Maximum Level of COVID-19 Vaccination in Rich and Democratic Countries, and in Other Political Systems

Coronavirus Disease 2019 (COVID-19) vaccinations play a main role in the immunization program of countries to decrease the numbers of COVID-19 related infected individuals and deaths. However, countries, after a certain share of people vaccinated against COVID-19 have to cope with vaccine hesitancy and resistance in population. One of the fundamental problems is the detection of the max share of people vaccinable between countries without the introduction of any rule that affects basic aspects of individual freedoms of people in public and private life. The study here confronts this problem with a global analysis based on N=150 countries, using relationships between socioeconomic, institutional and political variables, and levels of vaccination. Results reveal that the share of people vaccinated increases with the level of development (and democratization) of countries, achieving the maximum level of about 70%; beyond this level, the share of vaccination starts to decrease across countries. Moreover, findings reveal that governments with Monarchy and Parliamentary Monarchy have average share of people vaccinated higher than Mixed Executives. These main findings suggest that in developed and democratic countries the maximum level of vaccination has a physiological limit, but many Western (democratic) countries are applying restriction rules (e.g., green pass/vaccine passport) to overcome this max level reducing and regulating, at the same time, many aspects of public and private life of individuals. Discussion explains these sociopolitical phenomena with aspects of politics of fear, focused on deaths of COVID-19, and of strong leaders having domestic and international support that apply rules in contexts of social insecurity with consequential reduction of equity, trust and solidarity and increase of socioeconomic issues. All these results here could aid policymakers to prepare sustainable policy responses against COVID-19 in society without distressing basics of democracy with rules of autocratic systems that can generate economic and social deterioration, and problems for mental health and economic conditions of people in society.

. Maximum level of COVID-19 vaccination in rich and democratic countries, National Research Council of Italy 2 | Page index R0 assumes that everyone is susceptible to 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, season, etc. (Aschwanden, 2020(Aschwanden, , 2021Coccia, 2021a;Dashtbali and Mirzaie, 2021). Kwok et al. (2021) argue that the minimum proportion (%) of total population required to confer COVID-19 immunity change, such as it can be 5.66 in Kuwait and 85 in Bahrain. In this context, a fundamental problem in COVID-19 pandemic crisis is the detection of maximum level of vaccinated people between countries without compulsory actions on citizens and if the maximum level of vaccinated people changes according to the types of executives (e.g., mixed executives, monarchy, etc.). The natural acceptance of COVID-19 vaccines between countries can be a main proxy to assess the maximum level of consent in rich and democratic settings, whereas actions of nations for overcoming the max level of vaccinated people with autocratic interventions that reduce individual freedoms can show consequential socioeconomic issues.
This study in the presence of COVID-19 pandemic crisis can clarify some relations to design best practices of crisis management for vaccination plans directed to increase vaccinated people using rewards systems in democratic settings having little amount of oversight on public and private life rather than compulsory rules that reduces individual freedoms (cf., Coccia, 2019g). This study is part of a large research project 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, 2020(Coccia, , 2020a(Coccia, , 2020b(Coccia, , 2020c(Coccia, , 2021(Coccia, , 2021a(Coccia, , 2021b(Coccia, , 2021c(Coccia, , 2021d.

Source and sample
The sample of this study is N=150 countries worldwide.

| Page
Madagascar, etc. The data here considers all types of COVID-19 vaccines used in different countries, i.e., vaccines by Johnson & Johnson, Oxford/AstraZeneca, Pfizer/BioNTech, Sinopharm/Beijing, Sinovac, Sputnik V and Moderna (Ritchie et al., 2020). Of course, every country has been using a different combination of these COVID-19 vaccines to protect the population. Source: Our World in Data (2021).

-
Gross Domestic Product (GDP) per capita in 2020. GDP per capita (constant 2010 US$). GDP per capita is gross domestic product divided by midyear population. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of products. Countries are also categorized using the typology of executives as follows (Norris, 2008): Data are analyzed with descriptive statistics given by arithmetic mean and standard error of the mean, using the categorization of economic development, freedom status and type of executives between countries.
The normality of distributions of variables under study is checked with skewness and kurtosis coefficients and considering that some variables are not appropriate for parametric analyses, they are transformed in logarithmic scale for performing regression analysis.
After that, the analysis of simple regression applies quadratic models because they fit the scatter of data and detect nonlinear effects of relations understudy. The specification of log-log quadratic model is given by: where:  Statistical analyses are performed with the Statistics Software SPSSâ version 26.  Table 1 shows that partially free and rich countries have a higher share of people fully vaccinated against COVID-19, whereas free countries having a medium level of GDP per capita have a higher share of vaccinated people than partially free and not free countries.  Table 2 shows that countries with monarchy and parliamentary monarchy have a higher share of people fully vaccinated against COVID-19 than countries having mixed executives and presidential republic.

RESULTS
The function is given by the necessary condition to maximize the function j is: The first derivative equal to 0 is:

¨ PARTLY FREE Countries
The estimated relationship of FREE countries, based on results of table 3, is: The function is given by the necessary condition to maximize the function k is: The first derivative equal to 0 is: The estimated relationship in NOT FREE countries has not significant parameters as indicated in table 3 and we do not proceed with the approach of optimization because the results are misleading

¨ TOTAL Countries
The estimated relationship of total number of countries, based on results of table 3, is: The function is given by the necessary condition to maximize the function q is:  In general, the share of vaccinated against COVID-19 increases with the wealth of nations but it has a physiological maximum level of about 70% between countries at global level (in partly free countries is lower).
g*= 69.63% is the Max share of people vaccinated in countries.

DEMOCRATIC SETTINGS
Anttiroiko (2021) analyzes how socioeconomic context, institutional arrangements, culture, and technology level can affect policy responses to the pandemic crisis in Eastern and Western countries 2 . Studies show that in average policy responses in Europe over 2020 tended to be less stringent than countries in East Asia (Ritchie et al., 2020). Moreover, Anttiroiko (2021) highlights that Asian countries have applied with determination policy responses to cope with COVID-19 crisis because of the early diffusion of pandemic in their regions that has supported learning processes.
Instead, European countries have different culture, institutions, political systems and approaches to cope with crises and have also to face with privacy and human rights issues, protests against governments for lockdown, restriction measures, vaccine passports, etc. (Coccia, 2005a(Coccia, , 2017(Coccia, , 2017b2018a, 2019c, 2019dCoccia and Bellitto, 2018;Coccia and Benati, 2018)Findings here reveal that the share of vaccinated people against COVID-19 increases with the wealth of nations, but it has a physiological limit of about 70% between countries. One of the main issues is the vaccine hesitancy in a portion of population associated with individual freedoms of rich and democratic countries of the Green Pass in Israel, discussions continue regarding its modified reimplementation". Overall then, Green Pass or vaccine passport was originated to be an incentive to support vaccination plans, but some countries in Europe are using this bureaucratic tool to penalize people without vaccination, reducing individual freedoms, increasing the discrimination between people in social, cultural and sporting activities, fostering tensions between different social groups, and as a consequence reducing equity, trust and solidarity between people with consequential socioeconomic issues (Kosciejew et al., 2021;Waitzberg et al., 2021;Wilf-Miron et al., 2021). In the presence of persistent green pass regime, protests and socioeconomic issues are opened up, which will support authoritarian rules to reduce individual freedoms leveraging potential health risks (cf., Wong, 1991). The side effects of this policy of restrictions in countries can be explained with two main aspects that are discussed in following sections.

¨ Politics of fear
Hobbes (1996) maintains that having control over human fears meant holding power in the society. In general, the interaction between fear and politics is a main field of interest in science (Debiec and LeDoux, 2004;Robin, 2004). Gore (2004) argues that the politics of fear is directed to distort the political reality of a nation by creating fear in population that is disproportionate to actual dangers. In fact, in contexts of uncertainty, governments tend to create administration's policies with inconsistencies, ambiguities and little transparency to reduce accountability to the people and the public interest. Gore (2004) also argues that in specific circumstances: " there has been a disturbing willingness-even eagerness-to misrepresent the true nature of the policy involved and its real implications". In addition, Gore (2004)  S.] administration uses fear of the problems of old age to contrive an illusory drug bill that essentially transfers billions from the people to the pockets of the large pharmaceutical companies". Governments can use fear for purposes that are not disclosed, then fear itself can quickly become a self-perpetuating and free-wheeling force that weakens national character, diverting attention from real threats and other problems, sowing confusion (Lupia and Menning, 2009). Hence, the intentional use of fear to manipulate the political process can create many vulnerabilities in population, nation and society. Note: France introduced Green Pass on 21 July 2021; Italy on 6 August for museums, cultural places and events; 1 st September for transportation of long distance; 15 October for all working places and 6 th December 2021 also for urban transportation (subway, buses, etc.). Prewitt (2004) think that institutional fear is a fundamental aspect of liberal thought and constitutional democracy. Arato (2004) argues that Hobbes formulated "a fear of the state of nature, of the war against all, is what drives us to establish something like the modern state". Finally, Arato (2004) shows the important role of "institutional fear" that underpins the social contract in liberal theory. In particular, Arato (2004), focusing on case study of the U.S.A., maintains that liberalism can produce a weak state having a poor regulation of emergency powers, such that the "emergency regime" tends to be constructed largely outside the Constitution generating problematic aspects in society (Prewitt et al., 2004;Robin, 2004). A practical example is the COIVID-19 pandemic crisis, and European countries to increase the max share of people vaccinated (as estimated here, beyond 70% of population) tend to apply politics of fear associated with informal authoritarian rules that stress constitutional principles (e.g., immunity passport), reduce the individual freedoms and create socioeconomic problems, with low benefits to cope with Italy France Spain COVID-19 pandemic. In fact, figure 4 shows that the effects of Green pass regime, based on authoritarian rules, generate a moderate growth of vaccinations that disappears in the short-run, but it generates social issues for the reduction of individual freedoms, the increase of discrimination of people in social, cultural and sporting activities, the growth of tensions between different groups, reduction of equity, trust and solidarity too (Kosciejew et al., 2021;Waitzberg et al., 2021;Wilf-Miron et al., 2021).

¨ Strong leaders and authoritarian rules in democracies
The increase of vaccination in rich and democratic regions, by introducing restrictions and policies based on vaccine passport, is also associated with strong leaders having domestic and international support that can generate a substantial decline of democratic setting (Lavriča and Bieberb, 2021). This tendency of power in strong leaders, in the presence of crisis, is supported by a combination of social insecurity, cultural backlash and economic issues generated by pandemic crisis. To put it differently, the application of authoritarian rules in democratic systems is due to the emergence for strong leaders but also to social and economic insecurity that support authoritarian approaches that are exercised informally (Lavriča and Bieberb, 2021;cf., Coccia, 2019e). In fact, all political leaders guide restrictive interventions in a general framework in which they are considered "pragmatic reformers" and receive initially domestic and international support (Crowther 2017;Günay and Dzihic 2016;Vladisavljević 2019). Thus, the increasing public support to a strong political leader may be one of the causes of the rise in authoritarian rules in the Western countries in the presence of pandemic crisis, leveraging socioeconomic uncertainty and fear in society. These tendencies are generated in an institutional environment and countries having weaknesses of democratic institutions and balance of powers in the presence of emergencies and crisis.

CONCLUSIONS AND PROSPECTS
Findings here reveal that the share of vaccinated against COVID-19 increase with the wealth of nations, but it has a physiological maximum level of about 70% between (rich and democratic) countries. In addition, monarchy and parliamentary monarchy have a higher share of people fully vaccinated against COVID-19 than mixed executives and presidential republic. Some countries in Western world are straining democratic society with restrictions to individual freedoms to increase the maximum share of people fully vaccinated (estimated here) by introducing restriction policies, vaccine certificate and penalties as a rule that create socioeconomic issues, such as discrimination of people in social activities, tensions between different groups, reduction of equity, trust, etc. (Brown et al., 2021;Chantler et al., 2019;Coccia, 2018aCoccia, , 2021cDye and Mills, 2021;Kosciejew et al., 2021;Waitzberg et al., 2021;Wilf-Miron et al., 2021). In particular, results here can explain some abuses in democratic countries based on a combination of the politics of fear and informally authoritarian rules 3 applied by a strong leader under circumstances of social insecurity.
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 total vaccinations in manifold countries. Second, not all the possible confounding factors that affect the diffusion of vaccination are taken into consideration and in future these factors deserve to be controlled for supporting results here. Third, the lack of integration of data with cultural aspects may have influenced the results of vaccination across countries making comparative analyses a problematic approach (Angelopoulos et al., 2020;Coccia, 2018). Fourth, country-specific health and social norms may affect the vaccination and mitigation policies. Finally, the estimated relationships in this study focus on variables in specific months (based on recent data available) but an extension of the period under study is needed in future development of the research here. Thus, the generalization of this results should be done with caution. Future research should consider new data, when available, and when possible, to examine also other variables between countries to explain dynamic relationships under study over time and space and their interaction with vaccination, vaccine certificate, restriction policy and other social norms between countries. Despite these limitations, the results presented here suggests the maximum sustainable level of people vaccinated between rich and democratic countries (that is roughly 70%) and social and economic issues associated with the introductions of policy of restrictions and bureaucratic tools (e.g., immunity passport) to go beyond this limit using politics of fear and strong leaders. Hence, there is need for much more detailed research in these topics and this study encourages further investigations using lessons learned of COVID-19 pandemic crisis, also considering the interaction between effects of restrictions in societies and campaign of vaccination. Overall, then, many Western (democratic) countries are straining society with restrictions to individual freedoms to increase the maximum share of people fully vaccinated (with marginal results) by introducing vaccine passport and autocratic rules that impose restrictions to the movement of individuals who are not vaccinated, reducing equality and fairness between people. These aspects are applied using politics of fear and strong leadership nurtured by institutional context having weak democracy and vague separation of powers, when constitution expressly established that these functions have to be strong to address critical problem of abuse in democracy by our own rulers, our own political authorities who, if uncontrolled or made not accountable, can do great harm to society higher than (pandemic) crisis. To conclude, different factors between countries that are not only parameters related to medicine but also to social and political sciences can explain the effects of COVID-19 pandemic in society not only in terms of health but also in term of human and civil rights that should be accurately assessed to control future negative impact of pandemic crisis on public health, economy and society. It is worth raising the question whether our constitutional ordering of Western and democratic countries is still protecting us from fear and effective tangible democratic reduction that can became a hazardous process, similar to COVID-19 pandemic crisis, that direct future society towards terra incognita of uncertain social events.