Mathematical Analysis of COVID-19 Spread: New Zealand
Dr Himanshu Shekhar
Introduction: After monitoring the total number of infected cases for COVID-19 in India and its states, efforts are diverted to know the trends in other countries, one by one and arrive at the mathematical formulation for the COVID-19 infection trends. To start the activity, New Zealand is taken as first case, where COVID-19 is said to be controlled. The mathematical equations are derived for New Zealand.
Background: New Zealand is a cluster of islands located just on the south east side of Australia. The first case is reported there on 28 Feb 2020 and total confirmed cases on 16 May 2020 is 1498, only. It was only 1461 on 30 April 2020 and in last 16 days, it is only addition of 27 new cases. The case density is reported to be 231 per million population and now it is totally controlled. The variation of daily and total number of cases is taken from Internet.
Mathematical treatment: The daily variation of number of cases is plotted against number of days, assuming 20 March 2020, as start time. On that day 39 cases were reported. The plot is given.
Generally these type of variations are modeled as normal distribution curves. The normal distribution curve is mathematically given by two parameters – mean and standard deviation. The peak value of a normal distribution curve with zero mean and unit standard deviation is unity, as shown below.
The actual variation of New Zealand has two peaks and it can be mathematically modeled as combination of two normal distribution curve. The parameters for both the normal distribution curves is tabulated. As normal distribution curve has a unit peak, the amplitude is also used as another parameter for simulating both the peaks.
|
Curves
|
Mean
|
Std
Dev
|
Amplitude
|
|
I
|
6
|
16
|
85
|
|
II
|
14
|
14
|
90
|
With these parameters, the curves are plotted against actual number of cases and the correctness of developed mathematical formulation is established.
Conclusion: Combination of 2-normal distribution curve is able to match the COVID-19 daily new case profile of New Zealand. New Zealand has established a turnaround in around 14 days and within 25-30 days the number of cases has been controlled. Mathematically, the amplitude and standard deviation of both the peaks are almost similar, but second peak has bigger amplitude and lower standard deviation. The First peak (mean) at 6 days, second peak (mean) at 14 days and turn around in 21 days is the trend shown by New Zealand, mathematically.
India is a country of diversity. Any formula will not hold good for whole country. this is the biggest problem and movement of infected people has started. this is a great headache to the problem and it is very difficult to analyse the situation mathematically. that is why India invented zero. If movement of labour have not been taken place your mathematical prediction would have come true. this is my observation.
ReplyDeleteI fully agree with your concerns and the point raised. I presume that in such a big country like India, the disturbances caused by various forces are neutralized, by some parallel actions. I am analyzing all countries, where turnaround is achieved to understand the behaviour of the Pandemic. Hope that something will come out for India from the collected data. Thanks for reading my blogs and making constructive comments. Regards.
DeleteVery nice analysis for Newzealand.
DeleteWe can take cue from the analysis of other countries
and control the cases in India.
Great Himanshu Ji.
Thanks.
DeleteToday New Zealand is in News for completely eradicating COVID-19. So, I though it apt to re-share the old analysis of 16.05.2020. Regards.