A First Attempt to Build Novel Coronavirus Disease Model from WHO Situation Reports
Posted on 18 Mar 2020; 11:00 PM IST. Last Updated 18 Mar 2020; 11:00 PM IST.Summary: The following is an attempt to build a disease model for the Novel Coronavirus (Covid-19). The situation reports released by the World Health Organization (WHO), contain ample information about the disease, which could serve as guidance. It is hoped that this model could greatly help administrators around the world, to prepare in advance, and make better decisions for protecting their people.
The World Health Organization (WHO), was releasing Situation Reports for Novel Coronavirus (covid-19), since the onset of the disease. These datasets contains a lot of useful information, and what is needed may be a comprehensive explanation or model for the disease. The following is a first attempt to build a disease model, from the Situation reports released by WHO.
Definitions of Terms
A brief description of the terms, and their definitions employed in the analysis is provided below.
Disease Transmission Rate (DTR): The disease transmission rate identifies, how fast the disease can spread in the population. This is a very important measure, since it tells us, how many people may be exposed to the disease. It may be noted that the disease transmission rate is a dynamic measure, which is dependent upon both space and time, so it has a spread factor, and a time factor.
Disease Infection Rate (DIR): The disease infection rate identifies, the percentage of people are infected, after they are exposed to the disease. What this means is that a person may be exposed to the disease, but the disease may not develop to significant levels for detection. Mere exposure cannot be regarded as "infected".
The Novel Coronavirus (Covid-19) created another "hair-splitting" distinction, and confusion with regard to infected rate. The disease can remain asymptomatic (without symptoms), and in the absence of symptoms, an infected person looks as good as an uninfected person. The following figure, attempts to high-light the problem.
| UnExposed | ||
| Exposed | UnInfected | |
| Infected | Asymptomatic | |
| Symptomatic | ||
For the seasonal Flu, the infected rate numbers are 3% (low value) and 11% (high value). This number is not available for the Novel Coronavirus (covid-19). In a pandemic, it may not be possible to conduct medical tests to ratify these numbers, so it is estimated by back calculation techniques, described in the analysis portion of the article.
Symptomatic Factor (S-Factor):
The World Health Organization (WHO) reports detailed below, provide valuable information on Coronavirus Disease 2019 (COVID-19).
https://www.who.int/docs/default-source/coronaviruse/who-china-joint-mission-on-covid-19-final-report.pdf
https://www.who.int/dg/speeches/detail/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19---3-march-2020
What is noted from these report is 80% of the infected population exhibit no symptoms or have only mild symptoms, and only 20% require medical care. Only people who need medical care approach a medical facility, and are otherwise countable as "infected". We have no clue about people, who are infected but do not need medical care.
So, the information revealed by WHO plays a critical role, in later calculations, and this tells us that for every person we see in medical care, there are four more, we probably did not see or meet. In short, the total infected is 5, for every person who requires medical care.
This factor is called Symptomatic Factor or (S-factor), and the value of S-factor is 5 (this was given by WHO report). The term S-factor was coined by the author of this article.
Disease Fatality Rate (DFR): The disease fatality rate identifies, a statistic derived from number of deaths over the number of infected. The World Health Organization (WHO), has provided a value of 3.4 for this factor.
Analysis
Model for Disease Transmission
The Chinese CDC has recently released a report on the Epidemiological Characteristics of an Outbreak of 2019 Novel Coronavirus Diseases (COVID-19) in China. The report describes (in Figure-2), the spread of COVID-19 in China, from December 31, 2019 thru February 11, 2020, which is 42 days or 6 weeks. The report is available at this website.
Assumption-1: The first assumption is that the spread in 6 weeks covered just the Whuan City, in Hubei Province of China.
Assumption-2: The second assumption is that initially 1 person, is exposed to the disease.
From the above two assumptions, we can easily derive the Disease Transmission Rate (DTR) as: 10; which means that the disease spreads, (or diffuses, or exposes) 10 times in a week.
A roll out of the spread on a weekly basis is provided below.
after 1 week : 1 x 10 = 10 exposures;
after 2 weeks : 10 x 10 = 100 exposures;
after 3 weeks : 100 x 10 = 1,000 exposures;
after 4 weeks : 1,000 x 10 = 10,000 exposures;
after 5 weeks : 10,000 x 10 = 100,000 exposures;
after 6 weeks : 100,000 x 10 = 1,000,000 exposures;
after 7 weeks : 1,000,000 x 10 = 10,000,000 exposures;(or approx. the population size of Wuhan, China).
A DTR value of 13, could cover the entire Hubei province of 60 million, in the same 7 weeks.
Model for Disease Infection
The recent Coronavirus (COVID-19) Situation Report – 52, as of 12 March 2020, from World Health Organization (WHO), is available online at: https://www.who.int/docs/default-source/coronaviruse/20200312-sitrep-52-covid-19.pdf?sfvrsn=e2bfc9c0_2
From the WHO Situation report-52, we note the following figures, for Hubei Province,
Confirmed cases: 67781 (approx. 70,000); and Deaths: 3056 (approx. 3000);
The population of Hubei is 58.5 million (approx. 60 million), as per wikipedia data available at: https://en.wikipedia.org/wiki/Hubei.
The first step of the analysis, attempts to determine the infected. To get the count of infected, we need to multiply the confirmed cases reported by medical facilities by S-Factor.
Actual Infected = confirmed cases x S-Factor = 70,000 x 5 = 350,000.
The second step of the analysis, attempts to estimate the infection rate. To get this figure, we need to adopt a trial and error method. Initially, we assume that the infection rate is at about 3%, which incidentally is the low value for infection rate of seasonal flu.
Let "n" be the population of the region. At 3%, the infected population = 3n/100; We just found above, the actual infected as 350,000.
Equating, 3n/100 = 350,000, we get n = 35/3 million or 11.67 million. Here, the population count, is computed from the disease statistics, by the back calculation technique. This figure is far less than Hubei population, but closely matches the Wuhan (a city in Hubei province) population.
To get, the Hubei population of 60 million, we need to set the infection rate at 0.6; Ofcourse, there are some unconfirmed reports on internet, which support the 0.6% infection rate. There are also unconfirmed reports, which state that the body bags at Wuhan crematoriums are much higher than normal figures.
So, before advancing further, the analysis must establish the ground facts.
The Ground Facts
As stated above, Hubei (a province of China ) has a population of 60 million. From Wikipedia, we can easily note that the Chinese mortality rate is 7 per 1000 per year. This means, natural deaths in China per year per million is 7000. So, natural deaths in Hubei per year would be 420,000. This comes down to 35,000 per month (for Hubei), and natural deaths for the past two months (Jan and Feb of 2020), would be 70,000.
The WHO situation report for Hubei stated that there are approximately 70,000 cases, and 3000 deaths. This could be easily stretched to imply that very old people, who are just about to die (for other reasons), are affected by Novel Coronavirus, or conversely, the virus does not pose a grave danger to society.
Assuming the above is valid, the 3000 deaths due to the virus in 2 months, is less than 5% of 70,000, which is the number for natural deaths in 2 months. So, why the whole of China is alarmed?
The Cause for Alarm in China
The cause for alarm in China can be easily explained by the "back calculation" of population count, which we computed as 11.67 million for Hubei province. This count is far less than 60 million count of Hubei province, but closely matches the Wuhan City population count, which is just a fifth of Hubei population.
What this means is, the disease statistics have accounted for only a fifth of the population. So, the number of infected, and number of dead could be much more. How much more, is based on how effective the lock down was, and these figures are known only to China, and beyond the scope of this work.
Model for Disease Fatality
The World Health Organization (WHO), has conducted the study, and provided a value for fatality rate as 3.4.
From the values available for Hubei province, we can easily see that the disease fatality rate = 3000/70000 = 3/70 = 4.28%. This value assumes that the infected people received adequate critical care needed for survival. The Chinese (Hubei) value, has ample merit, since it reflects the state of the health care, when it was subjected to acute stress.
Conclusion
The modelling effort concludes with the following estimates for the crucial parameters needed in understanding the rate of spread, infection, and fatality. It is hoped that these values could provide "some guidance, if not all" on what an administrator in charge of a large province, could expect, form one of the greatest upheavals of this century.
| Low-Value | High-Value | |
| Disease Transmission Rate (DTR) | 10 | 13 |
| Disease Infection Rate (DIR) | 3 | unknown |
| Disease Fatality Rate (DFR) | 3.4 | 4.28 |
As per the model, for a region of about 10 million population, the infected could be 3% or 300,000, of which one fifth or 60,000 could require medical care. The fatality rate is 4% of infected receiving critical care, or 4% of 60,000, which is 2,400.
Note: The model may not adequately reflect reality, and the actual behaviour of the disease in a region, may vary considerably, from what is stated in this article. This analysis could atmost merely provide "some guidance, and not full guidance".