key: cord-0789673-wiqxuyhp authors: Last, Mark title: Towards the global equilibrium of COVID‐19: Statistical analysis of country‐level data date: 2022-04-22 journal: Health Sci Rep DOI: 10.1002/hsr2.592 sha: 63e69868ad06d73ca30049004b98fb1d37a1fc27 doc_id: 789673 cord_uid: wiqxuyhp In our study, we explore the COVID‐19 dynamics to test whether the virus has reached its equilibrium point and to identify the main factors explaining the current R and case fatality rate (CFR) variability across countries. We present a retrospective study of publicly available country‐level data from 50 countries having the highest number of confirmed COVID–19 cases at the end of September 2021. The mean values of country‐level moving averages of R and CFR went down respectively from 1.118 and 6.3% on June 30, 2020 to 1.083 and 3.6% on September 30, 2020 and to 1.015 and 1.8% by September 30, 2021. In parallel, the 10%–90% inter‐percentile range of R and CFR moving averages decreased, respectively, from 0.288 and 13.3% on June 30, 2020, to 0.151 and 7.7% on September 30, 2020, and to 0.107 and 3.3% by September 30, 2021. The slow decrease in the country‐level moving averages of R, approaching the level of 1.0 and accompanied by repeated outbreaks (“waves”) in various countries, may indicate that COVID‐19 has reached its point of stable endemic equilibrium. A regression analysis implies that only a prohibitively high level of herd immunity (about 63%) may stop the endemic by reaching a stable disease‐free equilibrium. It also appears that fully vaccinating about 70% of a country's population should be sufficient for bringing the CFR close to the level of the seasonal flu (about 0.1%). Thus, while the currently available vaccines prove to be effective in reducing the mortality from the existing COVID‐19 variants, they are unlikely to stop the spread of the virus in the foreseeable future. It is noteworthy that government measures restricting people's behavior (such as lockdowns) were not found to have statistically significant effects in the analyzed data. The first case of COVID-19 was reported in the Chinese city of Wuhan in December 2019. According to the Humanitarian Data Exchange website, 1 on January 22, 2020, there were 557 confirmed cases of COVID-19 in 29 different countries. On the same date, the global number of reported COVID-19 victims has reached 17, all of them from the Hubei province in China. Due to extensive international travel, the virus has spread quickly around the world, exceeding one million cases in 254 countries and territories by the end of March 2020 and 100,000 deaths 8 days later. The continuous response of national and regional authorities to the pandemic varied significantly from the near-absolute closure of international borders (e.g., Australia and New Zealand) and repeated lockdowns (e.g., New York City and Israel) to focusing on the protection of high-risk populations only (e.g., Sweden). As the pandemic continued to spread, each period of a steady increase in either the local or global amount of COVID-19 cases and deaths was always followed by an opposite, decreasing trend, frequently assumed to be a result of various intervention measures. However, in many cases, another, often a deadlier "wave" took place sometime later. Starting from December 2020, many countries, in the hope of "winning the pandemic," launched massive vaccination campaigns. By the end of July 2021, 1.14 billion people (14.6% of the world population) were fully vaccinated, while the global number of confirmed COVID-19 cases approached 200 million with about 4.2 million victims in 251 different countries and territories. While the primary focus of health care systems was on COVID-19, some other infectious diseases emerged in several countries, for example, the Zika virus in India. 2 Considering the widespread travel restrictions at the time of the pandemic, the COVID-19-related death toll in a given country depends mainly on the following two factors: the average value of the effective (time-varying) reproduction number R eff , or R t , which represents the average number of cases an infected person has generated in the country's population, and the average case fatality rate (CFR), calculated as a percentage of death outcomes out of all cases confirmed during a specific period. Thus, we focus our study on the comparative analysis of these two parameters at the country level. In a completely susceptible population, the effective reproduction number, R eff , equals to the basic reproduction number R 0 . R 0 is defined as the average number of secondary infections an infected person will cause in an "immunologically naive" population before he or she is effectively removed from that population as a result of recovery, hospitalization, quarantine, and so on. 3 The population is expected to reach "herd immunity" when the proportion of nonsusceptible ("immunologically experienced") individuals exceeds R 1 − 1∕ 0 . 4 A direct measurement of R 0 requires identifying the exact source of each infection case, which is rarely possible. However, the basic reproduction number can be estimated from the epidemiological data using a mathematical model such as susceptibleexposed-infected-recovered (SEIR). 5 In our previous work, 7 we explored the overall evolution of the basic reproduction number in Israel, Greece, Italy, and Sweden between March and July 2020 using the relationship between the daily reproduction numbers R t , the basic reproduction number R t ( ) 0 , and the cumulative percentage of confirmed cases p t , which is shown in Equation (1). The authors of Cao et al. 8 These and many other studies focused on analyzing the data that was available during the first months of the pandemic, also known as the COVID-19 "first wave." At the end of 2020, several COVID-19 vaccines became available for the adult population. Massive vaccination campaigns were launched across the globe in the hope of reaching "disease-free equilibrium," where the majority of the population is immunized by a vaccine providing a long-term immunity with high efficacy while providing "herd immunity" protection to those who cannot be immunized. Given the actual values of R 0 and vaccine efficacy VE, one can calculate the herd immunity threshold of vaccinated individuals f v using Equation ( 2) 10 : According to a previous forecast, 10 To explore the differences between countries, we have extracted the following 180-day moving averages of country-level factors from the Our World in Data COVID-19 data set 9 : • Average of Delta: Average share of analyzed SARS-CoV-2 sequences that were the Delta variant. This variable is not available for some low-middle-income countries (LMICs) due to insufficient genetic surveillance. 11, 12 • Average of total_cases_per_million: Average cumulative number of confirmed COVID-19 cases per one million people. • Average of people_vaccinated_per_hundred: Average daily percentage of population vaccinated with any number of doses. • Average of people_fully_vaccinated_per_hundred: Average daily percentage of fully vaccinated population. • Average of total_boosters_per_hundred: Average daily percentage of population vaccinated with a booster dose. • Average of stringency_index: The average daily value of the Government Response Stringency Index, a composite measure based on nine response indicators including school closures, workplace closures, and travel bans. • Average of population_density: Number of people divided by country's area in square kilometers. • Average of median_age: Median age of the country's population. • Average of aged_65_older: Share of the population that is 65 years and older. • Average of gdp_per_capita: Gross domestic product at purchasing power parity. • Average of cardiovasc_death_rate: Annual number of deaths from the cardiovascular disease per 100,000 people. • Average of diabetes_prevalence: Diabetes prevalence among people aged 20-79. • Average of female_smokers: share of female smokers. • Average of male_smokers: share of male smokers. • Average of hospital_beds_per_thousand: Hospital beds per 1000 people. As indicated by Ghosh et al., 13 in LMICs like India, this number can be significantly lower than in high-income countries, leading to an increased burn-out of healthcare workers during the pandemic. • Average of life_expectancy: Life expectancy at birth in 2019. • Average of human_development_index: A composite index measuring three basic aspects of human development-a long and healthy life, knowledge and a reasonable standard of living. Our estimations of the average R and CFR values in each country are based on the daily values of confirmed COVID-19 cases and deaths reported by the Our World in Data website. 9 The daily estimate of R on day t is calculated by Equation (3). where C Cum_ t is the cumulative number of confirmed cases on day t, w = 7 days is the size of the sliding window, and g = 4 days stands for the average duration of the COVID-19 generation period. 7 The daily estimate of CFR on day t is calculated by Equation (4). where D Cum_ t is the cumulative number of deaths on day t and The procedure stops when no variable meets the threshold_in criterion. In addition, at each step, the algorithm recalculates the p-values exceed threshold_out. In our analysis, we set threshold_in to 0.05 and threshold_out to 0.10. The descriptive statistics of all data variables are shown in Figure 1 . The increasingly low levels of the cross-country variance of R and CFR (see Figures 3 and 4) , along with the average value of R approaching the value of 1.0, may indicate that the COVID-19 pandemic has reached its point of stable endemic equilibrium. 15 According to the mathematical model of COVID-19 presented in Ahmed et al., 16 Our regression analysis has shown that the median age and the average density of a country's population are not statistically significantly associated with the average reproduction number. Contrary to Ahammed et al., 17 we have also found no statistically significant associations of any demographic parameter with CFR. Similar to the findings of Cao et al., 8 ACKNOWLEDGMENT I am very thankful to Prof. Isidore Last from Tel-Aviv University, Prof. Avi Rosenfeld from the Jerusalem College of Technology (JCT), and the anonymous reviewers for making insightful comments on this manuscript. The author declares no conflict of interest. The manuscript is an honest, accurate, and transparent account of the study being reported; no important aspects of the study have LAST | 9 of 10 been omitted; and any discrepancies from the study as planned (and, if relevant, registered) have been explained. All data used in this study is publicly available at https://ourworldindata. org/ and cited in the article. http://orcid.org/0000-0003-0748-7918 Humanitarian data exchange Dual burden of zika and covid-19 in india: challenges, opportunities and recommendations Effective containment explains subexponential growth in recent confirmed covid-19 cases in China Herd immunity to COVID-19: alluring and elusive Infectious Diseases of Humans: Dynamics and Control The reproduction number of covid-19 and its correlation with public health interventions The first wave of covid-19 in israel-initial analysis of publicly available data Covid-19 case-fatality rate and demographic and socioeconomic influencers: worldwide spatial regression analysis based on country-level data Coronavirus pandemic (COVID-19). 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