key: cord-0751995-ejshid8z
authors: Coccia, Mario
title: Optimal levels of vaccination to reduce COVID-19 infected individuals and deaths: A global analysis
date: 2021-11-02
journal: Environ Res
DOI: 10.1016/j.envres.2021.112314
sha: dbf8e86c229bffba65fe7b95ae3e551cbdcf9d33
doc_id: 751995
cord_uid: ejshid8z

Coronavirus disease 2019 (COVID-19) continues to be a pandemic threat that is generating a constant state of alert in manifold countries. One of the strategies of defense against infectious diseases is the vaccinations that decrease the numbers of COVID-19 related infected individuals and deaths. In this context, the optimal level of vaccination is a basic point to control pandemic crisis. The study here,−using global data of doses of vaccines administered per 100 inhabitants, confirmed cases and case fatality ratio of COVID-19 between countries from March to May 2021,− clarifies the optimal levels of vaccination for reducing the number of infected individuals and, consequently, numbers of deaths. Findings reveal that the average level of administering about 80 doses of vaccines per 100 inhabitants between countries can sustain a reduction of confirmed cases and numbers of deaths. In addition, results suggest that an intensive vaccination campaign in the initial phase of pandemic wave leads to a lower optimal level of doses administered per 100 inhabitants (roughly 47 doses of vaccines) for reducing infected individuals; however, the growth of pandemic wave moves up the optimal level of vaccines to about 90 doses for reducing the numbers of COVID-19 related infected individuals. All these results here could aid policymakers to prepare optimal strategies directed to a rapid COVID-19 vaccination rollout, before the takeoff of pandemic wave, to lessen negative effects of pandemic crisis on environment and socioeconomic systems.

Syndrome Coronavirus 2 (SARS-CoV-2), which appeared in late 2019 (Anand et al., 2021; Bontempi et al., 2020 Coccia, 2020 Coccia, , 2020a Coccia, , 2021 . COVID-19 is still circulating in 2021 with mutations of the novel coronavirus 1 that generate continuous COVID-19 infections and deaths in manifold countries (Johns Hopkins Center for System Science and Engineering, 2021; Huang et al., 2021; National Academy of Medicine, 2021; Vicenti et al., 2021) . Seligman et al. (2021) show some characteristics of people that are associated with COVID-19 mortality, such as: mean age of 71.6 years, nonwhite race/ethnicity, income below the median and less than a high school level of education. High numbers of COVID-19 related infected individuals and deaths worldwide have supported the development of different types of vaccines based on viral vector, protein subunit and nucleic acid-RNA (Abbasi, 2020; de Vlas and Coffeng, 2021; Jones and Helmreich, 2020) . In vector vaccines, genetic material from the COVID-19 virus is placed in a modified version of a different virus (called, viral vector) . When the viral vector gets into human cells, it delivers genetic material from the COVID-19 virus directed to instruct the cells to make copies of the S protein (the main protein used as a target in COVID-19 vaccines). After that, human cells display the S proteins on their surfaces and immune system responds by creating antibodies and defensive white blood cells to fight the novel coronavirus (viral vector vaccines for COVID-19 are by Janssen/Johnson & Johnson and University of Oxford/AstraZeneca). Protein subunit vaccine includes only the parts of a virus that best stimulate immune system. This type of COVID-19 vaccine has harmless S proteins. The immune system recognizes S proteins and creates antibodies and defensive white blood cells to fight the viral agent (e.g., the vaccine developed by Novavax, an American biotechnology company; cf., GAVI, 2021) . Instead, the messenger Ribonucleic acid (mRNA) vaccines use genetically engineered mRNA to give to cells instructions on how to make the S protein found on the surface of the SARS-CoV-2, creating antibodies to fight this novel coronavirus (Mayo Clinic, 2021) . The process of development of mRNA vaccines for COVID-19 is much faster than conventional vaccines to be redesigned and mass-produced (Cylus et al., 2021; Heaton, 2020; Jeyanathan et al., 2020; Komaroff, 2020) . The first path-breaking mRNA vaccines for COVID-19 are due to premier biopharmaceutical companies: Pfizer-BioNTech and Moderna (cf., Coccia, 2017 Coccia, , 2021a . The investigation of vaccination plans between countries is a crucial aspect to determine how the novel infectious disease can be controlled and/or eradicated in the population (Aldila et al., 2021) .

Vaccination has the potential effect to reduce the diffusion of COVID-19, to relax non-pharmaceutical measures and maintain low basic reproduction number, but an important point is to clarify the levels of administering of vaccines between countries to timely reduce negative effects in society (Anser et al., 2020) . Akamatsu et al. (2021) argue the vital role of governments to implement an efficient campaign of vaccination to substantially reduce infections in society, and avoid the collapse of healthcare system (cf., Coccia, 2021a Coccia, , 2022 . Aldila et al. (2021) maintain that higher levels of vaccination rate can eradicate COVID-19 in population by approaching herd immunity to protect vulnerable individuals (cf., Anderson et al., 2020; Randolph and Barreiro, 2020) . Herd immunity indicates that only a share of population needs to be immune and therefore no longer susceptible to a viral agent (by overcoming natural infection or through vaccination) for controlling large outbreaks (Fontanet and Cauchemez, 2020) . Scholars estimate the proportion of a population that needs to be vaccinated to support herd immunity, ceteris paribus (Redwan, 2021) . The threshold level depends on basic reproduction number, R0-the number of cases, on average, spawned by one infected individual in an otherwise fully susceptible (Coccia, 2020; Kwok et al., 2020) . In particular, the formula for calculating the herd-immunity threshold is 1-1/R0 and it indicates that the more people who become infected by everyone who has the virus, the higher the proportion of the population that needs to be immune to reach herd immunity. The index R0 assumes that everyone is susceptible to the virus, but the level changes as the epidemic evolves, since it depends on changes in susceptibility of the population, mitigation and restriction policies, circulation of variants, etc. (Aschwanden, 2020 (Aschwanden, , 2021 Coccia, 2021c Coccia, , 2021d . In addition, the relax of mitigation and containment measures can move up herd-immunity threshold in specific situation (Buss et al., 2021; Dashtbali and Mirzaie, 2021) . Kwok et al. (2021) argue that the estimates of effective reproduction number range from 1.06 to 6.64 and the minimum proportion (%) of total population required to confer COVID-19 immunity is 5.66 in Kuwait and 85 in Bahrain. Rosen et al. (2021) describe socioeconomic and organizational factors associated with the vaccination campaign in Israel (cf., Prieto Cruriel, et al. 2021) .

In this context, a fundamental problem in COVID-19 pandemic crisis is the optimal level of vaccination that supports J o u r n a l P r e -p r o o f a drastic reduction of COVID-19 infected individuals and deaths. The present study confronts this problem here by developing a statistical analysis to explain, at global level, different optimal levels of vaccination during the evolution of COVID-19 pandemic wave that trigger a reduction of infected individuals in society. Results can suggest best practices for vaccination plans to guide effective and timely policy responses for constraining negative effects of COVID-19 pandemic crisis and future epidemics of similar infectious diseases in environment and socioeconomic systems. This study is part of a large research project directed to explain drivers of transmission dynamics of COVID-19 and design effective policy responses to cope with and/or to prevent pandemic threats in society (Coccia, 2020b (Coccia, , 2021b . (21 day of the same month) to assure a certain level of protection in population that begins after a variable number of days (Faes et al., 2020; Zhang et al., 2020 

Firstly, data are analyzed with descriptive statistics of variables given by arithmetic mean and standard error of the mean. Data concerning doses of COVID-19 vaccines, confirmed cases and CFR of a specific day in the dataset can refer to different days because of difficulties in countries associated with gather or transmission of information.

Moreover, database here includes different COVID-19 vaccines having a different period of administering between the first and second dose to provide a certain level of protection that begins after a variable number of days (approximately after 10 -15 days the first dose) and remains for some months (about six months). In the presence of this just mentioned issue, the study here considers a time lag of 21 days from doses of vaccines and confirmed cases. In addition, this study considers a large sample of N=192 countries having a normal distribution that mitigates discrepancies among countries.

We assume different scenarios considering the evolution of COVID-19 pandemic wave and vaccination over time Secondly, the analysis of simple regression applies quadratic models because they fit the scatter of data to detect nonlinear effects of relations understudy.

The specification of model for three scenarios just described is given by:

where: Remark 2: Model [1] has a time lag effect between explanatory (t) and dependent variables (t+21 days) to reduce the endogeneity and provide reliable (estimated) parameters.

Thirdly, the optimization of the estimated relationships [1] is performed with the perspective of maximization of the equation [1] to find the optimal levels of doses of vaccines administered × 100 inhabitants (during the cycle of evolution of the COVID-19 pandemic) that support a consequential drastic reduction of confirmed cases of COVID-19 and negative effects in society. In particular, the estimated relationships [1] for three scenarios are objective J o u r n a l P r e -p r o o f functions of one (real) variable given by polynomial functions of second order. These estimated relations [1] are continuous and infinitely differentiable functions. The calculus applied on functional relation [1] provides the optimal levels of doses of vaccines administered × 100 inhabitants that reduce, subsequently, confirmed cases between countries in a specific stage of COVID-19 pandemic wave as described in scenarios A, B and C.

Finally, the optimal doses of vaccines administered, calculated as described in previous statistical and mathematical analyses, are used as cut-off points. In particular, average Case Fatality Ratios (%) and Mortality rates per 100 000 people are described for countries having lower or higher levels of doses of vaccines than cut-off points (i.e., optimal estimated value). This analysis also considers the population of countries in 2020 to assess if the size of countries plays a role in the policy responses and effects to cope with COVID-19 pandemic crisis.

Statistical analyses are performed with the Statistics Software SPSS version 26. Table 1 shows descriptive statistics of variables in March, April and May 2021. Significance: *** p-value <0.001¸** p-value <0.01, ¸* p-value <0.05

The estimated relationship, based on results of table 2, is:

The polynomial function is given by = 3.25 + 0.1874ℎ − 0.002 ℎ 2 the necessary condition to maximize is:

The first derivative equal to 0 is : pandemic in May 2021 between countries to support, after this threshold, a sharply decrease of infections that reduce negative effects of COVID-19 pandemic in society.  Effects of vaccination on Case Fatality Ratio (CFR) and mortality rates per 100 000 people of COVID-19 In general, these results suggest that countries with levels of vaccination above the optimal level of doses of vaccines have lower average values of CFR % and mortality rate, whereas the confirmed cases are higher likely because of pro-active testing activity across countries. Finally, results reveal that countries best performers in the administering of high levels of doses of vaccines per 100 inhabitants are mainly smaller countries, such as Israel (cf., Fig. 1 ).

The findings of the study here reveal that optimal level of vaccination is associated with the evolution of COVID-19 pandemic wave: a vaccination in the initial phase of pandemic wave has a lower optimal level of doses administered per 100 inhabitants to support the reduction of infected individuals, but the growth of pandemic wave moves up the optimal level of vaccines from 46.75 (March 2021) to about 90 doses of vaccines in May 2021. This study also reveals that high levels of vaccination can reduce case fatality ratios and mortality rates of COVID-19 associate with other factors of health, environmental and economic system.

This study suggests that the optimal strategy and policy response to pandemic crisis are a rapid vaccination rollout J o u r n a l P r e -p r o o f to reduce timely numbers of infected individuals and deaths, before the takeoff of pandemic wave. These results may be interpreted through the lens of different studies that focus on many factors contributing to the success of implementing a rapid roll out of COVID-19 vaccination for reducing confirmed cases and negative social impact (Coccia, 2021a (Coccia, , 2021e, 2022 . In fact, Sim et al. (2021) In general, optimal strategies to pandemic shocks should be based on strong public governance driven by adequate and effective leadership that engages with the communities and adjusts to population needs (Williams et al., 2020) .

In fact, good governance can support preparedness of nations for performing efficient campaigns of vaccination to reduce infections, mortality, morbidity, mental stress among the population and support economic recovery (Ardito et al., 2021; Coccia, 2017a Coccia, , 2018a Coccia, , 2019 Coccia, , 2021e, 2021f, 2021g, 2022 Coccia and Bellitto, 2018; Coccia and Benati, J o u r n a l P r e -p r o o f 2018; Kluge et al., 2020) . The public governance supporting efficient vaccination plans is not limited to health system, but it involves other functions of public administration to work properly for strengthening health, economic and social systems (Sagan et al., 2020) . As a matter of fact, effective crisis management of COVID-19 pandemic, supported by effective multi-level governance, should implement timely vaccine programmes to achieve, whenever possible, the goal indicated in scenario A (Abuza, 2020; Anttiroiko, 2021; Coccia, 2021a DeRoo et al., 2020; Frederiksen et al., 2020; Harrison and Wu, 2020; Ritchie et al., 2020 Ritchie et al., , 2020a ). Nevertheless, the optimal level of vaccination in the initial phase of pandemic has to face distribution and allocation hurdles, and in the presence of delays, governments have to cope with changes into the equation of herd-immunity with a strategy of vaccination directed to increase the thresholds of immunization of population to reduce infected individuals and negative effects in society (Callaway , 2021; Dooling et al., 2020; Vignesh et al., 2020) . In fact, the study here clearly shows that a delay of effective vaccination plan from March to May 2021, considering the evolutionary growth of pandemic wave, it moves forward the optimal threshold between countries from about 47 to 90 doses of vaccines per 100 people to trigger the reduction of the transmission dynamics of COVID-19 (Buss et al., 2021; ECDC, 2021; Mallapaty, 2021; Whittaker et al., 2021) . In short, the timely achievement of the optimal threshold of doses administered is a basic aspect of crisis management, because a quickly and thoroughly vaccination plan can constrain transmission dynamics and consequential socioeconomic issues (Akamatsu, 2021; Byun et al., 2021; Liu et al., 2021) . Engelbrecht and Scholes (2021) argue that if effective strategies of vaccination have delayed, the progress of pandemic wave may generate additional health and socioeconomic issues. Overall, then, the policy response based on an optimal level of vaccination, according to scenario A, is a significant challenge associated with manifold socio-cultural and politicaladministrative factors, and enormous public investments in health system of countries (Ethgen et al., 2019; Coccia, 2019 Coccia, , 2021g, 2022 . Hence, countries can adequately prepare to prevent, detect and respond to both epidemics and pandemics, over the next ten years, with a better governance, innovative partnerships, high public investments, and COVID-19 and future epidemics of novel viruses pose, more and more, a serious threat to security and public health of nations. An influenza pandemic can occur at any time with little warning; any delay in detecting a novel influenza strain; sharing of influenza virus samples; and in developing, producing, distributing, or administering a therapeutic or vaccine could result in significant additional morbidity and mortality, and deterioration of socioeconomic systems (Coccia, 2021 Huang et al., 2021) .

This study suggests that efficient strategies of vaccination have to be rapid and responsive in the initial phase of COVID-19 pandemic wave for reducing the impact of novel viral agents in society. These results here can help policymakers to design satisfying goals to cope with current pandemic applying effective vaccination strategies to prevent and/or cope with future outbreaks of the COVID-19 and similar epidemics. The most important policy implications of findings here are that, though high vaccination efforts of most advanced countries worldwide, the theoretical threshold for vanquishing COVID-19 seems to be out of reach at global level (in the medium run) because of the inequality in the distribution of vaccines, the uncertainty if and how vaccines prevent or not the transmission, the duration of immunity in vaccinated people and new variants that modify the herd-immunity equation (cf., Aschwanden, 2020 Aschwanden, , 2021 . In fact, on October 2021 about 48% of the world population has received at least one dose of a COVID-19 vaccine and in poor countries a mere 2.8% of people have received at least one dose (Our World in Data, 2021).

Although this study has provided interesting results, that are of course tentative, it has several limitations. First, a limitation of the study is the lack of data about doses administered and total vaccinations in manifold countries, mainly in the spring season of the year 2021, also for the difficulty of production and distribution of COVID-19 vaccines worldwide. Second, not all the possible confounding factors that affect the efficacy of vaccination are taken into consideration (such as, length of lockdown, facemask wearing, etc.) and in future these factors deserve to be controlled for supporting results here. Third, the lack of integration of data with age of vaccinated people (the priority given in many countries to elderly subjects, with a more compromised immune system) may have influenced the results of infected individuals and deaths across countries. In addition, structure of population and characteristics of J o u r n a l P r e -p r o o f patients (e.g., ethnicity, age, sex, and comorbidities) may vary between countries making comparative analysis in some cases a problematic approach (Angelopoulos et al., 2020; Coccia, 2018; WHO, 2020 possible, to examine also other variables between countries to explain dynamic relationships under study over time and space. Despite these limitations, the results presented here suggests the critical aspect of the relationship between the evolution of pandemic wave and timing of the vaccination rollout to achieve the goal of optimal threshold of vaccination at national level for reducing negative effects of pandemic crisis in society. However, there is need for much more detailed research in these topics and this study encourages further investigations for supporting optimal strategies of vaccination, using lessons learned of COVID-19, also considering the interaction between the evolution of pandemic wave and vaccination plan. To conclude, different factors between countries that are not only parameters related to medicine but also to other sciences can improve preparedness of countries for effective and rapid roll out of vaccination to control negative impact of pandemic crisis on public health, economy and society.

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☐XX The author, Mario Coccia, declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: