Assessing the Efficiency of Public Health and Medical Care Services in Curbing the COVID-19 Pandemic in Sub-Saharan Africa: A Retrospective Study

In the late of December 2019, a new coronavirus (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV 2) emerged from the city of Wuhan, China and was subsequently declared a pandemic by the World Health Organization (WHO) on March 11, 2020 after it had spread to many countries across the globe. On February 28, 2020, the Sub-Saharan Africa (SSA) reported its first case in Nigeria, and it has since spread to all countries in SSA. Several public health and medical care measures were rolled out by many countries to stem the tide of the spread at the height of the pandemic, between February 28, 2020 and February 28, 2021, period covered by this study. This paper evaluates the levels of health system efficiency of the COVID-19 public health measures and medical care services and their determinants across Sub-Saharan African (SSA) countries using country-level data for those countries. The data was analyzed using bootstrap data envelopment analysis (DEA) and other advanced econometric analyses that produce robust estimations of the relationship between health systems efficiency and their determinants. The general finding of the study suggests that there is more room for health systems in SSA to improve their technical efficiency in fighting the COVID-19 pandemic. The most important determinants of health system efficiency in the fight against the spread of the virus were GDP per capita, population density, temperature levels, and quality of governance. Adequate health system preparedness and human resource strategies geared towards recruiting and/or retaining well-qualified and experienced healthcare workers to provide professional services would prove critical in containing pandemics of this nature. efficiency of the studied countries in flattening the COVID-19 contagion curve (i.e. reducing the rate of infections). This was done by evaluating the output (the number of days left in the cycle) against the inputs directly employed to flatten the curve (number of COVID-19 tests per one million population, NPIs stringency index, and healthcare expenditure as a percentage of GDP). The first-stage analysis revealed that health systems in SSA could have improved the results obtained by 36% given the same resources and the public health measures implemented. Again, the average efficiency scores decreased from low-income (0.70) and lower-middle-income (0.63) countries to upper-middle-income countries (0.46). The second-stage procedure shows that temperature levels and population density are significantly and negatively correlated with the performance of health systems in reducing the rate of COVID-19 infections. The final empirical frontier model examined the efficiency of medical treatments of COVID-19 patients of the healthcare systems in the SSA. The examination was carried out using two outputs (number of recovered COVID-19 patients per thousand cases and survival rate of COVID-19 patients) against four inputs (number of COVID-19 tests per one million population, NPIs Stringency Index, number of inpatient beds per thousand population, and number of physicians per thousand population). In this model, it was observed that the average efficiency scores increases from the low-income and lower-middle-income countries to upper-middle-income countries. The second-stage analysis shows that good governance and aged population are significantly and positively correlated with the performance of health systems, whereas GDP per capita and prevalence of tobacco consumption worsen the performance from the perspective of medical treatment of COVID-19 patients. The general finding of the study suggests that there is more room for health systems in SSA to improve their technical efficiency in fighting the COVID-19 pandemic. The findings also suggest that specific environmental factors significantly influence the level of health systems efficiency. These findings provide important policy implications for health systems to improve the technical efficiency in curbing the COVID-19 pandemic in particular, and by inference any other health epidemic or pandemic that may occur in future, by learning from the good performers (benchmarks).

lockdown, doctors per thousand population, total COVID-19 tests per one million population, and health expenditure as the percentage of GDP. The results of the study showed that while 12 of the assessed countries were efficient 19 were inefficient in their use of resources to flatten the contagion curve. Germany, Canada, USA, and Austria were among the countries that were found to be inefficient. Both studies were conducted just in the early few months of the outbreak of the COVID-19 pandemic when most countries were at early stages of the viral infections. These two studies, therefore, are limited in scope in terms of examining the disease trajectories of the virus and its associated responses by various health systems. A lot has changed after these two studies were conducted. No study has been carried out in the setting of SSA, a region predominantly characterized by precarious health systems, widespread inadequate supply of health resources, and frequent outbreak of pandemics and epidemics such as Ebola, yellow fever, cholera, HIV-AIDS, and dengue fever (Mboussou et al., 2019). Even though the SSA is prone to outbreak of epidemics and pandemics, to the best of my knowledge, no research has been conducted to evaluate the efficiency with which mobilized resources are used to curb their spread. The study intends to assess the efficiency of health systems in SSA in fighting an outbreak of an epidemic or pandemic using the COVID-19 pandemic as a case study. This study is motivated to fill these gaps in the literature, making significant and original contribution by estimating the levels of efficiency in the fight against COVID-19 and identifying the sources of the inefficiencies in the SSA setting.

Conceptual Framework
In order to address the objectives of this study, three models were employed to assess the efficiency of healthcare resources spent on curbing the COVID-19 pandemic as depicted in Figure 1. Each of the three models included different input and output variables to distinguish between a production function that consisted of inputs that are mostly geared towards COVID-19 preventive and preparedness of public health measures (Model 1), a production function that incorporates inputs typically based on flattening the COVID-19 contagion curve (Model 2), and a production function that comprises mainly of inputs aimed at medical treatment of COVID-19 patients (Model 3). Table 1 presents the definitions and data sources of the input and output variables included in health production functions.

Level of Health System Efficiency Inputs Outputs
Model  This study adopted the two-stage approach, the efficiency indices were first estimated using the health production function (i.e. Efficiency of Healthcare Systems) and then analysis of the effect of health systems' environmental variables on the efficiency indices was undertaken (i.e. Determinants of Health System Efficiency). Thus, the datasets used for this study comprises two different sets of variables. The first set of variables considered were those underlying the health production functions that were used for the estimation of the efficiency indices. The second set of variables consisted of health system characteristics which are outside the purview of the managers of the health systems and healthcare policies that are somehow under the control of policy-makers and influence the functioning of the health production process across SSA countries.

Data Envelopment Analysis
Two major techniques are widely used in measuring healthcare system performance, namely the stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The DEA approach is particularly useful in measuring efficiency performance of non-profit oriented public organizations such as public healthcare facilities and public utilities. Thus, the use of the DEA approach dominates in literature with regard to measuring efficiency performance of healthcare systems (Hollingsworth & Peacock, 2009). The main advantage of DEA approach is that it can accommodate multiple inputs and multiple outputs measured in different units (Charnes et al., 1994). It is also capable of including exogenously determined environmental variables to explain the differences in the efficiency scores (Banker & Morey, 1994). The DEA model defines efficiency as the ratio of the weighted sum of outputs to the weighted sum of inputs (Mozaffari et al., 2022), which allows for the comparison of performance among countries as to how well each country converts inputs into outputs. Inefficiency is then measured as the ratio of actual to 'optimum' performance. The fundamental concept underpinning the DEA approach is the production function. It uses non-parametric technique of linear programming to estimate production frontiers without making any a priori assumptions about the functional form of the related production technology. Today, the scope of the use of DEA models has expanded beyond efficiency measurement to many applications in benchmarking and generating indices as have been reported in the literature (Emrouznejad et al., 2008). This study followed the DEA approach initially developed by Farrell (1957) and later improved by Charnes, Cooper, and Rhodes (called CCR model) in 1978. The CCR model was further enhanced by Banker, Charnes, and Cooper (called BCC model) in 1984. The CCR model assumes that production has a constant return to scale (CCR), denoting that any change in the input results in a proportionate change in the output. However, the BCC model assumes a variable return to scale (VRS) in production, meaning a change in input results in either an increase or a decrease in output. The ratio of the technical efficiency scores from the CCR model to the BCC model represents scale efficiency (Cooper, Seiford, & Tone, 2007). This study adopted VRS approach since the output variables (such as recovered COVID-19 cases) may not change proportionately with changes in the input variables (such as NPIs Stringency Index). Again, as explained in the literature (Hollingsworth & Smith, 2003;Olesen et al., 2015) the CCR formulation of DEA should not be used when the dataset include ratio rather than absolute numbers as input and/or output variables since the estimation of the efficiency scores is affected. According to Hollingsworth and Smith (2003), if it becomes necessary to use ratio variables in order to reflect accurately the underlying production function and due to the nature of the available data (as in the case of this study), the BCC formulation of DEA should be used as it is verified to handle such data well.
DEA models have different orientations including input-minimization and output-maximization (Aristovnik, 2012;Martic et al., 2009). The former minimizes inputs while maintaining the prevailing levels of outputs and the latter maximizes output while maintaining the current levels of inputs. This paper used the DEA output-maximization orientation because on the SSA region, the need for healthcare services are poorly met (Fullman et al., 2018), thus, it would be unethical to reduce the amount of healthcare services provided to achieve efficiency goal (Hernández & Sebastián, 2014). Again, the use of output-oriented model is justified in healthcare due to limited control of the managers of the healthcare system over inputs. In most countries in SSA, major decisions regarding investment and recruitment into the health sector are mostly taken by political government departments (Cheng et al., 2016). The study adopted VRS approach with output-maximization orientation DEA model to measure technical efficiency of health systems. Thus, assuming there are inputs and outputs for DMUs (health systems). Let represents the vector of outputs, the vector of the inputs, is the ( × ) input matrix, and is the ( × ) output matrix. Then the standard VRS output-oriented DEA is specified as: where is a scalar that satisfies ≥ 1 and − 1 measures the proportional output expansions which can be attained by the health system; and is a ( × ) vector of constant that measures the weights used to compute the location of an inefficient health system if it were to become efficient.

Second-Stage Analysis: Determinants of Health System Efficiency
The two-stage DEA is being used to investigate factors such as health-system characteristics and healthcare policies that are associated with the technical efficiency scores estimated at the first stage in the previous section. These factors (including NPIs) are usually under the control of health-policy decision makers but not under the control of decision-makers in the health production process such as healthcare providers and patients (de Cos and Moral-Benito, 2014). In most of the DEA literature, Tobit regression is usually employed to account for the effects of these factors (often referred to as environmental variables) on the technical efficiency. This is done by regressing the technical efficiency scores estimated at the first stage against a set of environmental variables as follows: where is the technical efficiency score, is the vector of environmental variables that affect the technical efficiency health system, is a vector of the parameters to be estimated, and is the error term which is assumed to be identical, independently and truncated normally distributed with constant variance σ and zero mean. This analysis plays a crucial role in providing useful information on available alternatives to improve efficiency performance of health systems. However, Simar and Wilson (2007) argued that such conventional statistical inferences are inappropriate since the first-stage DEA scores and the environmental variables in the second-stage are highly dependent on each other and hence would violate the basic assumptions of regression analysis. Therefore, Simar and Wilson (2007) recommended the use of bootstrap DEA methods. This study employed the bootstrap DEA model to investigate the determinants of health system performance in curbing COVID-19 pandemic. Algorithm #2 suggested by Simar and Wilson (2007) is used in this study (see Appendix F for the details). For more details on the bootstrap DEA methodology in healthcare studies see Simar and Wilson (2007;2018).

The Output Variables
The COVID-19 pandemic has acted like a litmus test on the capacity and designs of health systems across the globe. There have been similar pandemics in the recent past -Lassa fever, Ebola virus disease, SARS, Zika virus, and H1N1 -and the threat of more frequent future pandemics is real due to increase in international and domestic travel and trade that makes for a very rapid international spread of any highly infectious virus (Sundararaman et al., 2020). It is, therefore, important to learn the right lessons with regard to building a resilient healthcare systems capable of preventing or resisting health emergency shocks by learning from the current COVID-19 experience. Kruk et al. (2015) defined Health systems resilience as "the capacity of health actors, institutions, and populations to prepare for and effectively respond to crises; maintain core functions when a crisis hits; and, informed by lessons learned during the crisis, reorganize if conditions require it". Response to a crisis needs "both a vigorous public health response and a highly proactive and functioning health-care delivery system" (Kruk et al. 2015). Both these systems must work in concert during a crisis-and indeed they can do so only if designed such long before crisis strikes-which is the element of health systems preparedness. For this reason, Model 1 was designed to assess the health systems' efficiency in terms of how resources were utilized to enhance the resilience of health systems during pandemics. Thus, for Model 1, we are interested in data relating to delaying or preventing the outbreak and curbing the rapid spread of the COVID-19 virus, i.e. how resilient the countries are able to resist this global pandemic. Therefore, we selected one output variable -COVID-19 positivity rate. Positivity rate is the ratio of the total confirmed positive COVID-19 cases to the total number of COVID-19 tests times 100. Again, we make an assumption that a country with a lower positivity rate has a strong health system to protect its citizens during pandemics. We needed to transform this variable to meet DEA assumptions. The DEA techniques require that output variables are measured in such a way that "more is better". Since the COVID-19 positivity rate (CPR) does not meet this requirement, we computed COVID-19 negativity rate (CNR) as follows: The several non-pharmaceutical interventions (NPIs) to flatten the COVID-19 curve have been discussed in the literature (Block et al., 2020;Arshed et al., 2020;and Breitenbach et al., 2020). This approach may not totally eradicate the COVID-19 disease, but it will potentially reduce the stress on health systems (Giesecke, 2020; World Health Organisation, 2020a). A considerable amount of resources and policy interventions including economic lockdowns have been instituted across the globe to achieve the goal of flattening the curve (Koh, 2020; Sharma, Talan, and Jain, 2020; Arshed, 2020). Many countries have struggled in different ways to flatten the curve, but different results emanate. Model 2 of this paper aims at measuring the efficiency of health systems in flattening the COVID-19 trajectory curve during the first wave of infections. In this regard, we are interested in data relating to the speed at which the curve was flattened, that is, how quickly countries were able to reduce the rate of infections. Thus, the paper adopted an output variable which is computed as the difference between the date when the first case was detected to the date when the COVID-19 infections started to fall steadily, showing that infections were markedly declining. In order to avoid misspecification of the model and ensure that countries that flatten their curves earlier are not represented by low values, this output variable was inverted (see Breitenbach et al., 2020;Arshed et al., 2020; Appendix E for COVID-19 epidemiological curves).
The COVID-19 pandemic has been characterized by significant morbidity and mortality of varying degrees across countries. Medical treatments have been administered to COVID-19 patients in order to control the viral infection. Medical resources such as medical personnel, inpatient hospital beds, ventilators, and others have come under intense usage since the outbreak of the pandemic. Different medical treatment measures have been taken by each country with differing outcomes. In this paper, Model 3 seeks to compare the relative performance of each sampled country as to whether the resources used in treating COVID-19 patients are being used efficiently or not. In order to empirically carry out this assessment, two output variables were selected -case fatality rate and recovered cases per 1000 confirmed cases. The COVID-19 case fatality rate (CFR), which is measured as the ratio of total confirmed deaths to total confirmed cases times 100, was transformed into case survival rate (CSR) to meet DEA model requirement of 'more is better' as follows: = × 100.

Input Variables
The input variables used in the production function of this paper included physicians' density, inpatient beds density, health spending as a proportion of GDP, and the average of 13 International Health Core Capacity Scores (IHRCCS). These input variables are widely used in studies of health production efficiency (Breitenbach et al., 2020;Shirouyehzad et al., 2020;See and Yen, 2018;Ambapour, 2015;Sinimole, 2012;Spinks and Hollingsworth, 2009). The average of the IHRCCS is used to reflect the resilience, emergency preparedness capacity against health threat, and the overall public health of national health systems (Sundararaman et al., 2020). The 13 core capacities are: (1) Legislation and financing; (2) IHR Coordination and National Focal Point Functions; (3) Zoonotic events and the Human-Animal Health Interface; (4) Food safety; (5) Laboratory; (6) Surveillance; (7) Human resources; (8) National Health Emergency Framework; (9) Health Service Provision; (10) Risk communication; (11) Points of entry; (12) Chemical events; (13) Radiation emergencies (World Health Organization, 2005). They are all measured on the scale between 0 (minimum score) and 100 (maximum score). Appendix A details the scores for each capacity for all the sampled countries plus the definitions of all the capacities.
Since this paper analyzes the efficiency of health systems in combating the COVID-19 pandemic, we chose two inputs that are unique to COVID-19 for the three models: total COVID-19 tests per one million population and non-pharmaceutical interventions (NPIs) stringency index (SI (3) cancelling of public events; (4) restrictions on gathering size; (5) public transport closure; (6) workplace closure; (7) internal movement restrictions; (8) international movement restrictions; and (9) public information campaigns. Each of the nine indicators were rescaled to a value from 0 to 100 (100 = strictest). Then the nine scores were averaged to get the composite Stringency Index (For more details on the construction of the NPIs Stringency Index see Appendix B). Table 1 presents the definitions and the sources of data used in the three DEA models.

Explanatory Variables
In order to investigate the effect of health systems characteristics and healthcare policies on health systems efficiency, we selected some explanatory variables which are defined in Table 2. Based on literature seven explanatory variables were selected as determinants of health system efficiency: (1)

Governance Quality
World Bank's Worldwide Governance Indicators (WGI) are a research dataset summarizing views on the quality of governance in both industrial and developing countries. These indicators which have been published since 1996 covers six dimensions of governance: control of corruption, government effectiveness, political stability, regulatory quality, rule of law, and absence of violence. This variable is included in the second-stage analysis to assess the impact of the quality of governance in health systems performance in curbing the COVID-19 pandemic. A plethora of empirical evidence indicate a positive correlation between health system performance and quality of governance (Ibrahim et al., 2018;Wranik, 2012). The quality of governance was measured as the average of all the six dimensions from 2016 to 2018. This variable is adopted in Model 3.

Size of Economy
GDP per capita vary markedly across the SSA countries. One empirical study by Mo et al. (2020) found an evidence of a positive relationship between GDP and the spread of COVID-19 virus. A low GDP per capita implies low economic activities and less human interactions. Hence, it is not surprising that territories with higher GPD may appear to have higher COVID-19 cumulative cases. This variable is employed in all the three models.

Tobacco Use Prevalence
Tobacco use prevalence was employed as a proxy of the population's lifestyle and behavior which can impact the severity of the spread of the COVID-19 virus. According to Guan et al. (2020), people who smoke have 3.25 higher odds of developing severe forms of COVID-19 disease as compared to non-smokers. Accumulating evidence indicates that tobacco use affects health outcomes and also the health system efficiency (Allin, Grignon, and Wang, 2016; Afonso and St. Aubyn, 2011; Johansson and Sundquist, 1999). Tobacco use prevalence was measured as the proportion of the population aged 15 years and above who regularly smoke. This variable is employed in all the three models.

Aged Population
Another social environmental variable in the models of this paper is the aged population, which provides a measure of age-related risk of severe COVID-19 disease. COVID-19 is often more severe in the people advanced in years or with underlying health conditions like lung or heart diseases, diabetes, or conditions that affect their immune system (Novosad et al., 2020;Ghisolfi et al., 2020;Okeahalam et al., 2020). Holts et al., (2020) provides a strong evidence of age-related gradient for risk of severe COVID-19 disease, hospitalization and deaths. The aged population was measured as the proportion of the population aged 65 years and above.

Population Density
Evidence from several empirical studies shows that population density has a significant effect on health system performance (Ahmed et al., 2019;See and Yen, 2018;Greene, 2010;and Kumbhakar, 2010). In this study, we postulate that a health system with a lower population density would have significant positive impact on health system efficiency in the midst of the COVID-19 pandemic due to its implications for social distancing and quality of healthcare services. This variable is measured as the size of the average population living on a kilometer of land area.

Temperature Levels
The relationship between temperature levels and the spread of COVID-19 virus is well documented in the literature (Aidoo et al., 2021;Roy, 2020;Kassem, 2020;Corripio and Raso 2020;Wang, Rodrigues, and Barmejo, 2020). The consensus among these studies is that there is an inverse relationship between the spread of COVID-19 virus and temperature. For instance, Aidoo et al. (2021) found that the risk of the spread significantly decreases when average temperature exceeds 29 o C. Wang, Rodrigues, and Barmejo (2020) estimated that every 1°C increase in the minimum temperature leads to a decrease in the cumulative number of cases by 0.86. The average monthly temperature for each country is included in the Model 2.

Level of Economic Development
A categorical variable of three income groupings -low-income, lower-middle-income, and upper-middle-income -of the studied countries was created to examine the influence of their level of development on health system performance in curbing the COVID-19 virus. Table 2 presents the definitions and the sources of variables used in the second-stage analysis.
We also employed the Simar and Wilson (2007) double bootstrap DEA approach to estimate robust bias-corrected efficiency scores from the bootstrapped regression analysis to identify factors associated with these estimated efficiency scores. The simarwilson command in STATA Version 15 was used in the analyses.

Data Sources
Data for the study were obtained from three main sources: the John Hopkins University COVID-19 Data Repository (https://coronavirus.jhu.edu), Worldometer COVID-19 Data Repository (https://worldometer.info), and COVID-19 Data Hub developed by Guidotti and Ardia (2020) (https://covid19datahub.io). COVID-19 indicators of confirmed, recovered, death cases and other quantitative related data were sourced from databases of John Hopkins University and Worldometer COVID-19 databases. However, qualitative indicators on government policy interventions data were sourced from COVID-19 Data Hub developed by Guidotti and Ardia (2020). Due to wide fluctuations in the daily trends of confirmed, recovered, and death cases as a result of irregular intervals of reporting, the study used 21-day moving averages of reported cases in order to better appreciate the trends. This is a cross-sectional study using data on 46 countries in SSA. These countries were selected based on the fact that the relevant COVID-19 data required for the study's analyses were regularly reported on during the study period, which was between December 29, 2019 and February 28, 2021. According to the list provided by United Nations Statistics Division, there are 50 Sub-Saharan African countries and territories. Six countries and territories (i.e. Tanzania, Sudan, South Sudan, Djibouti, Eritrea, Reunion, and Mayotte) were excluded from the study due to missing data of some selected relevant variables in the databases.    governments' interventions are generally associated with lower COVID-19 cases.

First-stage DEA Results: Efficiency Scores, Rankings, and Classifications of Countries
The efficiency scores for all the selected SSA countries' health systems in this study were computed using STATA packages of teradial and simarwilson. The results of the original DEA scores, bootstrap bias estimates and Farrell bias-corrected output-oriented efficiency scores under VRS, which range from one to infinity, are presented at Appendix C. For easy reading and analysis, the Farrell bias-corrected efficiency scores were converted into Shepherd bias-corrected efficiency scores, which range from zero to one, are ranked and presented in Table 1.4 for each of the three models in this study.
In the given sample of 44 SSA countries, 20 countries are classified as low-income, 17 countries as middle-lower-income, and 7 countries as upper-middle-income or high-income (World Bank, 2020). Based on the proposed methodology, in the first stage of this study, the efficiency of public health measures instituted by the various health systems in the SSA countries to curb the spread of contagious diseases in general and COVID-19 virus in particular were evaluated. In this stage, the average of the 13 IHRCCs, NPIs Stringency Index, and the number of COVID-19 tests per one million population were used as input variables whilst spared days and COVID-19 cases per one million population were used as output variables. The results for the three income groups are presented in Figure 4.   The results show that the average efficiency score for the COVID-19 public health division for the low-income countries is 0.60 whereas that of middle-lower-income countries and upper-middle-income countries are 0.51 and 0.50, respectively. From Figure 4, we observe that Central African Republic, Lesotho, and Equatorial Guinea obtained efficiency scores greater than 0.61 and were ranked at the top of the low-income, lower-middle-income, and upper-middle income groups, respectively. Thus, these countries offer useful information for the less efficient countries within the same income groups as they are considered as good references. At the other end of the spectrum, Togo (low-income country), Senegal (middle-income country), and South Africa (upper-middle-income country) had the worst health systems among their respective income groups. The results from the bootstrap DEA framework suggest that with the given capacity and resources, more efficient utilization of their resources could potentially enhance output by 45% in terms of COVID-19 cases per one million population.
In the second model of this study, we examine the efficiency with which health systems in SSA are able to flatten the COVID-19 contagion curve using the NPIs Stringency Index, number of COVID-19 tests per one million population, and healthcare expenditure as a percentage of GDP as input variables and the number of days left in the cycle as the only output variable. The results as presented on Figure 5 show that Guinea-Bissau and Liberia (Low-income countries), Sao Tome & Principe and Cote d'Ivoire (Lower-middle-income countries), and Equatorial Guinea and Mauritius (Upper-middle income countries) are more efficient in comparison to other countries in their respective income groups. Therefore, these countries serve as good peers for the less efficient countries within their respective income groups. The average efficiency score for low-income countries in flattening the curve is 0.70 whereas the middle income and upper-middle income countries registered an average scores of 0.63 and 0.46, respectively. In the third model, based on the proposed methodology, DEA is performed to assess the efficiency performance of health systems in the medical treatment of COVID-19 patients. In this model, NPIs stringency index, number of COVID-19 laboratory tests per one million population, physicians per thousand population, and inpatient beds per thousand population were used as inputs whereas the number of recovered COVID-19 patients per thousand confirmed cases and the inverse of the number of deaths per thousand COVID-19 cases were used as outputs. The results for the 44 studied SSA countries are presented on Figure 6.
The results show that Madagascar (low-income countries), Zimbabwe (lower-middle-income countries), and South Africa (upper-middle-income countries) have had poor performance in the medical treatment of COVID-19 patients in comparison with other countries in their respective income groups in this study. However, countries such as Malawi (low-income countries), Senegal (lower-middle-income countries), and Mauritius (upper-middle-income countries) serve as good role models for the less efficient countries to emulate from in the treatment of COVID-19 patients.

Upper-middle-income countries
to divide the scatter plot into four areas: A, B, C, and D as shown in Figure 7. From the plot, it can be observed that countries such as Central Africa Republic (CAR), Mauritius, Niger, Malawi, Equatorial Guinea, Burundi, and Eritrea which are in area B of the plot have been efficient in both public health measures and medical treatment of COVID-19 patients, and can serve as benchmarks. Countries in area A of the plot such as Rwanda, Ghana, Senegal, Gabon, and Seychelles have efficiently carried out medical treatment of COVID-19 infected persons but have been poor in implementing public health measures to curb the spread of the virus. These countries can serve as good references regarding medical treatments of COVID-19 patients.
On the other hand, countries in area C of the Figure7 -Lesotho, Mali, Angola, Chad, and, Democratic Republic of Congo -have been more efficient in the implementation of the public health measures aimed at curbing the spread of the COVID-19 virus but poor in the medical treatment of persons infected with the virus. These countries can serve as benchmarks for implementing public health measures to fight the spread of the COVID-19 virus. Countries in area D are those in worst situation with poor performance in both medical treatment and implementation of public health measures. There is an urgent need for these countries to improve their current conditions. The countries in the area D are South Africa, Zimbabwe, Kenya, Mauritania, Eswatini, Gambia, Cote d'Ivoire, and Congo Republic.

The Results of Second-Stage Bootstrap DEA
The differences in the efficiency scores of the studied SSA countries' health systems computed by bootstrap bias-corrected DEA could be explained by health systems characteristics which were not included in the first-stage DEA. In this study, after careful review of both COVID-19 literature and health systems studies, GDP per capita (GDP), population density (DENSITY), aged population (AGED), average temperature levels (TEMPERATURE), prevalence of tobacco use (TOBACCO), governance quality (GOVERNANCE), and categorical variable of income groups (LOW-INCOME, LOWER-MIDDLE-INCOME, and UPPER-MIDDLE-INCOME countries), using low-income countries as a reference category, were included as explanatory variables in the second-stage of bootstrap DEA framework. Some of the variables are excluded in some of the three models employed in this study due to collinearity problems and insignificant results. Table 5 presents the estimation results from the bootstrap procedures employing algorithm #2 from Simar and Wilson (2007). The regression procedure uses the estimated inefficiencies ( . . * > 1) generated in the first-stage DEA as dependent variable. Thus, a positive coefficient implies that an increase in a relevant explanatory variable is associated with an increase in inefficiency of the countries' health systems.
GDP per capita is included in the analysis to capture the impact of the level of economic activities on the performance of health systems in fighting the COVID-19 pandemic. The relationship between GDP per capita and health system inefficiency is found to be positive for model 1 ( = 0.177, < 0.01) and model 3 ( = 0.0254, < 0.01). This suggests that higher levels of GDP are associated with poor health system performance in curbing the spread of the disease, particularly in the use of public health measures and medical treatment of COVID-19 infected persons, and portends a conclusion that higher levels of economic growth pose real risk for the spread of infectious diseases. In fact, a simple Spearman correlation test shows that the cumulative cases per one million population were positively correlated with GDP per capita ( = 0.64, < 0.01). This result is consistent with those obtained in an earlier empirical studies, such as Mo et al. (2020), where increases in GDP was found to increase cumulative COVID-19 cases and Hadad, Hadad, and Simon-Tuvel (2013) where increases in GDP per capita was found to decrease health system efficiency.
Empirically, the tobacco use have not had any significant effect on the performance of health systems efficiency as far as COVID-19 public health measures in model 1 and efforts to flatten the contagion curve in model 2 are concerned. However, in terms of medical treatment of COVID-19 patients, the prevalence of tobacco use have had a significant negative impact ( = 0.0027, < 0.01) on health systems efficiency. That is, higher levels of tobacco use are associated with health system inefficiency in the medical treatment of COVID-19 patients. This is in line with earlier empirical studies, such as Allin, Grignon, and Wang (2016) and Afonso and St. Aubyn (2011), which found tobacco use to be significantly associated with lower health systems efficiency. Notes. Standard errors in parentheses. Dependent variables: inefficiency scores ( . . * > 1). *** p<0.01, ** p<0.05, * p<0.1.
The proportion of aged population is included in the second-stage analysis to assess the effect of age-related risk of severe COVID-19 disease resulting from underlying health conditions that affect their immune systems on health systems performance. Interestingly, it was not found to be associated with the health system's efficiency according to both models 1 and 2. However, as depicted in Table 5, in model 3, aged population was estimated to be negative ( = −0.0081, < 0.01), which indicates that countries with more aged population are more likely to be more efficient in medical treatment of COVID-19 patients. This result contradicts a priori expectation but not surprising considering the youthfulness of populations across many SSA countries with a very negligible proportion of the aged population.
The negative relationship between governance quality and health systems inefficiency, which indicates that well governed countries are more likely to have efficient health systems in medical treatment of COVID-19 patients, coincides with Ibrahim et al. (2018) and Wranik (2012).
Temperature is found to be positively associated with health system inefficiency ( = 1.647, < 0.05) in flattening the COVID-19 contagion curve. The implication of this result is that countries with higher levels of temperature are likely to be more efficient in reducing the rate of transmission of the COVID-19 virus. The finding is similar to other earlier empirical studies (Aidoo et al., 2021;Roy, 2020;Kassem, 2020;Corripio and Raso 2020;Wang, Rodrigues, and Barmejo, 2020) all of which found temperature to be negatively associated with the rate of COVID-19 virus infections. The comparatively low COVID-19 cases in the SSA region may be attributed to the gjhs.ccsenet.org Global Journal of Health Science Vol. 14, No. 4; higher levels of temperature in the sub-region.
Again, from Table 5, it is observed that among the three categories of countries the low-income countries performance in implementation of COVID-19 public health measures (Model 1) and in flattening the COVID-19 contagion curve (Model 2) is better as compared to lower-middle-income and upper-middle-income countries. However, in terms of medical treatment of COVID-19 patients (Model 3), the performance of lower-middle-income and upper-middle-income countries is significantly better than low-income countries.
Population density is included in the second-stage analysis to investigate the impact of social distancing on health system efficiency in the fight against the spread of COVID-19 virus. The estimated coefficient for the population density variable is positive for both model 1 ( = 0.0925, < 0.01) and model 2 ( = 4,754, < 0.05). The results favor the proposition that higher population density does not bode well for social distancing, a public health measure essential in the fight against the spread of the COVID-19 virus. However, the effect differs among the three income groups. The negative impact of population density on efficiency performance is more intense among low-income countries relative to lower-middle-income countries and upper-middle-income countries. These findings are in line with most previous literature (see Kumbhakar, 2010;Greene, 2010;and See and Yen, 2018).

Sensitivity Analyses and Robustness Checks
In this study, across all the three models employed, the number of DMUs were far in excess of the requirement that the DMUs should be three times more than the number of input and output variables used (Golany and Roll, 1989;Masiye, 2007), hence, it was not a binding constraint (Hollingsworth and Peacock, 2008).
Sensitivity analyses were conducted using two different DEA estimation techniques and various combinations of input and output variables. The two estimation techniques employed here were implemented using two Stata commands: teradial and simarwilson. The teradial command fits DEA models where original radial technical efficiency measures are computed (Fare 1998;Fare and Lovell 1978;Fare, Grosskopf, and Lovell 1994a;Badunenko and Mozharovskyi, 2016) whilst the simarwilson command implements DEA two-stage bootstrap bias-corrected radial technical efficiency measures (Simar and Wilson, 1998;2000;2002;2018). The comparison of the technical efficiency estimates from the two estimation techniques (see Appendix C) showed a highly significant positive Spearman rank correlation across all the three models: Model 1 ( = 0.98, < 0.01); Model 2 ( = 0.84, < 0.01); and Model 3 ( = 0.59, < 0.01). Again, consistent results were obtained from various combinations of input and output variables, which strengthens the validity of the findings from this study. For example, the sensitivity of the results obtained from Model 3 was tested, particularly because two of the inputs employed (i.e. inpatient beds per thousand population and physicians per thousand population) are less frequently reported on across SSA countries. When they were replaced by health expenditure per capita (constant at 2011 PPP), it was found that the results did not change significantly.
In order to assess the robustness of the results obtained from the bootstrap regression procedures in the second-stage analysis, the more usual truncated regression procedure was also applied (see Appendix D). The striking similarities of the estimated coefficients in terms of both numerical values and statistical significance across different models and estimation methods confer robustness to the empirical evidence, which enhances confidence in the arrived conclusions.
According to Greene (2004), there is no well-defined theory to guide the selection of environmental and policy variables in the second-stage regression analysis. The choice then becomes empirical. However, in order to discriminate between different competing specifications of the models, the log likelihood ratio test for nested models was used. The test statistics, as reported on Table 6, favor model specifications with interaction terms (A) as against parsimonious specifications (B), at least for Models 1 and 3, since the inclusion of the interaction terms improves the fitness of the models. Accordingly, we report results of model specifications involving the interaction terms for all the three models.

Conclusion and Policy Implications
This study has examined the technical efficiency and its determinants of health systems of 44 SSA countries in curbing the COVID-19 pandemic using three different empirical DEA models. A review of the existing literature revealed an acute insufficient empirical research related to the efficiency of health systems in fighting an outbreak of diseases in general and COVID-19 in particular. Even though several studies have been undertaken to assess how countries in the sub-region can improve their health systems to contain outbreaks of diseases or pandemics, there is little or no known study that examines the efficiency of health systems in fighting pandemics. This paper contributes to fill this gap in the empirical literature. The overarching goal of this study was to assess the technical efficiency of health systems in SSA in curbing the COVID-19 pandemic and identifying the sources of inefficiencies. This general goal was divided into three specific objectives, using three different empirical frontier models to achieve the respective objectives.
The first empirical frontier model was to assess the technical efficiency of public health measures instituted by the various health systems in SSA to contain an outbreak of epidemic or pandemic in general and COVID-19 contagion in particular. The study evaluated the public health measures by assessing the outputs (inverse of COVID-19 cases per one million population) against the inputs directly used as public health measures (average of 13 IHRCC indicators and average of NPI stringency measures). The results from the first stage revealed that inefficiencies were quite high and that countries could have increased the results by 45% using the same resources. It was observed that the average efficiency scores decreased from low-income countries to lower-middle-income and upper-middle-income countries. This finding contradicts some international studies (Ahmed et al., 2019;Grosskopf, Self, and Zaim, 2006) which found that health systems performance was relatively more efficient in the developed countries. The second-stage analysis shows that GDP per capita and population density significantly worsen the health systems performance in terms of using public health measures to curb the spread of COVID-19 virus.
The second empirical model focused on measurement of the level of technical efficiency of the studied countries in flattening the COVID-19 contagion curve (i.e. reducing the rate of infections). This was done by evaluating the output (the number of days left in the cycle) against the inputs directly employed to flatten the curve (number of COVID-19 tests per one million population, NPIs stringency index, and healthcare expenditure as a percentage of GDP). The first-stage analysis revealed that health systems in SSA could have improved the results obtained by 36% given the same resources and the public health measures implemented. Again, the average efficiency scores decreased from low-income (0.70) and lower-middle-income (0.63) countries to upper-middle-income countries (0.46). The second-stage procedure shows that temperature levels and population density are significantly and negatively correlated with the performance of health systems in reducing the rate of COVID-19 infections.
The final empirical frontier model examined the efficiency of medical treatments of COVID-19 patients of the healthcare systems in the SSA. The examination was carried out using two outputs (number of recovered COVID-19 patients per thousand cases and survival rate of COVID-19 patients) against four inputs (number of COVID-19 tests per one million population, NPIs Stringency Index, number of inpatient beds per thousand population, and number of physicians per thousand population). In this model, it was observed that the average efficiency scores increases from the low-income and lower-middle-income countries to upper-middle-income countries. The second-stage analysis shows that good governance and aged population are significantly and positively correlated with the performance of health systems, whereas GDP per capita and prevalence of tobacco consumption worsen the performance from the perspective of medical treatment of COVID-19 patients.
The general finding of the study suggests that there is more room for health systems in SSA to improve their technical efficiency in fighting the COVID-19 pandemic. The findings also suggest that specific environmental factors significantly influence the level of health systems efficiency. These findings provide important policy implications for health systems to improve the technical efficiency in curbing the COVID-19 pandemic in particular, and by inference any other health epidemic or pandemic that may occur in future, by learning from the good performers (benchmarks).
One major revelation from this study is that countries that have made key investments in their health infrastructure and human resources are more efficient in managing the COVID-19 pandemic, at least in terms of the medical treatment of people who become infected with the virus. This implies the need for investment and political will to improve the public health institutions, medical facilities, and scientific expertise to prevent, control, and manage future outbreaks of epidemics. Second, the African Center for Disease Control and Prevention (i.e. Africa CDC) and its five regional collaborating centres must be supported by the Africa Union to carry out its mandate of strengthening and improving the capacity of public health institutions on the sub-region to detect and respond quickly and effectively to threats and outbreaks of diseases based on data-and science-driven interventions. Third, countries in the SSA must take this COVID-19 pandemic period as an opportunity to invest in research into local traditional medicines to reduce reliance on the West for orthodox medicine and vaccines.
Again, Ministries of health, which are mandated to supervise and regulate healthcare delivery, in the various countries must prioritize efficiency of healthcare facilities and personnel prior to and during outbreak of health pandemics. They can do this by strengthening their supervision, monitoring, and training divisions. At the facility level, timely design and distribution of protocols in caring for infected persons, right at the onset of the pandemic and human resource strategies geared towards recruiting and/or retaining well-qualified and experienced healthcare workers to provide professional services would prove critical in containing pandemics of this nature. This can be done by providing both intrinsic and extrinsic motivational packages, not only at the height of pandemics, but throughout their working lifespan.
This current study, like any other research work, suffers from some limitations which present an opportunity for refining and extending the frontiers of the outcomes of this study. The empirical analyses of this study are based on a snapshot of cross-sectional data spanning from 2016 to 2021 and the regression results are largely explorative, hence, places some restrictions on the current relevance and conclusions regarding the levels of health systems efficiency and the sources of inefficiency. It is, therefore, recommended that an extensive qualitative research be conducted in future to carry out in-depth analyses of best performing health systems in order to share best practices across the sub-region.
Another limitation of this study might emanate from the use of the DEA methodology. Since DEA is sensitive to the numeric values in the dataset and relies on the most efficient DMUs for frontier estimation, the use of different set of variables might give different results and conclusions (Hollingsworth and Peacock, 2008). Further, the use of relatively small number of DMUs might have led to overestimation of efficiency scores (Spinks and Hollingsworth, 2009). Future studies might increase the number of DMUs and explore additional variables, as data become available, in order to enhance the understanding of health system efficiency with a greater degree of complexity in curbing outbreak of epidemics and pandemics.
Findings from this study indicate that the most important determinants of health system efficiency in dealing with the COVID-19 pandemic are GDP per capita, population density, governance quality, tobacco use prevalence, and temperature levels. However, health systems have additional policy and environmental features that are not captured here, but might contribute to efficiency, such as financing mechanism, gatekeeping arrangements, burden of diseases, different political institutions, degree of centralization of decision-making within each system, hhealth-seeking behaviors, inter alia. Future studies might explore the use of these alternative health systems features in efficiency estimation and its determinants. Again, since untimely access to healthcare can either kill or reduce the quality of life of those who survive, future research could improve the outcome variables by measuring preventable years lost both to death and to poor quality of life.