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Bioinformatic Modelling of SARS-CoV-2 Pandemic With a Focus on Country-Specic Dynamics

One of the seminal events since 2019 has been the outbreak of the SARS-CoV-2 pandemic. Countries have adopted various policies to deal with it, but they also differ in their socio-geographical characteristics and in the public health care facilities. The aim of our study was to investigate differences between epidemiological parameters across countries. The analysed data represents SARS-CoV-2 repository provided by the Johns Hopkins University. Separately for each country we estimated recovery and mortality rates using the SIRD model applied to the first 30, 60, 150 and 300 days of the pandemic. Moreover, a mixture of normal distributions was fitted to the number of confirmed cases and deaths during the first 300 days. The estimates of peaks ’ means and variances were used to identify countries with outlying parameters. For the period of 300 days Belgium, Cyprus, France, the Netherlands, Serbia and the UK were classified as outliers by all three outlier detection methods. Yemen was classified as an outlier for each of the four considered timeframes, due to high mortality rates. During the first 300 days of the pandemic the majority of countries underwent three peaks in the number of confirmed cases, except Australia and Kazakhstan with two peaks.

One of the most seminal global events since 2019 has been the outbreak of the SARS-CoV-2 (Severe Acute Respiratory Syndrome -Coronavirus -2) infections in humans, which occurred in December in China 1 and has been following worldwide spread in 2020 (see e.g. WHO Coronavirus disease situation reports at www.who.int/emergencies/diseases/novelcoronavirus-2019/situationreports). It is commonly believed that the current pandemic has had its roots in the seafood market located in Wuhan 2 . Since late 2019 the virus has spread globally and evolved into several strains throughout the course of 2020 and 2021. Two most common means of infection with the SARS-CoV-2 virus are the so-called respiratory droplets and touching an infected surface. When an infected person sneezes or coughs the viral particles become airborne, can travel up to several meters and infect an oral or nasal cavity of a nearby person 3 . SARS-CoV-2 can survive up to several hours on most surfaces and even several days on certain surfaces 4 . When a person touches an infected surface, it is easy to transfer viruses onto one's mucus membranes such as eyes, nose, or mouth. The main location of viral replication are lung epithelial cells where a pathogen uses its S protein to bind with the ACE2 receptor of a host cell 5 . After binding, a virus is ready to infect a cell either via direct entry, where the membrane of the host cell and the viral envelope fuse together, or by endocytosis, where an entire virus is being engulfed by a part of the cellular membrane 6 .
Inside a host cell, a virus uses cellular machinery (mainly the endoplasmic reticulum and the Golgi Apparatus) to assemble new virions. The release of newly produced viruses places a lot of stress on human cells and consequently leads to apoptosis 7 and leads to a major immune response, often referred to as a cytokine storm. This strong inflammation leads to an excess build-up of mucus, mostly in the alveoli. Such a condition is responsible for shortness of breath, which is one of the most common symptoms of the SARS-CoV-2 infection.
Various countries have adopted different policies to deal with the dynamics of this pandemic and, atop of those policies, countries also differ in terms of their socio-geographical characteristics (such as climate, total population and population density, etc.) as well as in the public health care facilities. The aim of our study was to fit SIRD models to early (30 days), mid-(60 and 150 days), and long-term (300 days) time-frames of SARS-CoV-2 pandemic, separately to each country, in order to estimate country-specific pandemic parameters.
However, the SIRD model only allows for fitting one peak of infection during the pandemic, what in the case of SARS-CoV-2 results in averaging over multiple peaks. Therefore, in addition to SIRD, linear mixture models were fitted to the same set of data in order to estimate fluctuations in the dynamics of the pandemic. The final goal of the study was the assessment of (dis)similarities between countries applying outlier detection methodology.

Methods
Study population. The analysed data comprised cumulative daily numbers of: confirmed cases, deaths and recoveries, reported for 191 countries, beginning from the 21 st of January 2020. This data set represents SARS-CoV-2 Data Repository provided and curated by the Center for Systems Science and Engineering at Johns Hopkins University 8 and was obtained via Github (github.com/CSSEGISandData/COVID-19) using a custom written Python scripts.
Separately for each country, the pandemic's dynamics was modelled for the period of 30 days (D30), 60 days (D60), 150 days (D150), and 300 days (D300), beginning from the first day in which the number of confirmed cases in a given country exceeded zero, what resulted in various calendar datesdepending on a country. SIRD model. The SIRD model and the least squares estimators for its parameters were implemented using custom written Python scripts following Anastassopoulou et al. 9 . In brief, the model is defined by the following equations: Further on, two-sample t-tests were calculated for the two consecutive means and standard deviations estimated for each country in order to determine whether this assumption was appropriate i.e. the difference between the estimated means exists. The difference between the means was determined as nonsignificant based on a P-value threshold above 0.05 after a multiple testing correction based on the Bonferroni approach, meaning that two, instead of three, components were sufficient for a given country during the first 300 pandemic days.

Results
Epidemiological parameters. Based on recovery and mortality rates estimated from the SIRD model no marked overlap between outliers detected by the three methods as well as between time periods (D30, D60, D150, and D300) was observed ( Fig. 1  Considering the longest time span (D300), for each country, mortality rates were lower than recovery rates. Except Yemen, which was classified as an outlying country, all the remaining countries revealed mortality rates below 10%. On the other hand, estimated recovery rates varied greatly between countries from as low as less than 1% in Serbia and the UK, to over 95% in Bahrain, Djibouti, Ghana, Qatar, and Uzbekistan (Fig. 2).

Discussion
Globally, a much greater variation was observed in recovery rates than in mortality rates.
Significant sources of heterogeneity in SARS-CoV-2 associated mortality rates across countries are differences in governmental policies related to social aspects of life during the pandemic 11 , country globalization level 12 , and genetic differences between country-and continent-specific populations 13 . Some of our findings reflect the abovementioned sources of inter-country variation. Australia which was outlying in the numbers of confirmed cases over time by showing two, rather than three peaks over the first 300 days of the pandemic, and China outlying by having all three peaks of confirmed deaths estimated in a short time-span one to another were previously mentioned by Pearce et al. 14 as countries that imposed early restrictions to social contacts. Moreover, high mortality rates estimated by us using the SIRD model aligned with highly globalised countries (Belgium, France, United Kingdom, Italy, Hungary, and Netherlands for D150). However, neither the patterns of outlying countries nor the sole estimated mortality rates did align with their geographical locations as it may have been expected providing genetic differences between populations, a phenomenon also observed by Balmford et al. 11 .

Conclusions
Considering both major outcomes of the SARS-CoV-2 pandemic, i.e. the recovery and death, the heterogeneity between countries exists. Obviously, the goal is to be classified as an outlying country based on exceptionally low mortality rates and high recovery rates.
Liechtenstein was the closest to this favourable pattern being a "positive" outlier for D30, D60 and D150. On the other end, Yemen represents a "negative" outlier with high mortality rates for all four considered periods and low recovery rates for D30 and D60. We believe that the observed country-specific differences result from a mixture of factors including the biology of the virus strains, different policies adopted by countries to mitigate the spread of infections, but also different accuracy of data reporting.

Figure 2
Country-specific ̂ (recovery rate) and ̂ (mortality rate) from the SIRD model fitted to the first 300 (D300) days of pandemic.    Tables   Table 1 Country-specific estimates of (recovery rate) and (mortality rate) from the SIRD model fitted to the first 30 (D30), 60 (D60), 150 (D150), and 300 (D300) days of the pandemic, for countries classified as outliers. Outliers classified by one methodwhite, by two methodslight grey, by three methodsdark grey.

Declarations Funding
No external funding was involved.

Conflicts of interest/Competing interests
None declared.

Availability of data and material
The input data underlying this article is publicly available from the SARS-CoV-2 Data Repository at https://github.com/CSSEGISandData/COVID-19.

Code availability
Python code is available upon request from the corresponding author.

Ethics approval
Not applicable.

Consent to participate
Not applicable.

Figure 2
Country-speci c β (recovery rate) and γ (mortality rate) from the SIRD model tted to the rst 300 (D300) days of pandemic.

Figure 3
Differences in days between two consecutive peaks of the number of con rmed cases estimated by the linear mixture model for the rst 300 days of the pandemic. Clustering based on country-speci c means of three normal distributions tted by the linear mixture model to the rst 300 (D300) days of pandemic. Countries classi ed as outliers are marked in red.

Figure 5
Estimated means of peaks of the number of daily deaths estimated by the linear mixture model for the rst 300 days of the pandemic. Means corresponding to China, which was classi ed as an outlier, are marked in red. Standard deviations were calculated excluding China.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. Table1.pdf