I thought that I write another short essay on COVID-19 to analyze the effectiveness of the lockdown - the so called social distancing.
The idea of social distancing is perfectly logical. The virus is like a fire and people are like the wood, if people separate the fire dies down with minimum losses.
To model the infection rate I use the Gompertz Curve https://en.wikipedia.org/wiki/Gompertz_function
You can look it up. It is a Sigmoid function which has four parameters, (a), (e), (b), and (c). The parameter (a) is an asymptote, (e) is called the Euler's constant equal to 2.71828, (b) is a parameter that governs the displacement along the x-axis, and (c) is the growth rate.
I take the data of the total infection cases in NZ from the World Health Organization (daily) Situation Report from the data we started reporting, which was Feb 28 up to Mar 27 to illustrate the fit of the data to the Gompertz Curve. For (a=0.1), (b=0.2) and (c=0.5) along with (e) fixed at 2.71828, the data seem to fit remarkably well.
The idea of social distancing is perfectly logical. The virus is like a fire and people are like the wood, if people separate the fire dies down with minimum losses.
To model the infection rate I use the Gompertz Curve https://en.wikipedia.org/wiki/Gompertz_function
You can look it up. It is a Sigmoid function which has four parameters, (a), (e), (b), and (c). The parameter (a) is an asymptote, (e) is called the Euler's constant equal to 2.71828, (b) is a parameter that governs the displacement along the x-axis, and (c) is the growth rate.
I take the data of the total infection cases in NZ from the World Health Organization (daily) Situation Report from the data we started reporting, which was Feb 28 up to Mar 27 to illustrate the fit of the data to the Gompertz Curve. For (a=0.1), (b=0.2) and (c=0.5) along with (e) fixed at 2.71828, the data seem to fit remarkably well.
Then I have two scenarios. The first scenario is about an effective and enforced lockdown, i.e. an effective social distancing. Under such scenario, the infection growth rate (c) falls significantly, and sooner. The second scenario is a less effective lockdown, whereby the growth rate falls at a slower rate and takes more time. Here are the assumed growth rate scenarios.
Here is the projection of the infection rate under the effective lockdown scenario. The infection rate peaks at 2,630 cases on April 3, then takes a nosedive very similar to the Chinese case.
And here is the less effective lockdown (less effective social distancing), where the infection peaks at a staggering 78,203 cases on April 15.
This is quite a
significant increase in two weeks period, a
staggering 75,573 more cases.
It emphasizes the importance and effectiveness of the lockdown and strict
social distancing, which seems to be crucial to defeat the virus.
See
Greenstone and Nigam (2020).[1] In a rather more elaborate model, they projected that moderate social distancing would save 1.7 million lives between March 1 and October 1 in the United States.
[1] Greenstone, M. and V. Nigam. (2020).
Does Social Distancing Matter? University of Chicago - Becker Friedman Institute for Economics WP No. 2020-26
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