Coronavirus - Spread Vs Recovery Rate using weibull analysis and median rank approach

1. COVID-19 Coronavirus
Spread Vs Recovery Rate
Weibull Analysis - Issue No. 1
According to World meter web site, The coronavirus
COVID-19 is affecting 162 countries and
territories around the world and 1 international
conveyance (the Diamond Princess cruise ship
harbored in Yokohama, Japan). And a day by day
tracking data published, including Total Coronavirus
Cases and Recovery Cases at 15 Mar 2020 (Cases -
169,577).
Data Sampling:
According to the Data published - Total
Coronavirus Cases and Recovery Cases we ranked
the effected countries (higher to lower one) and
select the first 27 countries which indicate by the
pie graph ( why 27 countries – because they cover
97% from the total cases and 100% in recovery
cases) period of analysis :22 Jan 2020 to 15 Mar
2020)
However, in a real life, data can be represent by distributions, which can be define by a
MEAN and VARIANCE. Consequently, we can study the Hazard Rate So by assigning the
right distribution, examining a goodness of fit for the real life data and evaluating R square,
we can define the Rate of SPREAD and Rate of RECOVERY of the distribution. Moreover,
the best distribution that can be represent the real life data is Weibull (Three Parameters).
By: Mohammed Salem Awad
Aviation Consultant
Data Source:
https://www.worldometers.info/coronavirus/

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Weibull Distribution:
Weibull Distribution define by three parameters,
i.e shape, scale and location (x;,,).
Weibull become Exponential when shape
parameter equal one, thus we can define the
hazard function and we will use two analysis
First: Total Coronavirus Cases.
Second: Total Recovery Cases.
Analysis:
We used median rank approach to define the
Weibull parameters, which are used to find the
Hazard rate.
Parameters Evaluation:
As shown in the figure, we take twice (ln) for
cumulative distribution function, this lead to
straight-line form. Where () shape parameter is
slope of line,  is a scale parameter and  is a
location parameter.
The Hazard Function =
𝒉( 𝒙; ,,) =


(
𝒙−

)
−𝟏
a) Total Coronavirus Cases
 = 2039.67
 = 0.4712
 = 225
At R- square = 97.5 %
b) Recovery Cases
 = 161.03
 = 0.4068
 = 9
At R- square = 81.7 %

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Results:
By using the above parameters, we can develop a Total Coronavirus and Recovery cases
Rates.
Obviously, the rate of Recovery is higher than rate of Total Coronavirus i.e mean a positive
sign that Coronavirus will diminish soon. But the parameters of Weibull analysis – shape
parameter both are less than one – this tend that we are in the first stage of bathtub curve.
And its needs time to reach stable state. i.
e ( = 1).
Conclusions:
In these hard time, world needs, some tools to monitor the overall impacts and behaviors
coronavirus data. One of perfect tool, is Weibull, it will trace /monitor the impacts of this
virus and predicts its rate of spread compare to treatment that done by world in terms of
recovery cases.
At this time the study shows, the gap between spread and recovery rate is still small.
Therefore, we have to repeat this analysis by updating the data, and it is good for spread rate
to go lower and lower, while we have to work hard to increase the rate of recovery.

4. 44
Appendix:
Case: Total Coronavirus Cases
Analysis to find SHAPE and SCALE parameters for top 27 countries