COVID-19 — Disrupted world order -A parameter study -Part-1
This study attempts to explore the behavior of COVID-19 outbreak across different countries and compares India’s position with respect to other countries based on some growth parameters.
Pandemic COVID-19 has already taken the world by storm, engulfed towns and cities in a blink of an eye. One by one countries are falling apart like a domino effect and the global leaders across the world are grappling with this inconvenient truth. With no vaccines round the corner, the best we can do is to self-quarantine and like everyone, I too have quarantined myself (the least I can do to help).
We are living in the world of data and over the last few days, one of the most important achievements of World Health Organization and John Hopkins University (thanks to co-operation of all the countries) was a meticulous collation of COVID-19 datasets. Soon the data was made public and I was amazed by the enormous amount of insightful analysis provided by data scientists, kagglers across the world.
I too wanted to contribute and thus here goes a very naive analysis on COVID-19 outbreak thanks to the wonderful dataset below which includes time series of confirmed , deaths, and recovery data across different countries. The datasets can be found at John Hopkins CSSEGISandData .
I started by looking at the time series of confirmed, recovery and death cases across different countries. Since almost all countries have COVID-19 cases, for providing a clear representation of the time series, I have chosen countries where confirmed cases have been more than 150 as of 20.03.2020.
The plots below show a time series of confirmed cases by country and clearly China, Italy, Iran, Spain are all leading the charts. India, however, inspite of being the second most populated country, has shown commendable ‘resistance’ to Corona Virus outbreak.
So far China and Italy have witnessed large number of deaths; while China was able to take control of the pandemic,conditions in Italy are worsening with each day. The success rate in South Korea in tackling the virus appears to be the highest in plots below. Here, for the plots, I have selected countries that had more than 1 deaths and 10 recoveries as of 20.03.2020.
While China shows highest recovery to confirmed cases, it appears to have effectively controlled death rates as well; a territory where Italy and Indonesia have clearly failed followed by Iraq and Iran. Based on the datasets it seems that UK and Spain are too heading towards a disaster. It is worth mentioning that apart from China and South Korea, Iran deserves special mention as well when it comes to recovery to confirmed cases so far. These three countries are gradually paving the way for a systematic efficient combat against COVID-19.
The time series of confirmed cases in China provided one interpretable insight about the virus outbreak- the confirmed cases follow a logistic growth curve. The logistic growth curve (also known as population curve) qualifies as an ideal model for these cases; the outbreak will initially be expected to occur at an exponential rate followed by a gradual slowdown due to government measures, vaccination programs, immunity development against the virus and so on. Hence, I have extended a similar model for investigation of COVID-19 outbreak in other countries as well.
The logistic function introduced by Pierre François Verhulst can be expressed as :
x_0 is the time duration at midpoint of the curve, L is the maximum value of curve and k represents growth rate.
In order to scale the curve between (0–1) we can set L = 1. In this analysis, I have kept both functionalities for users to view and try out. However, the analysis below is performed after scaling the confirmed cases between 0 to 1 i.e. for example if number of cases increase from 0 to 3000 for one country while 0 to 30000 for the other, growth rates for both countries can be compared after standardising them to the same scale between 0 and 1.
Using the aforementioned model we estimate the parameters for all the countries in the analysis. Next, a density based clustering (DSCAN) is performed in this parameter space to group countries with similar parameter coordinates (states). Details of DBSCAN algorithm can be found here .
The clustering algorithm was able to detect 7 outliers (detected by blue points). China, Japan, South-Korea, Kuwait and Singapore. As evident from the plots below, the time series of confirmed cases in China and Korea increased exponentially at the beginning and is slowly saturating with time, while the remaining four countries follow a steeper trend.
I was particularly interested in identifying the position of my country India with respect to other countries in terms of the parameter set based on the number of confirmed cases till 20.03.2020.
The top 15 countries with parameter states (points/ tiny blobs in Figure 5) closest to India were — ‘Italy’, ‘Lebanon’, ‘Iceland’, ‘Sweden’, ‘Egypt’, ‘Norway’, ‘Iraq’, ‘Greece’, ‘Denmark’. ‘France’, ‘Philippines’, ‘Netherlands’, ‘Finland’, and ‘Belgium’.
Surprising it may seem, but the naive parameter study puts Italy closest to India in terms of sharing the parameter combinations . However, COVID-19 outbreak, is a far more complex problem and hence the findings are likely to differ with time and inclusion of several other parameters.
The second part of this study will be focussing entirely on India and understand the possible pathways of virus outbreak over time. The notebook (with both scaled and unscaled parameters) can be found here.
Lets continue our fight against COVID-19 through safe physical distancing, self quarantine because ‘PREVENTION IS ALWAYS BETTER THAN CURE’.