Introduction

After the identification of the first case of a novel coronavirus in Wuhan, China, it soon spread to practically every country on the globe. Consequently, it becomes a global disaster and affects every nation, counting Asian countries1. Among the Asian countries, India, Iran, South Korea, Turkey, and Vietnam are the worst-affected nations. Unlike any other virus that has emerged in the past, coronaviruses affect humankind in an enormous and drastic manner. It is remarked as the most severe global disaster experienced by people in the global context since World War II2. The virus, on the one hand, has severe health apprehensions and, on the other hand, brings enormous socio-economic challenges and casualties for the people. In fact, according to recent studies, the recession that emerged from the Corona pandemic was considered the worst of the century because it exacerbated the negative consequences of the 2009 recession3,4.

Existing literature

The virus poses a dissimilar risk level for different age groups5. In reality, a person's age has a substantial role in Corona contamination. Older adults who were 60 years of age or older with pre-existing health abnormalities experienced greater risk than other groups. Contrarily, the risk of pandemic appeared to be minimal among children and adolescents. According to the WHO report6, only 6.3% of older children and adolescents were infected by the virus on a global scale, while only 0.1% died due to disease. These figures are significantly lower than those of other older age groups. Studies have identified numerous factors that have been linked to early adolescents' decreased incidence of Coronavirus. One of the key factors in young people and adolescents having lower virus risks than older people may be the absence of numerous health difficulties, including cancer, renal failure, obesity, and many other disorders7. Additionally, unlike older adults, these groups have a stronger and more adaptive immune system, which may reduce the potential risk of SARS-CoV-28. Besides these factors, studies also confirm that children and adolescents have more sophisticated lymphocytes and natural killer cells to fight against the virus than older adults8,9. This may be another reason for the lower severity among this group.

Even though the severity of the coronavirus is less likely among children and adolescents (particularly in the absence of underlying illnesses), it still affects them in many different ways than other groups10. Firstly, the outbreak of coronavirus raises health emergencies and risks among this group (although of lesser magnitude)11. Secondly, lockdown and school closures associated with the pandemic not only restrict physical activities but also their normal lifestyle12,13. Lastly and most importantly, health emergencies and social distancing bring unprecedented change, which ultimately increases mental health problems14,15. Further, studies claim that the level of anxiety, depression, and substance misuse among adolescents has increased considerably at the time of the Corona pandemic around the globe16,17. According to these emerging studies, the fear of the virus, social isolation, the demands of the new method of schooling, etc., are among the significant causes of such a difficult state18.

In addition, the WHO report6, asserts that even if there is a reduction in the number of instances of viral contamination among adolescents, this result may still be the result of inadequate testing and a lack of general symptoms to detect infection cases in the aforementioned category. According to some claims, it is still feasible for them to get the virus even if their symptoms may not resemble those of other older age groups and instead appear to be a common cold or flu19,20. Understanding the virus's detrimental effects on health, an untreated single incident may raise the likelihood of chronic health problems. Additionally, they might also increase the risk of spreading the virus among people10. It should be noted that the spread of this lethal virus poses a long-term health hazard21,22,23,24. As a result, persons who contracted corona should continue taking their medications, and adolescents are no exception25. Although their death rate was minimal due to their high immunity level, adolescents were also the group that was most negatively impacted by the corona26. Adolescents' mental health and academic progress have been jeopardised because of school closures and family economic turmoil caused by the COVID-19 lockdown24,27. Due to their higher likelihood of being asymptomatic positive, adolescents' corona infection severity was understated28. However, adolescents needed a longer hospital stay to recuperate28. The majority of South Asian countries routinely reported coronavirus case counts, but they did not disclose the virus's effects, such as unstable mental health disorders. Therefore, the true effect of mental health issues linked to the coronavirus is yet unknown or may even be underreported24.

Comprehensive research has been conducted to comprehend the various difficulties relating to the Coronavirus and adolescents. Nevertheless, the efficacy of a nation in regulating coronavirus infection among adolescents is not appropriately addressed. Consequently, there exists a research gap that must be filled in order to develop effective health policies.

Objectives, motivation and novelty of the study

Accordingly, the present study includes three objectives to explore. Initially, the behavioural changes among adolescents in selected Asian countries are explored before, during, and after the pandemic. Then the efficacy of selected Asian countries in regulating the spread of coronavirus among adolescents is examined. Finally, the study involves itself in unravelling the factors responsible for inefficiency in regulating the same. In this regard, the study explores the consequences of Female Political Participation, Good governance practices, and tobacco use among adolescents on a nation’s efficiency in regulating the spread of Coronavirus among adolescents. Notably, the behavioural transmission among the adolescents in selected Asian countries is explored based on two variables, viz., "adolescent suicidal mortality rate (per 100,000)" and "tobacco use in adolescents (%)". The choice of the variables to analyse behavioural changes among adolescents in selected Asian countries is strictly dictated by the availability of the data. The motivation for this investigation is twofold: firstly, adolescents are the future human capital of a country, and health and education are crucial components of that capital. The stage of adolescence is a special phase of human life for building a concrete foundation for excellent health. The extent to which a nation is effective in creating a good health foundation for its demographic dividend must thus be investigated. The present study is exactly doing the same by inquiring about the efficacy of a country in regulating coronavirus infection among adolescents. Secondly, although the coronavirus is a global catastrophe, the present inquiry considered only Asian countries. This is because after the identification of the virus in China, Asian countries, including India, Japan, Taiwan, Thailand, and Vietnam, were the epicenter of the first wave of the virus. Additionally, since most Asian countries followed similar socio-economic and political structures, it is intellectually justifiable to focus on the Asian continent. Furthermore, any empirical research on a pandemic may only be done once the data is available, or by the end of the pandemic. Such empirical analysis helps in understanding the aftermath of the pandemic and aids in the formulation of policies to handle any adverse circumstances and recover from the aftershock. Moreover, the identification of the determinants of inefficiency in regulating adolescent corona infection allows the concerned government to pinpoint the areas that require their attention in order to create a society that is fully developed. Adolescents are the foundation of the economy of the future and the main source of human capital, so every nation's policy must be adequate for their growth and welfare. This justifies conducting such an empirical investigation even after the pandemic has ended. Again, existing literature evidences that corona infestation results in long-term health hazard21,22,23,24. Therefore, even after recovery, it is crucial that the infected person be treated with care. Corona-affected individuals must also get routine health examinations, and adolescents are not an exception in this regard. Adolescents are considered to be the future human capital of any nation; therefore, maintaining good health is a prerequisite for their transformation from humans to human capital. Due to this problem, the current study is still absolutely pertinent even after the epidemic has ended.

The study is novel in various aspects. It is perhaps the first study to involve itself in exploring the relative efficacy of different Asian countries in regulating the spread of Coronavirus among adolescents. Moreover, the identification of the factors responsible for inefficiency in regulating the adolescent coronavirus also makes the study unique. Furthermore, the choice of variables for identifying the factors responsible for the inefficiency of a nation in regulating adolescent coronavirus spread also makes the study novel.

The study is structured as described:

Section "Materials and methodology" presents the data sources, variables, and econometric model to examine the objectives following a brief introduction and specification of the objectives. The empirical results are presented in section "Results". Section "Discussion" presents the social-demographic and economic ramifications of the research findings. Finally, in section "Conclusion, limitation and future study direction", the study comes to a conclusion, offers policy recommendations, identifies its limitations, and specifies its course of further research.

Materials and methodology

The theoretical underpinnings of the stochastic frontier model are discussed in this section. Additionally, this section includes the data sources, variables, and econometric model needed to experimentally investigate the aforementioned aims.

Theoretical foundation

The study aims to scrutinise the efficiency of selected Asian countries in controlling the spread of Corona among the adolescent population. The empirical analysis will be facilitated by Stochastic Frontier Analysis (SFA). Notably, there are well-accepted approaches concerning efficiency measurement, viz., parametric and non-parametric. The SFA is supposed to be a highly acclaimed parametric technique. Contrarily, Data Envelopment Analysis (DEA) is considered the best non-parametric method to measure efficiency. Both approaches have their strengths and weaknesses. DEA is preferred over AFA when price data is not well defined or a concrete output-input orientation cannot be established29,30. Accordingly, the DEA has wide applications in health economics, crime efficiency, etc29,30. However, if the output-input relation is well-defined, then SFA is preferred over DEA for several reasons, including the non-inclusion of "statistical noise", non-utilisation of all information, and the improper identification of the decision-making unit’s efficiency.

Initially, Evans et al.31 and Murray, and Frenk32 and afterward Sankar, and Kathuria33 and Kathuria and Sankar 34, successfully conceptualised the SFA approach to measure health system efficiency. The current paper follows Evans et al.31, Murray, and Frenk32, Sankar, and Kathuria33 and Kathuria and Sankar34, health efficiency concepts. Thus, the Stochastic Production Frontier (SPF) is used to compare the efficiency of the selected Asian countries in regulating adolescent Corona infection. The output indicator in the present paper is the reciprocal of the adolescent Corona infection rate. The output is measured on the vertical axis of Fig. 1. The horizontal axis measures the appropriate societal inputs set.

Figure 1
figure 1

Source: Adapted from Murray and Frenk, (1999) and Evans, et al., (2000).

Performances in regulating adolescent Coronavirus infection.

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Given the set of inputs and state of technology, the maximum attainable output is presented by the frontierr35, and it is presented by the upper line in Fig. 1. Contrarily, the lower line in the figure is the achieved health outcome in the absence of any health facilities. The prime difference between health outcome and firm output is that in the absence of input, output will surely be zero; conversely, health outcome will be a non-zero minimal amount in the absence of health expenditures, simply because all citizens of a country will not die together. Figure 1 presents both the maximum possible as well as the country’s attainable health output, and they are (e + f + g) units and (e + f) units, respectively. Under this diegesis, system performance is the ratio of achieved to potential output36,37 that is,

$$System\;performance = \frac{f}{f + g}$$
(1)

where f is the achieved and (f + g) is the potential output.

Equation 1 is interpreted as "system achieved compared to its potential" after Murray, and Frenk32. Notably, "Farrell’s35, output-based measure of technical efficiency"38 under the present framework allows us to conduct inter as well as intra country health performance comparisons of efficiency in regulating adolescent Corona infection. Farrell’s35, measure of technical efficiency is the ratio of observed to maximum attainable output. Based on SFA, the measurement of the technical efficiency of a country to regulate adolescent Corona infection is facilitated in the paper. The basic model used to explore the said objectives empirically is Battese, and Coelli39 technical inefficiency effects model. The said model allows us to recognise the output-input relationship and the determinants of a country’s inefficiency to regulate adolescent Corona infection simultaneously.

Data

This investigation solely relies on secondary data that has been assembled from several secondary sources. The study collected information from 21 Asian nations for the years 2020, 2021, and 2022. Afghanistan, Bangladesh, Cambodia, China, India, Indonesia, Iran, Israel, Japan, Jordan, Kazakhstan, Kyrgyzstan, Lebanon, Malaysia, Nepal, Pakistan, Philippines, Sri Lanka, Thailand, Turkey, and Vietnam are on the list of Asian nations that are covered. The selection of countries as well as data periods is strictly subject to data availability. In this investigation, the data for the main concerned variable, that is, Coronavirus infection among adolescents, and other variables such as hospital beds per thousand and Stringency index are compiled from https://ourworldindata.org/covid-vaccinations. In contrast, data from the World Bank is gathered on per-capita GDP, doctors per 1000 people, nurses and midwives per 1,000 people, population density (people per square km of land area), Internet use (%), urbanisation (%), and regular paid employment (%). Data for Female Political Participation (% in lower parliament) and Tobacco use in adolescents (%) are compiled from http://archive.ipu.org/wmn-e/classif.htm#1 and the World Health Organisation (WHO), respectively. Table 1 includes a detailed description of the variables, their definitions, and their sources:

Table 1 Overview of variables.
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Variables

The list and classifications of the variables utilised in this study are highlighted in this section. We used Stochastic Frontier Analysis (SFA) since our main goal is to examine country-wide efficacy in controlling the severe course of coronavirus among adolescents. However, three sets of variables- output, input, and exogenous are indispensable for establishing input–output orientation using SFA. Below are the specific descriptions of these variables:

Output variable

According to the WHO, the term adolescent is defined as a group of people whose age is between 10 to 19 years. It is a special stage of human life for building a concrete foundation for excellent health. Further, adolescents are the key contributors to the future workforce of any country40. Therefore, healthy adolescents not only help in human capital formation but also reduce the burden of health expenditure. In the end, this serves as fuel for a nation's economic development. Considering the significance of adolescent health, the present study considers Coronavirus infection among adolescents as an output variable. Although the death rate of adolescents due to the virus, mental health, depression, etc., can reflect the health status of this group during the Corona pandemic, we emphasised only the infection rate based on the availability of data. The decision regarding the output variable is strictly based on data availability. Here, "reciprocal of coronavirus infection among adolescents" is selected as our outcome variable because our primary objective is to investigate the efficiency of Asian nations in regulating coronavirus infection among adolescents. We thought about reciprocal with the concept that the lower the value, the more efficient it will be in controlling adolescent coronavirus infection. We can take into account the "death rate of adolescents from coronavirus" in particular. A zero value in this situation might lead to inconsistencies in later empirical research; hence, the relevant nation should be removed from the analysis. Furthermore, adolescents are not particularly vulnerable to coronavirus; therefore, a fatality rate of nil is extremely typical. We select "reciprocal of the coronavirus infection among adolescents" as our outcome variable in light of this restriction.

Input variables

A precise array of inputs is essential for the assessment of the Stochastic Production Frontier (SFA), akin to the output variables. The input variables that represent a nation's health infrastructure and wellness must be included when our aim is to assess the efficiency of health outcomes. Consequently, we have included an assortment of factors that depict a country's health infrastructure, such as the percentage of the population that has received all recommended vaccinations (Fully vaccinated (%)), the number of hospital beds per thousand people, the per-capita GDP, the number of doctors, nurses, and midwives per thousand people, and the population density (the number of people per square kilometre of land), among others. These factors are regarded as inputs because they have a direct or indirect impact on a country's health scenario and outcome. Moreover, the variables hospital beds per thousand, doctors per thousand, and nurses and midwives (per 1000) serve as direct indications of the scenario of the health infrastructure. Furthermore, the country's economic health and population and demographic features are represented by per-capita GDP and population density, respectively, which indirectly affect health outcomes. A higher GDP per capita increases resource availability, which increases the likelihood that health expenditures may increase. Contrarily, rapid illness dissemination, especially infectious diseases, makes epidemics more likely in areas with increased population density31,41. The input variables can be measured in a variety of ways, including in monetary form, percentage form, physical form, etc. It is quite challenging to find data in a comparable style because the study contains information pertaining to many Asian countries. Consequently, we incorporate both physical and monetary input variables. Simultaneously, some input variables are expressed in percentage form as well. Table 1 lists the descriptions of the variables.

Exogenous variables

It is a fundamental tenet that better health outcomes result from non-health factors as well as greater access to healthcare services and infrastructure38. This is because health factors are not sufficient to achieve a positive health outcome. Positive health outcomes require precise socially and economically directed conditions and programmes along with health services or infrastructure42,43. Accordingly, in this study, we used a number of non-health factors that are indirectly related to preventing Coronavirus infection in adolescents, including Female Political Participation (% in lower parliament), Stringency index, Internet use (%), Urbanisation (%), Tobacco use in adolescents (%), and Regular wage employment (%). All these factors are termed exogenous variables (the details are presented in Table 1). In this instance, the variables Female Political Participation (% in lower parliament) and Stringency index are used to quantify the effect of female leaders on political decision-making and the government's response to controlling the pandemic scenario, respectively. Simultaneously, urbanisation is used to analyse the aftermath of industrialization and corresponding rural–urban migration on the spread of coronavirus among adolescents in a country. Internet usage serves as a proxy for the level of digitalization and information availability connected to the coronavirus epidemic and its consequent circumstances. Tobacco use in adolescents (%), and Regular wage employment (%) are two exogenous variables that are used in the study to demonstrate negative health behaviours and sustained employment conditions, respectively. These variables also show the effects of these exogenous variables on the spread of the Coronavirus among adolescents.

Econometric model

The efficiency estimates in this paper will be facilitated by the application SFA, and accordingly, we will estimate SPF. The corresponding SPF for panel specification is given by equation (1):

$$y_{it} = g\left( {x_{it} ,\beta } \right)\exp (V_{it} )TE_{it}$$
(2)

Here y presents health output, x and \(\beta\) are vectors of arguments and the corresponding vector of parameters to be estimated of the production frontier. x includes a number of indicators representing access and availability of health infrastructure resources which have direct aftermath on health outcome. All variables are transformed into logarithm form to take care of the heteroscedasticity problem. \(\exp (V_{it} )\) presents the random error component which is outside the control of the country. The equation includes another error component \(TE_{it}\) and it is expressed as \(TE_{it} = \exp \left( { - U_{it} } \right)\) after Kumbhakar44. The assumption related to \(TE_{it}\) is \(TE_{i} \le 1\) hence \(U_{i} \ge 0\)44. Thus the error is one-sided. Equation (2) in modified form may be written as:

$$y_{it} = g\left( {x_{it} ,\beta } \right)\exp (V_{it} )\exp \left( { - U_{it} } \right)$$
(3)

The assumptions concerning the two error terms are:

$$V_{it} \sim IIDN\left( {0,\sigma_{V}^{2} } \right)\;{\text{and}}\;U_{it} \sim IIDN\left( {\omega_{it} \theta ,\sigma_{U}^{2} } \right).$$

Here, \(\omega_{it}\) is a (pxq) vector of exogenous variables which are supposed to influence the controllable inefficiency of the country related to health outcome. The corresponding unknown parameters are presented by \(\theta\), a vector of (qxp).

The corresponding distribution of both error terms (random and technical efficiency) are Normal-Truncated Normal as directed in Stevenson45. Notably, both the error terms are independent of each other and also independent of the explanatory variables. After Battese and Coelli39, the identification of the determinants of technical efficiency is facilitated by the following equation:

$$TE_{it} = \exp ( - U_{it} ) = \exp ( - \omega_{it} \theta - \varepsilon_{it} )$$
(4)

\(\varepsilon_{it}\), the random variable follow truncated normal distribution with ‘0’ mean and \(\sigma_{U}^{2}\) variance. Here, \(\varepsilon_{it} \ge - \omega_{it} \theta\), implying point of truncation is \(- \omega_{it} \theta\). The maximum likelihood estimators of the parameters of both stochastic production frontier and the inefficiency effects model can be obtained simultaneously by using FRONTIER-4.139,46. The corresponding variance parameters are:

\(\sigma^{2} = \sigma_{V}^{2} + \sigma_{U}^{2}\) and \(\gamma = \frac{{\sigma_{U}^{2} }}{{\sigma^{2} }}\), where \(\gamma\) ranges from 0 to 1 based on the dominant force of \(\sigma\) and \(\sigma_{u}\) respectively.

Based on our specified list of output, inputs and exogenous variables, the Battese and Coelli39 assuming a log-linear version of the Cobb–Douglas model can be expressed as follows:

$$\begin{aligned} & \ln \left( {\frac{1}{{Y_{it} }}} \right) = \alpha_{0} + \alpha_{Vaccinated} \ln (Vaccinated) + \alpha_{Beds} \ln (Beds) + \alpha_{PGDP} \ln (PGDP) + \alpha_{Doctors} \ln (Doctors) \\ & \quad + \alpha_{Nurses} \ln (Nurses) + \alpha_{Population\;density} \ln (Population\;density) + \left( {V_{it} - U_{it} } \right) \\ \end{aligned}$$
(5)

Here, ln presents natural logarithm.

The corresponding inefficiency effects equation is present as follows:

$$\begin{aligned} & U_{it} = \theta_{0} + \theta_{WPP} \ln (FPP) + \theta_{SI} \ln (SI) + \theta_{Internet} \ln (Internet) + \theta_{Urban} \ln (Urban) \\ & \quad + \theta_{Tobacco} \ln (Tobacco) + \theta_{Employment} \ln (Employment) + \varepsilon_{it} \\ \end{aligned}$$
(6)

Here, \(U_{it}\) is ith country’s controllable inefficiency for tth time period and FPP is the Female Political Participation (% in lower parliament), SI is Stringency index, Internet is Internet use (%), Urban is Urbanisation (%), Tobacco is Tobacco use in adolescents (%) and Employment presents Regular wage employment (%).

The application of the statistical packages FRONTIER-4.146 gives maximum likelihood estimates of parameters of (5) and (6) simultaneously.

Results

The empirical results of this pre-dominantly empirical study is presented in this section.

Adolescent behavioural changes in selected Asian countries in pre-and-post pandemic scenario

The adolescents’ behavioural changes in the current paper are analysed based on two indicators, viz., adolescent suicidal mortality rate (per 100,000) and tobacco use in adolescents (%) from 2019 to 2023. The choice of the variables and the study period for this purpose are completely dictated by the availability of the data. For the entire study period, Kazakhstan reports the highest mean for "adolescent suicidal mortality rate (per 100,000)", followed by India, and the lowest corresponding figure is obtained for Afghanistan. Contrarily, considering tobacco use in adolescents (%), the highest figure is obtained for Lebanon for the entire study period, and the corresponding lowest figure is reported for Cambodia in 2019 and Israel for the subsequent study period. Thus, we can say that there is not much variation in the adolescents’ behaviour considering these two indicators before and after the pandemic. The information is presented graphically in Figs. 2 and 3, respectively.

Figure 2
figure 2

Source: Authors’ own presentation based on World Bank data.

Adolescent suicidal mortality rate (per 100,000) across Asian Countries.

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Figure 3
figure 3

Source: Authors’ own presentation based on World Bank data.

Tobacco use in adolescents (%) across Asian countries.

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The summary statistics of these two variables for selected Asian countries are presented in Table 2.

Table 2 Summary statistics of adolescent behavioural changes in selected Asian countries.
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Table 2 discloses that the highest mean of the variable, "adolescent suicidal mortality rate (per 100,000)" is reported for Kyrgyzstan (6.97), and the country is followed by Pakistan (5.95). Notably, Pakistan reports the lowest SD (0.01), while Kyrgyzstan (1.22) reports the corresponding highest figure. This means that although the adolescent suicidal mortality rate (per 100,000) in Kyrgyzstan is high, the highest SD indicates it will not persist in the future; however, the same conclusion is not true for Pakistan. The high value of SD indicates that the higher mean value is also likely to persist in the future.

The highest mean value of tobacco use in adolescents (%) is obtained in Lebanon (29.05), followed by Malaysia (23.2). The corresponding SD value for Cambodia is also high (4.95). This indicates the tendency towards higher tobacco consumption among adolescents’ is likely to persist in Cambodia in the near future. Contrarily, Japan reports the lowest mean, 1.86, in this regard, and the corresponding SD is also very low, 0.93. This indicates Japan will be successful in maintaining a lower tobacco addiction among adolescents in the near future also.

Two-way ANOVA of adolescent behavioural changes in selected Asian countries

The discussion above makes it clear that no appreciable behavioural changes were noticed in Asian adolescents’ population before or during the epidemic. However, it is noteworthy that adolescent behaviour varies among Asian nations. Only a graph or the analysis of descriptive statistics may not be able to clearly show such a discrepancy. Conducting an ANOVA test is the best technique to identify differences in adolescent behaviour among Asian nations. A two-way non-parametric ANOVA will be appropriate for this purpose because we are dealing with panel data. This study used a two-way non-parametric ANOVA test, and the results are shown in Table 3 for both indicators.

Table 3 Two-way ANOVA of adolescent behavioural changes in selected Asian countries.
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The table reveals that there are two comparable F-statistics to represent differences in the two specified variables by country and by year. Notably, both the F-statistics, which are, country- and year-wise, are significant at the 1% level for the two variables, viz., adolescent suicidal mortality rate (per 100,000) and tobacco usage in adolescents (%). The associated F-statistics value is excessive in each of the four situations. This enables us to rule out the null hypothesis that there is no regional variation, and we draw the conclusion that adolescents conduct varies significantly among Asian nations. These behavioural variations may affect how Asian adolescents' Corona infection is regulated.

Disparities in adolescent corona infection of selected Asian countries

The outbreak of Corona has several consequences for human life. Every age group on the planet, including adolescents, is impacted. Although adolescents seem to be at relatively low risk for the virus, it substantially disrupts their lives in a number of ways. Health issues, social exclusion, and school closures have an impact on people's physical and mental health as well as their social lives. Research focused on the insinuations of Corona suggests that the level of anxiety, depression, and substance abuse among the adolescent population has significantly increased around the globe during the Corona pandemic16,17. Several current studies indicate that the fear of the virus, social isolation, and the demands of the new educational model are some of the key factors contributing to this difficult situation18.

Despite the fact that there has been less Corona contamination among adolescents, WHO, 6 states that this may be because there hasn't been enough testing and there aren't any overt signs of infection among the aforementioned demographic. It is undeniably true, nevertheless, that the infection may raise the likelihood of long-term health issues. Figure 4 shows disparities in adolescent Corona infection among selected Asian nations.

Figure 4
figure 4

Source: Authors’ own presentation based on World Bank data.

Total number of adolescents' Coronavirus infection across selected Asian countries.

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The aforementioned graph demonstrates the stark differences in the spread of Coronavirus infection among adolescents in the selected Asian nations. From 2020 to 2022, India was one of these countries that seemed to be most impacted. In fact, as seen in Fig. 5, India had an increase in the number of infected adolescents during the time period.

Figure 5
figure 5

Source: Authors’ own presentation based on World Bank data.

Pie-chart of total number of adolescents' Coronavirus infection in India over time.

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Following India, Jordan, Thailand, Kazakhstan, and China are the most severely affected nations concerning adolescent Corona confirmed cases during the period. Interestingly, it is also seen from Fig. 4 that, although China is the first country where the Coronavirus has been detected and has endured many condemnations, it is effectively able to arrest the virus spread among adolescents in 2020 to a greater extent.

The discrepancies in regulating adolescents’ coronavirus infection may also be noticed from the summary statistics as presented in Table 4.

Table 4 Summary statistics of adolescent Corona infection in selected Asian countries.
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Table 4 discloses that the highest average infection rate among adolescents’ is obtained for India (3,924,522) and the corresponding lowest figure is for Cambodia (8647.567). The maximum dispersion in regulating adolescents’ coronavirus infection, as dictated by SD, is obtained again for India, and the lowest figure is reported for Afghanistan. This indicates that India's success in lowering coronavirus infection among adolescents will only be fleeting.

Discrepancies in countries performances encourage us to explore the efficacy of Asian countries in regulating adolescent Corona spread. However, a country's efficiency in controlling adolescents’ Corona cannot be understood solely by diagrammatic analysis. To understand a country's efficacy in controlling severe infections among adolescents, an in-depth assessment is needed. Prior to that, it's crucial to examine regional variations in regulating adolescents’ coronavirus infection.

Two-way ANOVA of adolescent Corona infection of selected Asian countries

After scrutinising the nation-wide scenario of coronavirus infection among adolescents in Asia, we noted that there is considerable variation in the extent of infection. However, it is not possible to establish the fact only by considering a diagrammatic explanation. In this regard, ANOVA is one of the important techniques that helps to examine whether there is any significant variation or not. Particularly in this paper, we have employed a two-way ANOVA to establish if there is any significant variation in coronavirus infection among adolescents or not. The result of the ANOVA is displayed in Table 5:

Table 5 Two-way ANOVA of adolescent Corona infection in selected Asian countries.
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The result of the ANOVA visualised in Table 5 provides two different types of F statistics. The F statistic concerning nation-wise variation suggests that there is significant variation in the extent of Corona infection among adolescents in selected Asian countries. This is true because the F statistic (4.59) with 20 degrees of freedom is statistically meaningful with less than 1% significance. Again, the significant value of the F statistic (3.87) concerning year-wise variation also confirms the existence of significant variation in the extent of infection during the periods. Therefore, the result of the ANOVA confirms that the extent of infection varies not only across years but also across selected Asian nations. In this light, it will be appropriate to examine the efficiency of different Asian countries in regulating adolescents’ coronavirus infection.

Pesaran's test of cross sectional independence

A common phenomenon of panel data is that it exhibits erroneous cross-sectional dependency in error47. Such inter-correlation not only makes the estimators of either fixed effects or random effects models unbiased but also inconsistent. Thus, prior to estimating any model of panel data it is necessary to check cross-sectional independence of the error. In this regard, the Pesaran test48, is the most acclaimed method. The test result is presented in Table 6.

Table 6 Pesaran's test of cross sectional independence.
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The test result concludes no cross-sectional dependence, as the corresponding "Pesaran’s test of cross-sectional independence" value is −1.252 with a probability of 1.7893. Moreover, the value of the "average absolute value of the off-diagonal elements" is 0.651. Thus, we accept the null hypothesis of no cross-sectional correlation in errors.

Factors influencing adolescent Corona infection of selected Asian countries

We used the panel regression approach to examine the key factors of Coronavirus infection in adolescents, as our inquiry is based on panel data. Fixed Effects (FE) and Random Effects (RE) regression are two distinct types of regression results that are produced using panel regression analysis. The findings are shown in Table 7.

Table 7 Random-effects GLS regression and Fixed-effects (within) regression of stochastic production frontier function for whole panel.
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We begin our investigation with the RE model. The findings demonstrate that Full vaccination, Doctor per 1000, and Stringency index all significantly affect the control of adolescent Corona infections. Among these factors, the negative value of the estimated coefficients of full vaccination suggests that the higher the level of fully vaccinated adolescents, the lower the likelihood of infection among them. Again, negative doctor per 1000 coefficients suggest that having more physicians around will assist to reduce infection. As evaluated by the Stringency Index, the model also predicts that a stronger government response to the virus will help reduce infection in the chosen nations. Contrarily, the results of the FEM show that the only important influences on adolescents’ infection are full vaccination and the doctor per 1000 variables. Similar to REF, FEM shows that full vaccination and the number of doctors per 1000 patients have a detrimental effect on adolescents’ infections. This suggests that increasing the use of these predictors might lower the risk of infection among adolescents in the Asian nation. The discussion section talks about the possible reasons for these empirical findings.

We may assume that REM is more appropriate than FEM based on the values \(R^{2}\) (Within), \(R^{2}\) (Between), and \(R^{2}\) (Overall) for goodness of fit. Nevertheless, selecting the best model is not reasonable based solely on the quality of fit. In this case, the Hausman test is required to confirm that the particular panel regression model is adequate and suitable. The subsequent section analyses the outcome of the Hausman test.

Hausman test and model selection

For panel regression analysis, there are two different types of effects models: Fixed Effects Model and Random Effects Model. We may compare the two models using the Hausman test for specification, which also helps us select the best model for analysis. Table 8 presents an overview of the test's outcomes.

Table 8 Hausman Test to choose between Random Effects and Fixed Effects Model.
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The results of the Hausman test presented in Table 8 suggest that the value of \(\chi_{10}^{2}\) is 15.24 and it is not statistically meaningful as its probability is, Prob \(> \chi^{2}\) = 0.123. Therefore, the test results authenticate that the RE model is suitable for this inquiry. This again authorises us to apply the technical inefficiency effects model in the SFA framework. Consequently, we have utilised the technical inefficiency effects model in the stochastic production function related to panel data49.

Efficiency estimates across Asian countries in regulating adolescent Corona

The efficiency estimates of different Asian countries in regulating adolescent Corona infection are discussed in this section. The divergences in the data are ensured by the summary statistics of the involved regression variables (see Table A.1). The efficiency score of all the Asian countries in regulating Corona is presented in Table 9. The benchmark for separating efficient countries from inefficient ones is the overall panel mean efficiency score of 0.371850. Correspondingly, if a country’s efficiency score exceeds the overall panel mean efficiency score, the country will be recognised as technically efficient; otherwise, it will be technically inefficient. In particular, the efficiency score of Malaysia is 0.7263, greater than the overall mean efficiency score of 0.3718, and thus the country is considered to be technically efficient in regulating adolescent Corona infection.

Table 9 Efficiency score of regulating adolescent Corona infection of Asian countries.
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Based on this benchmark, 10 out of 21 countries have become efficient in regulating adolescent CORONA infection. This indicates that, on average, 48% of countries are efficient in regulating adolescent CORONA infection. Furthermore, based on this benchmark, the highest efficiency is obtained for Kazakhstan (0.9557), followed by Israel (0.8761) and Kyrgyzstan (0.8326). Contrarily, the least efficient country on the list is Afghanistan (0.0004), followed by India (0.0056) and Pakistan (0.0134). As the analysis involved panel data, we have also performed a year-wise comparison of efficiency. Considering yearly mean efficiency as a benchmark, we observe that in 2020, 2021, and 2022, only 10, 9, and 8 countries, respectively, out of 21 are efficient in regulating adolescent Corona infection. This indicates, based on yearly mean efficiency scores of 48%, 43%, and 38%, that countries are efficient in regulating adolescent CORONA infection in 2020, 2021, and 2022, respectively. The best and worst performers on the list are Kazakhstan and Afghanistan, respectively, in 2020, and the ranks remain unaltered in the subsequent years as well.

Notably, the efficiency score is a relative performance score, and it is only an indicator of how well one country is performing relative to the other in regulating adolescent CORONA infection. This efficiency score does not specify a hierarchy in relation to real health outcomes. In particular, the panel mean efficiency score of Bangladesh is only 0.0191 and holds the 18th rank in the list. The country is recognised as technically inefficient based on our benchmark. However, when considering the actual adolescent Corona infection rate, Bangladesh holds the 8th position with a mean adolescent Corona infection of 85,152.97. The efficiency score of the existing health system stipulates that if Bangladesh could operate its health system as efficiently as Kazakhstan, the country could regulate adolescent Corona infection more appropriately.

Technical inefficiency effects: determinants of efficiency

The output-input orientation as well as the determinants of country specific inefficiency are discussed in this section. The empirical findings related to technical inefficiency effects model is presented in Table 10.

Table 10 Maximum likelihood estimates of the SPF of regulating adolescent Corona infection for selected Asian countries.
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The first part of the analysis involves the discussion of the output-input relationship in the SPF framework. The output variable is the reciprocal of the adolescent Corona infection. The analysis involves six inputs and vaccinated, beds, doctors, nurses, and population density have statistically meaningful influences on output. The sign of the estimated coefficients predicts that an escalation of vaccinated, doctors, nurses reduces adolescent Corona infection. Contrarily, an increase in beds and population density increases adolescent Corona infection. The possible explanation of such an empirical result is discussed in the discussion section.

Particularly intriguing are the actual findings of the estimated coefficients of the inefficiency impacts coefficients. The negative sign of the computed coefficient predicts that the country's controllable inefficiency in regulating adolescent Corona infection may be diminished by focusing on these elements. The current analysis involves six exogenous variables.

The factors that have a substantial impact on the country's inability to reduce the adolescent Corona infection are SI, urban, internet, tobacco and employment. Here, SI is a proxy for good governance. The improvement of SI, internet and employment escalates the efficiency of a country to regulating adolescent Corona infection. Contrarily, an increase in adolescent tobacco consumption and urbanization enhances the inefficiency of a country's efforts to regulate adolescent Corona infection. All the estimated coefficients are significant at a permissible level. Here, WPP is the proxy for women’s political empowerment. Interestingly, the sign of the WPP predicts that an enhancement of women’s political empowerment escalates the efficiency of the country in regulating adolescent Corona infection. However, because of the time invariances of the data, the estimated coefficient becomes statistically insignificant. The discussion section deals with the explanation of such empirical results.

Notably, each of the included variance parameter is significant at various levels. The statistical significance of the variance parameter, \(\gamma\) validates the assumption of a half normal distribution of the error term. Here, the value of \(\hat{\sigma }_{s}^{2}\) is 2.569 which is statistically significant, implies the accuracy of the provided assumptions about the distribution of the composite error term. The value of \(\gamma\) is 0.251 and it is statistically significant at the 1% level. This insinuates that country-specific technical efficiency is crucial in explaining the overall variability of the health system. Additionally, the model is viable, as seen by the estimate linked to the sigma-squared of the technical inefficiency effects, which is rather substantial. Indicating that the inefficiency effects are anticipated to be particularly important for Asian countries in lowering the adolescent Corona infection, the estimate for the variance parameter,\(\gamma\) is considerably different from "0". The variance parameters' statistical significance validates the model and makes it appropriate for usage.

The model convergences is authenticated by the Log(likelihood) value of -119.784 and the high value of Likelihood Ratio Chi-squares 25.817 also take the adequacy of the specification into consideration.

Discussion

The possible explanation of the empirical result is presented in this section. As we have utilised39, "technical inefficiency effects" model. Hence, it has two subsequent parts of estimates, viz., the production frontier and the inefficiency parameters. The output-input relation reveals that the regulation of adolescent Coronavirus spread is influenced by Vaccinated, Beds, Doctors, Nurses and Population density at various levels of significance. A better adolescent’s vaccination status decreases the risk of contracting Corona, according to the sign of the estimates for the regressor "Vaccinated". The patent conclusion is reinstated as a result. Vaccination serves as a preventative measure since it is well acknowledged that "prevention is better than cure51,52". The risk that a person would be seriously or even at all afflicted by the virus decreases with vaccination, and this is true for adolescents everywhere38,53,39, model is considered to be time-invariant. However, as we considered a very short panel for our analysis, this limitation had little impact on the final score. Moreover, the "adolescent suicidal mortality rate (per 100,000) and tobacco usage in adolescents (%)" data are used to illustrate the behavioural changes among adolescents in Asian countries. In this instance, "number of adolescents suffering from mental depression" would be a more pertinent metric. However, the lack of data prevents us from taking this variable into account. Additionally, the listed two variables are taken into account for 2019 to 2023 while studying the modifiable change in adolescents' behaviour. The results could change if more time periods were included. Again, the lack of data forced us to focus exclusively on those five time points.

Regarding the study's future direction, we want to emphasise that, subject to the availability of pertinent data, we are serious about expanding the study to include all Asian nations as well as the rural and urban economies separately. We also prefer to take into account a few other factors, such as female political leaders, standard of living, number adolescents’ mental depression cases, etc., that might affect how well a nation controls an infectious disease. Additionally, we intend to continue the study for a longer period of time to capture pre-and-post pandemic scenario.