaccination is economical even without considering the prioritization issue. Because COVID-19 is highly infectious with a relatively high cost of treatment, vaccination is very likely to save considerable medical costs even taking into account the cost of the vaccine. Second, priority vaccination for adults over 25-59 years old reduces the number of infections and thereby saves money.
Priority vaccination for adults aged over 60 years reduces the population's mortality rate and thereby achieves better health outcomes, which is more economical than priority vaccination for other age groups. These ndings corroborate the views of most people and are in line with the WHO and the United States Food and Drug Administration's understanding of COVID-19 vaccines. Therefore, from the perspective of the public budget, priority should be given to vaccinating adults over 25-59 years old; but from the perspective of health value, priority should be given to vaccinating adults over 60 years old.
In the United States, the incidence of COVID-19 cases can be markedly reduced by daily administration of ~ 1 million doses of the P zer vaccine. Priority vaccination for adults aged 25-59 years and over 60 years can reduce $31,664.2 million and $30,082.9 million in medical costs, respectively, compared with no vaccine intervention. The ICERs for priority vaccination for adults aged 25-59 years and over 60 years are -$57,655.5/QALY and -$34,316.8/QALY, respectively, both of which are less than zero. The results of sensitivity analysis show that irrespective of the vaccine type and prioritization of the vaccination program selected, the vaccine group has an absolute advantage over the control group, and the results are extremely stable. Large-scale vaccination is undoubtedly a wise move owing to the high cost of treatment for COVID-19. Although the cost of the vaccine is not low, the necessary treatment approaches involving the ICU and ventilators require high costs. Meanwhile, vaccine intervention is not only effective for the interveners per se, but also provides indirect protection and achieves greater health bene ts than expected.
Comparing the vaccination programs with different prioritization orders, priority vaccination for adults aged over 60 years achieves the best health outcomes.
The ICER of priority vaccination for adults aged over 60 years vs. 25-59 years is $4,829.3/QALY. Priority vaccination for adults aged over 60 years is therefore more effective and economical when taking one-time GDP per capita of the United States in 2020 as the willingness-to-pay threshold. Priority vaccination for adults aged 25-59 years can indeed reduce the number of new COVID-19 cases; however, the mortality rate is highest in adults aged over 60 years who have been infected with the disease; prioritizing this age group for vaccination can reduce the number of deaths and achieve greater health bene ts. This conclusion is also extremely stable according to the results of sensitivity analysis.
Here, scenario analysis reveals that vaccination can achieve more health outcomes than no intervention. Furthermore, all the other four COVID-19 vaccines included in the scenario analysis are signi cantly economical with one-time GDP per capita of the United States as the willingness-to-pay threshold, among which priority vaccination for adults aged over 60 years is the best program. Comparing different vaccines reveals that the BNT162b2 vaccine has an absolute advantage.

Strengths and limitations
Although the United States has now launched universal vaccinations and have applied products from multiple brands which against our assumption, it is di cult for the complexity of reality to be included in the model. With that being said, this research is not meaningless given the fact that it remains di cult to build reasonable and effective models with lack of parameter inputs. We took United States as our study setting because it is the only country with the most complete parameters till now. Since many countries have launched the plan of universal vaccinations but facing the same allocation problems as the United States. As well as other low-income and middle-income countries who do not have enough vaccine resources. We hope the study ow could provide useful reference to discuss the economic value of different vaccination strategies in other countries.
Additionally, the development of acute infectious diseases is often di cult to accurately estimate. Consequently, very few studies have been carried out and published on the economic evaluation of COVID-19 vaccines, and most studies have only estimated the development of the COVID-19 pandemic. The several economic evaluations of COVID-19 vaccines that have been published so far [20,27] mainly focus on evaluating the economy of COVID-19 vaccination without comparing the economy of vaccination strategies with different prioritization orders. This is the rst study to evaluate the economic value of the prioritization strategies of COVID-19 vaccination by age groups.
To the best of our knowledge, there have been no studies comprehensively considering and comparing multiple vaccination programs and exploring the economy of different vaccines, as implemented in this study. This study is carried out based on a relatively comprehensive consideration in the scope permitted by actual conditions. We take into account the spread between people and the cross-protection by vaccines and repeatedly weigh clinically important parameters such as vaccine protection rate and treatment cost. We not only draw the conclusion that the vaccine intervention program is absolutely superior to no intervention but also compare the economy of different vaccine intervention programs. The model and results provide a reference of age prioritization for vaccination in most countries that have already carried out universal vaccination or other countries who will have a chance to conduct largescale vaccination in the future.
This study is not without limitations. First, taking into account the disease characteristics, the simulation period of the study was set to 180 days. Although it cannot completely simulate that all people in the United States are vaccinated, we still obtained the results of vaccine economy and the appropriate vaccination program within the priority simulation period. Second, the mutation of the virus is inevitable yet di cult to estimate, and we had to ignore virus mutation. Third, whether the adverse reactions of the vaccines are mostly mild as stated in the literature is still to be discussed or veri ed by real-world reports.
Meanwhile, the sequelae of people recovered also lack strong reports to con rm, and we had to use relevant research reports on similar respiratory diseases as in uenza as an alternative. Fourth, we did not consider the cost associated with diagnostic monitoring. Although these assumptions and substitutions are necessary, they could affect the accuracy of the prediction results to a certain extent.

Conclusion
Currently, COVID-19 vaccines have been on the market for a short time and the population vaccination rate is generally low. Many low-income countries have not started vaccination. Therefore, both the effectiveness and safety of the vaccines lack strong real-world evidence for corroboration. Nonetheless, vaccines are undoubtedly an important part in many of the prevention strategies for COVID-19. So far, Israel is the only country that has achieved universal vaccination, whereas most countries in the world are still far from achieving universal vaccination [38].
This study indicates that COVID-19 vaccination in the United States provides signi cant health and economic bene ts. Despite the high price of the vaccine, compared with the high cost of treatment, vaccination is still an extremely cost-effective choice based on a healthcare perspective. Age grouping is indeed a desirable option of prioritization for vaccination. However, whether there is a greater risk of infection for some occupations, such as medical workers, and whether these occupations should be considered for priority vaccination remain to be studied.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. COVID19model.zip