Click Here“Beautiful Math”

There are thousands of languages spoken on planet earth. And the greatest of them all may be mathematics; “Language of the Universe”. If this is true, then COVID-19 speaks math. Let’s examine New Zealand data to explore this hypothesis.

THE New Zealand COVID-19 story may be the “gold standard” that other countries should emulate, if it is not too late.

Here is the progression curve of total cases, starting from the first day that more than 5 were confirmed. It is “S” shaped. Other names for it are sigmoid curve and logistic function.

Color Code for the Plots:

Orange = Data

Turquoise = Mathematical Functions

All of the line plots are interactive. So let your cursor do some walking.

Question: Does any part of this curve exhibit exponential growth?

We found that the growth was indeed very close to expoential through day 14.

Day 14 was the inflection point in the curve. From then on, the growth rate slowed to produce the “S” curve we have already seen.

## Estimated Asymptote = 1490

As the case growth curve approaches the asymptote, the number of new daily cases will approach zero. Thus the mathematical curve we are looking for is Normal/Gaussian/Bell-Shaped.

Question: What do hte New Zealand data show?

This plot looks a lot like a bell.

Question: Will there be a second wave as shelter-in-place restrictions are eased? We shall see.

But wait, let’s do a little mathemagic. How about a smoothie?

A seven day moving average, for example.

Is the result pretty good, or what? Hopefully with more days of data, the theoretical curve will not dip below zero new cases.

Remember, there is no such thing as a perfect model. There may be some that are useful and require tweaking from time to time.

Smooth the Data

## Estimated Asymptote = 1490
How has New Zealand achieved these results?

The R pakage Covdata provides access to a database that chronicles the issuance of national directives throughout the world.

The first one started on February 3.

“Close doors on foreign travellers from China.”

##                                                                                                                                                                                                                                                                                                                                                                                event_description
## 1                                                                                                                                                                                                                                                                                                                                            NZ to close doors on foreign travellers from China.
## 2                                                                                                                                                                                                                                                        Any foreign travellers who leave or transit mainland China after 2 February 2020 New Zealand time will be refused entry to New Zealand.
## 3                                                                                                                                                                                                                                                            All new arrivals from other countries must self-quarantine for 14 days (except for those arriving from selected Pacific countries).
## 4                                                                                                                                                                            New Zealand imposes External border restrictions:  Cruise ships cannot enter to New Zealand’s territorial waters effective from 23:59 Saturday 14 March 2020. This will remain in place until at least 30 June 2020
## 5                                                                                                                                                                                                                                                      Gatherings or events where 500 or more people are together in one place outdoors, or 100 people indoors, at one time should be cancelled.
## 6                                                                                                                                                                                                    New Zealanders are advised not to travel overseas at this time. The New Zealand Government has raised its travel advice to “do not travel” – the highest level – regardless of destination.
## 7                                                                                                                                                                                                                                                                                                            NZ to close its borders to anyone not a citizen or permanent resident, PM confirms.
## 8                                                                                                                                                                     People to start working from home if possible. If people cannot work remotely then employers should allow for shift work, physical distancing within the workplace, staggered meal breaks and flexible leave arrangements.
## 9                                                                                                                                                                                                     Councils around the country are proactively closing community facilities including swimming pools, libraries, recreation centres, community centres, the City Gallery, museums and venues.
## 10                                                                                                                                                                                                                                                                   People over 70 years-old or those with compromised immune systems or respiratory conditions are being told to stay at home.
## 11                                                                                                                                                                                                                                                                                                 NZ announces new recommendation regarding social distancing for public transport at March 21.
## 12                                                                                                                                                                                                                                                                                                                                                    Nation steps up to COVID-19 Alert Level 2.
## 13                                                                                                                                                                                                                                                             New Zealand ,March 21, Declaration of emergency:  Prime Minister Jacinda Ardern has announced a four-level Covid-19 alert system.
## 14                                                                                                                                                                                                                                                                                                                                                         Limit non-essential travel around NZ.
## 15                                                                                                                                                                                                                                               Prime Minister Jacinda Ardern has announced a four-level Covid-19 alert system and asked people to stop non-essential travel within New Zealand
## 16 New rules for hospitality sector under Covid-19. People going to bars, restaurants and casinos will be expected to stay at least a metre away from each other, and venues will have to do head counts to make sure there are not >100 people indoors. A register of guest details will also have to be kept for four weeks, including full name, address and contact phone and email details.
## 17                                                                                                                                                                                                                                                                 New Zealand is enforcing an internal border restriction by limiting "travel in areas with cluster or community transmission".
## 18                                                                                                                                                                                                                                                                                                        NZ announces new restrictions of mass gatherings as further restrictions were applied.
## 19                                                                   The Department of Conservation is closing its visitor centres to the public from today, and from tomorrow will cancel all walking hut and campsite bookings for the rest of the season (up to 30 June 2020). Rangers will visit tracks and facilities, alerting people about the changes and checking people are complying.
## 20                                                                                                                                                                                                                      New Zealand's Covid-19 alert level has risen to three and the country will go into a full lockdown at 11.59pm on Wednesday, Prime Minister Jacinda Ardern has confirmed.
## 21                                                                                                                                                                                                                                                                                                  NZ applies further restrictions on mass gatherings: "Mass gatherings cancelled" of any size.
## 22                                                                                                                                                                                                                                                                                                                   NZ announces that "affected educational facilities" are closed at March 22.
## 23                                                                                                                                                                                                                                                         NZ announces that public venues are closed (e.g. libraries, museums, cinemas, food courts, gyms, pools, amusement parks) at March 22.
## 24                                                                                                                                                                                                                                                                                                           NZ is enforcing an internal border restriction as "travel is severely limited" now.
## 25                                                                                                                                                                                                                                                                                                                                                             People instructed to stay at home
## 26                                                                                                                                                                                                                                                                                                                                                                 NZ has reached alert level 4.
## 27                                                                                                                                                                                                                                                                                                                                                            NZ: Educational facilities closed.
## 28                                                                                                                                                                                                                                                                               Businesses closed except for essential services (e.g. supermarkets, pharmacies, clinics) and lifeline utilities
## 29                                                                                                                                                                                                                                                                                                                            Government bans travel from Iran in response to coronavirus threat

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