Little's Law on COVID-19

Introduction

Little's Law (a.k.a. Little's theorem, result, lemma, law, or formula) is a well known formula in queueing theory, and it has been widely used to estimate the long-term average number of customers in a stable system. The goal of this study is

1. to apply Little's Law to COVID-19 open datasets;

2. to investigate how health systems of different countries respond to COVID-19 pandemic; and

3. to provide a quick assessment of the severity of the epidemic in each country.

This study is still ongoing, and more results will be made available on this website.

Method

Data Source

The Humanitarian Data Exchange (https://data.humdata.org). The dataset contains daily cumulative number of confirmed, death and recovered cases from 2020/01/22. For simplicity, we sum up the values from different regions of the same country.

• • Daily statistics of the confirmed cases of each country [download]

  • Daily statistics of the death cases of each country [download]

  • Daily statistics of the recovered cases of each country [download]

Little's Theorem

The Little's Law was proposed by John Little in 1961, and it states that the average number N of customers in a stationary system is equal to the average arrival rate λ multiplied by the average time T that a customer spends in the system, i.e.,

N = λ T

Little's Law in COVID-19 Pandemic Cases

• • N represents the prevalence of COVID-19, which is the proportion of infected people in a given time period, i.e., the total number of the confirmed cases minus the death cases and the recovered cases.

  • λ represents the incidence rate per day (#/day).

  • T represents the average recovery time (i.e., the time from onset to clinical recovery or death) of confirmed cases.

The Little's Law holds when the pandemic is under a good control. In such cases, T is espected to be stable in a reasonable range, and the value of N may vary with λ up to a certain value that represents the capacity of a health system.

When an outbreak occurs, the Little's Law no more holds, and λ may increases sharply resulting in an extensive number of active confirmed cases (N) out of its health system capacity. During that period, the value of T also increases due to limited healthcare resources, and it may become even far greater than the reasonable range.

To recover from the outbreak, it is essential to lower N under its health system capacity, and there are two ways:

1. to reduce λ by promoting mask-wearing, strengthening quarantine measures, tightening border control, etc.; and

2. to reduce T by improving treatments (i.e., increasing recovery rate), patient prioritization, etc.

Results

• Asia: Taiwan, Japan, Thailand, Vetniam, Singapore, Philippines, Hong Kong, Macau, China, Korea

• Europe: Italy, Iceland, France, United Kingdom, Germany, Spain, Portugal, Russia, Swedem, Czechia

• America & Oceania: US, Mexico, Brazil, Argentina, Chile, Venezuela, New Zealand, Australia

• Countries: India, Iran, Israel, Turkey, Egypt, Nigeria, Kenya

Selected Cases

• Countries that are about completely recovered

  • onset rate is less than 3 cases/day

  • average recovery time is less than 20 days

  • # of total confirmed cases is greater than 400 cases

• Countries that are under well controlled

  • average recovery time is less than 20 days

  • onset rate is less than 50 cases/day

  • # of total confirmed cases is greater than 400 cases

• Countries that are under outbreak (average recovery time is greater than 120 days)

• Countries that have rare confirmed cases (less than 20 confirmed cases)

• Countries that have high death rate (greater than 10%)

• Countries that have flights to Taiwan

Overall Distribution

Download

GitHub: https://github.com/cclljj/COVID19-Analysis

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