Curbing COVID-19: A Retrospective Disease Progression Analysis

Kamron Soldozy
May 30, 2020
19 min read

Kamron Soldozy and Soumya Gottipati

Abstract

Objective: COVID-19 has not affected all countries equally: whereas China and South Korea are thought to have effectively controlled the growth of the disease, many countries have yet to ‘flatten the curve’, including Italy, Spain, Germany, and the United States. We set out to quantitatively characterize the status of COVID-19 - including the relative impact of the disease and its temporal stage in affected nations.

Methods: For these countries, we analyzed the developing and aggregate confirmed case, recovery, and death counts, and fit the growth of the confirmed COVID-19 case count using a log linear model.

Results: We demonstrate that South Korea and China are nearing the end stages of the epidemic, that the number of confirmed COVID-19 cases is decreasing in Italy, Spain, and Germany, but increasing in the US. Additionally, after identifying six major policy interventions implemented by these countries, we found that China responded to COVID-19 relatively slowly, and that the US has not exhausted all legislative options to combat contagion. Next, we demonstrate that a nation’s quality of health care and democraticness negatively and positively correlate with the recent - but not initial - log linear growth of the confirmed case count of COVID-19, respectively (p-value = 0.012 and 0.025), and that there is no significant correlation with a nation’s population density (p-value = .17).

Conclusion: Our findings establish the empirical foundation for the abstraction of globally-sourced policy measures for use in individual countries.

Introduction

Ever since the initial outbreak of 2019 novel coronavirus (COVID-19) in Wuhan, China, the disease has spread rapidly, impacting medical, social, economic, and political paradigms on a global scale. In just five months, the virus has infected over half a million people around the world, overwhelming healthcare and resource management systems in numerous countries and resulting in over 30,000 total deaths as of March 28th, 2020 (Novel Coronavirus (2019-nCoV) situation reports, 2020). Although COVID-19 was deemed a Public Health Emergency of International Concern by the World Health Organization (Rolling Updates on Coronavirus Disease, 2020), countries vary widely in terms of current case count as well as present transmission rates. Some countries - namely China and South Korea - are thought to have effectively controlled the growth rate of new cases, at least in part due to apt policy changes aimed towards curbing transmission of disease (Javier Hernández, 2020; Kenneth Rapoza, 2020). Despite reports of decreasing new cases of COVID-19 in China and South Korea, many countries across the world are believed to remain in a state of exponential growth and are said to have yet to ‘flatten the curve’ of disease transmission (Joel Shannon, 2020; Zhao et al., 2020). These countries include Italy, Spain, Germany, and most notably the United States, which at present has the highest number of confirmed COVID-19 patients in the world, coupled with one of the largest growth rates among affected countries (Smith et al., 2020).

Yet popular characterizations of affected nations as having ‘flattened the curve’ or having successfully curbed the epidemic are not grounded in empirical analysis of the epidemiological data. Indeed, the status of COVID-19 - including the relative impact of the disease and its temporal stage - have yet to be quantitatively characterized among affected nations. For this reason, we analyzed the developing and aggregate confirmed case, recovery, and death counts to robustly characterize the relative impact and stages of the pandemic in South Korea, China, Italy, Spain, Germany, and the US.

Methods

We selected the five countries with the highest confirmed COVID-19 case counts at the time of writing this manuscript, along with South Korea, considering its popular consideration as having successfully curbed COVID-19. Data on case count, death rates, and recovery rates per day was sourced from Johns Hopkins Medical School (Johns Hopkins Coronavirus Resource Center, 2020). Data analysis was performed in Python, using the pandas, numpy, matplotlib, and datetime packages for data importation and visualization. In order to better compare the growth of COVID-19 in multiple countries differing in initial onset of the disease, the data was also reformatted to reflect daily case counts as a function of days since the first or tenth case, rather than by date. Total confirmed case counts per country were also plotted on a log-linear scale, and the sklearn linear_model package was used to linearly fit the natural logarithm of total case counts per country as a function of the number of days since the first case during two different time intervals: an early and a later period. The early period was defined with respect to the first day on which there were 10 confirmed cases of COVID-19 in each affected nation, and was 12 days in length. The later period was also 12 days in length, the interval for which began on the first day after the end of the early period. The scipy.stats toolbox was used to conduct significance testing comparing the linear regressions of the early and later periods.

After identifying the policy interventions implemented by each nation through a thorough reading of government updates and news reports and quantifying the relative timeliness of their implementation, we tested the rapidity with which the growth of COVID-19 changed with respect to medical supply acquisition and school closure policies. That is, after conducting linear regression on the log-linear number of confirmed case counts for 10 days leading to the implementation of specific policy interventions, we continuously computed linear models for 10 day intervals increasingly offset in time by one day increments until the log-linear slopes of the models were significantly different. We then took the mean of the number of days until the linear fits were significantly different across the multiple countries and policy interventions for which this analysis was performed.

We then correlated the previously computed early and later log-linear growth rates with political, social, and demographic characteristics of affected nations. More specifically, we sourced information on the health care quality of 12 nations from The World Health Report 2000 (World Health Organization, 2000). We also utilized the democracy index of each country, retrieved from the the Economist Intelligence Unit (Democracy Index 2019, 2019), as well as the population density of each country retrieved from the World Population Review (Countries By Density Population, 2020).

Results

Popular Characterization of Covid-19 Across Countries

Recent reports indicate that China’s first confirmed COVID-19 case traced back to November 17, 2019 (Josephine Ma, 2020). As of March 18, 2020, it was alleged that the local transmission of COVID-19 fell to zero (Javier Hernández, 2020). Indeed, it is widely accepted that the COVID-19 pandemic has effectively ended in China. Many ascribe this feat to the authoritarian control of the Chinese government, which is believed to have enabled dramatic, rapid efforts to limit contagion - albeit at the cost of privacy and individual liberties of the nation’s citizens (Zhong & Mozur, 2020). It follows that many nations have turned to China as a model for both understanding and optimally responding to the pandemic (Cyranoski, 2020), although many have questioned the transferability of these policies in other nations considering the large population size and especially authoritarian tendencies of its government (Kupferschmidt et al., 2020).

Despite being relatively unpopulated and democratic, South Korea is similarly believed to have curbed the epidemic (Fisher & Sang-Hun, 2020). Importantly, well before the onset of the first case of COVID-19 in South Korea, the South Korean government was considered to have taken public health crisis preparedness seriously as a result of previous experiences with infectious diseases (Lee et al., 2013). Akin to China, the South Korean response to COVID-19 has been analyzed as a perhaps more transferrable solution for relatively democratic nations currently at the heart of the epidemic (Kenneth Rapoza, 2020).

The State of COVID-19: A Quantitative Analysis

In Figure 1, we plot the total confirmed COVID-19 case count within six countries. The graphs are both sigmoidally shaped, indicating an initially exponentially growing - but later decreasing - total confirmed COVID-19 case count. The same cannot be said for other nations, including Germany, Spain, Italy, and the US, for which the graphs look exclusively exponential. Interestingly, the data also reveal that the number of days since the first predicted case in South Korea and China are not consistent: whereas South Korea’s confirmed case count appears to flatline after only 60 days since the first confirmed case, it takes double that amount of time in China for a similar effect to be discerned in the graph (Figure 1B). Numerically, the relatively unchanging total confirmed case count of COVID-19 over time within these countries falls in line with the understanding that the pandemic is reaching its end in China and South Korea.

The relative quantity of recovered cases to confirmed cases of COVID-19 is an informative metric to gauge the temporal ‘stage’ of COVID-19 in a given country. Of China’s 81,897 confirmed cases, 74,720 have recovered; of the 9,332 confirmed cases in South Korea, over 4,500 have recovered. Comparatively, the US reports that less than 1,000 of the 101,657 confirmed cases have recovered. Indeed, the relative quantity of deaths relative to confirmed cases in the US is high among the affected nations (Figure 2). Additionally, on March 29th, the US reported more confirmed deaths caused by COVID-19 than recoveries, unlike any other nation analyzed in the present report. Although they do not report as many deaths relative to recoveries, Italy, Spain, and Germany similarly report a meager recovery count relative to the total number of confirmed cases of COVID-19, indicating that these countries are not near the end stage of the epidemic.

Notably, in China, the ongoing percentage of recovered cases closely resembles the sigmoidal trajectory of the total confirmed cases over time, although offset by approximately two weeks (Figure 3). This evidences the relative completion of the pandemic in China, as the relative slowing of the growth of the total case count has allowed the recovery rate to increase and eventually match the case count. In South Korea, the ongoing percentage of recovered cases may be following a similarly sigmoidal trajectory, especially given the recent sustained increases in recoveries and the relatively unchanging total confirmed case count. In Germany, Italy, and Spain, the recovery rates are just now beginning to rise. In the US, the recovery rate remains relatively unchanging. Instead, the death rate is increasing more than the recovery rate.

These data suggest that China, South Korea, Italy, Germany, Spain, and the US can be categorized on the grounds of their relative temporal stage within the epidemic. Broadly defined, China and South Korea can be conceptualized as having curbed the epidemic, and Italy, Germany, Spain, and the US can be thought of as currently being at the heart of it. Yet multiple parameters relating to the United States - including the unchanging, relatively small recovery rate and the relatively higher death rate - suggest that the US is not operating on a similar timescale to Italy, Germany, and Spain, and may be at a distinctly earlier stage of the epidemic.

To more robustly test this phenomenon, we linearly fit the logarithmized number of confirmed cases of COVID-19 during two windows of time: an early period, corresponding to the initial growth of the disease, and a later period, corresponding to the growth of the disease in recent weeks (Figure 4A). The slopes of these linear fits - a measure of the growth of COVID-19 during each of the early and later windows of time - significantly decreased in China, South Korea, Italy, Spain, and Germany, but increased in the US (Figure 4B). Thus, the US can be categorized separately from the other countries, in that it is relatively at the earliest stage of the epidemic. Additionally, this finding conveys the promissory conclusion that rapid policy intervention and other efforts to limit contagion would perhaps be most effective in the US, as they would take effect earlier on in the trajectory of the disease and its growth. Indeed, considering the dramatically higher confirmed case count in the US relative to all other nations, policy intervention would likely have dramatic effects on COVID-19 contagion in America.

Interestingly, the later growth rates - but not the early ones - of COVID-19 in many countries significantly correlates negatively with quality of healthcare, and positively with democratic index, a measure for the degree to which a country is democratic (Figure 5). That is, the relative growth of the number of confirmed COVID-19 cases tends to be lower in countries with better healthcare and higher in countries with higher democracy scores during the later time window. However, both the early and later growth rates of COVID-19 did not significantly correlate with population density across these same countries.

Global Policy Identification and Analysis

After a thorough review of the policy strategies and their orders of implementation by China and South Korea, we identified 6 major policy actions that characterize significant portions of each countries’ approach thus far: residential lockdown, increase of testing, hospital construction, medical supply acquisition, location tracking of positive patients, and school closure. Figure 6A shows if/when these policies were implemented in terms of days since the first case, plotted against the total number of confirmed cases in each country.

South Korea’s rapid initiatives in widespread testing for cases and tracing of possible disease transmission sites (accomplished through location tracking apps that identified and warned of public locations that confirmed patients had recently been) is believed to have helped stymie the growth rate before it could dramatically increase (Fisher & Sang-Hun, 2020). South Korea also implemented a large scale lockdown in its most impacted regions approximately 30 days after the first known case, further contributing to efforts to flatten the curve (Jung-a & Buseong, 2020).

Although China employed similar policies, it did so in a different order, and with a decreased emphasis on rapid testing relative to South Korea. China first attempted to contain the disease through extensive lockdown (with location-tracking used to restrict contact with COVID-19 carriers) (Kupferschmidt et al.), and later through the rapid construction of makeshift hospitals (Allen-Ebrahimian, 2020; , 2020; Umlauf, 2020; Yuliya Talmazan, 2020). China, however, implemented policy action relatively much later than South Korea, which may aid in explaining why China’s confirmed case count grew for much longer before beginning to flatten (Figure 6B). China’s delay in taking significant policy action and eventual control of the spread of COVID-19 may bode well for countries like the U.S. and Italy; as evidenced by Figure 6B, both the U.S. and Italy began to implement some of the major policy interventions before China did, meaning that there could be a possibility of slowing the exponential growth rate of the virus in or before the 120 days it took China to do so (Figure 1B).

To this point the efficacy of various policy strategies has been considered qualitatively. Although it is impossible - both qualitatively and quantitatively - to discern causative impacts of legislation on COVID-19 growth, we determined the average number of days after policy onset at which there were significant decreases in the growth of COVID-19 (Figure 7). For the policies for which we performed this analysis - medical supply acquisition and widespread school closure - there was no significant difference in the number of days after policy onset at which the growth of COVID-19 decreased. Remarkably, however, the mean number of days for both policy types was incredibly small: 4.6 days and 3.6 days, respectively (standard error = 2.99, 1.44, respectively). This finding exhibits the malleability of the COVID-19 growth rate: these policies may have rapid, perhaps even demonstrable effects on growth rate that operates on the time scale of days.

Discussion

Existing Policy Measures

Of the six major policy interventions we identified in South Korea, Italy, and China, the US has thus far incorporated three of them: ramped COVID-19 testing, medical supply acquisition, and school closure. On March 16th, many schools announced short-term closures at the recommendation of the Centers for Disease Control and Prevention (Chavez, 2020). Additionally, around the same date, COVID-19 testing became widely available (Fritze, John & Jackson, David, 2020). And around March 21st, private companies began to repurpose their operations to create medical masks and hospital garments (Taylor, 2020), including fashion designers and automakers (Paynter, Sarah, 2020).

To this point, privacy concerns have hampered government efforts to use location-tracking to enforce quarantine efforts and track COVID-19 patients (Timberg, 2020), although some apps are in development that would do so using voluntarily-submitted patient information (Grind, 2020), and other research efforts are drawing on cellular network data (Zandonella, 2020). However, the implementation of location-tracking and quarantine enforcement remain impractical at the national level considering there is no national standard for quarantining. Indeed, the lack of a national precedent similarly characterizes the state of residential lockdown policy in the US: although over half of states have called for residential lockdowns, the strictness of these lockdowns varies dramatically across states (Gershman, 2020). For example, whereas Texas Governor Greg Abbot has recently resisted calls for a residential lockdown in Texas (Fernandez & Montgomery, 2020), Californian Governor Gavin Newsom has ordered a strict lockdown, permitting only mandatory excursions (Gershman, 2020).

Finally, at both the federal and state level, there have been relatively few efforts to construct emergency hospitals. In New York, Governor Cuomo has called for the conversion of its Jacob K. Javits Center into a 1,000 bed medical facility (Quito, 2020). Additionally, in Chicago, there are plans to turn the McCormick Place into a 3,000 bed hospital - however, it is anticipated to take multiple weeks until construction is completed (Phil Rogers, 2020). In addition to increasing the number of available hospital beds, the building of a separate hospital dedicated to COVID-19 cases is anticipated to stem the growth of the disease, protecting non-COVID-19 patients and many medical staff (Quito, 2020).

US Policy: Plausible Policy Measures

It is critical to establish that policy measures from other countries cannot simply be extrapolated to the US. Indeed, the population density, quality of healthcare, and type of government (democratic vs authoritarian) differ dramatically among the countries we have analyzed, and in many cases, correlate significantly with the recent growth rates of the total confirmed COVID-19 cases. For these reasons, we do not simply argue that the remaining policy measures we identified in the previous section be opportunistically pursued by US public officials. Specifically, we exclude location-tracking policy from our determination of plausible policy measures, considering the legislative barriers to implementation of such policy in a relatively democratic nation.

The first plausible policy intervention we identify in the US is the rapid construction of hospitals in emerging US COVID-19 epicenters. The relative capacities for nations to rapidly construct hospitals may begin to explain the correlation of healthcare index and decreased growth rates of confirmed case counts in later time periods. A second potential policy measure available to the US is a cohesive, federally-driven residential lockdown procedure akin to the one utilized by other countries, especially those with lower democratic indices, who have successfully decreased their growth rate. However, legal battles regarding the federal government’s authority to enact lockdown procedures remain controversial: advocates for a federal lockdown drawn on Section 264 of Title 42 of the U.S. Code, which states that “the Surgeon General… is authorized to make and enforce such regulations as in his judgement are necessary to prevent the introduction, transmission, or spread of communicable diseases from foreign countries into the States or possessions, or from one State or possession into any other State or possession” (Regulations to control communicable diseases, 1944). Opponents argue that such regulation would be an overextension of federal authority (Naylor, 2020). As of March 28th, many states had yet to incorporate any residential lockdown procedure whatsoever (Gershman, 2020).

Conclusion

In this manuscript, we robustly characterized the relative statuses of COVID-19 in many countries, including China, South Korea, Italy, Germany, Spain, and the US. After comparing the relative developing and aggregate confirmed case, death, and recovery counts, we then linearly fit the logarithmized number of confirmed cases of COVID-19 during two windows of time: an early period, corresponding to the initial growth of the disease, and a later period, corresponding to the growth of the disease in recent weeks. Using these findings, we categorize these affected nations into three categories: those that have curbed the epidemic - China and South Korea, those that have yet to curb the epidemic but are experiencing decreasing growth in confirmed COVID-19 cases - Italy, Germany, and Spain, and those that have yet to curb the epidemic but are experiencing increasing growth in confirmed COVID-19 cases, indicating their relatively early stage in the epidemic - the US. For 12 affected nations, we further found that the later growth rates - but not the early ones - correlated positively with the relative democraticness of affected nations and negatively with the quality of healthcare, and that both the early and later growth rates did not correlate with a nation’s population density.

Finally, we quantified the relative timeliness of various policy implementations enacted by four countries (US, Italy, South Korea, and China), identifying six major policies shared among many of the countries. Our analysis of the changing log-linear growth rate relative to the dates of policy implementation indicates the potential capacity for legislative intervention to have dramatic influences on the COVID-19 growth rate. Ultimately, by characterizing both the relative statuses of COVID-19 and policy interventions in affected nations, our findings establish an empirical foundation for the abstraction of globally-sourced policy measures for use in individual countries.

Figure 1. Total COVID-19 Cases for Different Countries

(A) Confirmed COVID-19 cases plotted datewise for various countries. (B) Confirmed COVID-19 cases plotted relative to the day of the first confirmed case within each respective country. Data for this and all subsequent figures is sourced from the Johns Hopkins Medical School (Johns Hopkins Coronavirus Resource Center, 2020).

Figure 2. Cases, Recoveries, and Deaths for Various Countries.

The plot demonstrates the relative number of confirmed cases, recoveries, and deaths in Italy, the US, South Korea, Spain, China, and Germany. Notably, in the US, the number of deaths is greater than the number of recoveries as of March 28th, 2020.

Figure 3. Cases, Recovery Rate, and Death Rate for Multiple Countries over Time

Depicted are the total number of confirmed cases, the recovery rate, and the death rate in Italy, the US, South Korea, Spain, China, and Germany over time (with respect to the first confirmed case in each of these countries). The recovery and death rates are offset by an additional 35 days, as these rates vary dramatically at smaller total confirmed case counts. Notably, the recovery rate of China closely resembles the sigmoidal shape of the total case count trajectory. The recovery rate in South Korea may be following a similar trend, and the recovery rates in Italy, Spain, and Germany, the recovery rates are beginning to rise. The recovery rate in the US has not yet begun to rise to a similar extent.

Figure 4. Log Linear Fit Modeling for Various Countries

(A) Linearly fitting the logarithmized confirmed total case count to linear models. The log linear fit is computed at two different time windows for each country: one early, and one later. Each time window is twelve days long. Selection of the time windows was done qualitatively to ensure that selections of data were not misrepresentative of the growing confirmed COVID-19 case count for any particular country. (B) Comparing the Log Linear Fit of Cases per Country across the Early and Later Time Windows. Asterisks indicate the significance levels at which the log linear fits were significantly different. Notably, the US is the only country for which the log linear fit is significantly greater at the later time window, rather than significantly smaller.

Figure 5. Correlating Early and Later COVID-19 Growth and Country-Specific Quantities

(A) Comparing health care rankings and log linear COVID-19 growth. Although early log linear COVID-19 growth was insignificantly correlated with the democratic indices of various countries, later log linear COVID-19 growth was significantly correlated, with a negative correlation. Thus, as the health care quality rose, the later COVID-19 growth rate decreased. The health care quality indices were retrieved from The World Health Report 2000 (World Health Organization, 2000). (B) Comparing democracy indices and log linear COVID-19 growth. Although early log linear COVID-19 growth was insignificantly correlated with the democratic indices of various countries, later log linear COVID-19 growth was significantly correlated, with a positive correlation. The democracy indices were retrieved from The Economist Intelligence Unit (Democracy Index 2019, 2019). (C) Comparing population density and COVID-19 Growth. Both the early and later log linear COVID-19 growths were insignificantly correlated with the population densities of various countries. The population densities were retrieved from the World Population Review (Countries By Density Population, 2020).

Figure 6. Policy Responses to COVID-19 per Country

(A) Policy responses by country plotted with respect to the first confirmed COVID-19 case. The vertical bars indicate the day on which different policy initiatives were taken. In the US, a lack of a vertical bar indicates that the policy has not been enacted, and in other countries, that an exact date could not be found. Notably, China and Italy took residential lockdown to be their first major policy response, whereas South Korea began location-tracking very early on. (B) Policy Response Times Plotted Relative to the First Confirmed COVID-19 Case. Notably, China enacted policy changes quite late relative to other countries, which may bode well for the US and Italy. The US has yet to use location-tracking or apply a national residential lockdown to combat COVID-19.

Figure 7. Analyzing Log Linear Growth Change with Respect to Policy Onset Dates

We computed a log linear fit for a 10 day window before the onset of ramped medical supply acquisition and school closure in Italy, China, and South Korea. Then, we continuously computed a new log linear fit for a 10 day window offset forward by a single day. This process was repeated until the original log linear slope was significantly different from the new one at alpha = 0.001. The mean number of days until the log linear growth rate (slope) was significantly different for medical supply acquisition and school closure is depicted in the figure. These quantities were not statistically significantly different. Dates corresponding to other policy reform were unable to be attained for these three countries for other policy reforms.

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