Tag Archives: SARS

COVID-19 is worse than SARS, especially for China.

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The corona virus, COVID-19 is already a lot worse than SARS, and it’s likely to get even worse. As of today, there are 78,993 known cases and 2,444 deaths. By comparison, from the first appearance of SARS about December 1 2002, there have been a total of 8439 cases and 813 deaths. It seems the first COVID-19 patient was also about December 1, but the COVID-19 infection moved much faster. Both are viral infections, but it seems the COVID virus is infectious for more days, including days when the patient is asymptomatic. Quarantine is being used to stop COVID-19; it was successful with SARS. As shown below, by July 2003 SARS had stopped, essentially. I don’t think COVID-19 will stop so easily.

The process of SARS, worldwide; a dramatic rise and it’s over by July 2003. Source: Int J Health Geogr. 2004; 3: 2. Published online 2004 Jan 28. doi: 10.1186/1476-072X-3-2.

We see that COVID-19 started in November, like SARS, but we already have 10 times more cases than the SARS total, and 150 times more than we had at this time during the SARS epidemic. If the disease stops in July, as with SARS, we should expect to see about a total of 150 times the current number of cases: about 12 million cases by July 2020. Assuming a death rate of 2.5%, that suggests 1/4 million dead. This is a best case scenario, and it’s not good. It’s about as bad as the Hong Kong flu pandemic of 1968-69, a pandemic that killed 60,000 approximately in the US, and which remains with us, somewhat today. By the summer of 69, the spreading rate R° (R-naught) fell below 1 for and the disease began to die out, a process I discussed previously regarding measles and the atom bomb, but the disease re-emerged, less infectious the next winter and the next. A good quarantine is essential to make this best option happen, but I don’t believe the Chinese have a good-enough quarantine.

Several things suggest that the Chinese will not be able to stop this disease, and thus that the spread of COVID-19 will be worse than that of the HK flu and much worse than SARS. For one, both those disease centered in Hong Kong, a free, modern country, with resources to spend, and a willingness to trust its citizens. In fighting SARS, HK passed out germ masks — as many as anyone needed, and posted maps of infection showing places where you can go safely and where you should only go with caution. China is a closed, autocratic country, and it has not treated quarantine this way. Little information is available, and there are not enough masks. The few good masks in China go to the police. Health workers are dying. China has rounded up anyone who talks about the disease, or who they think may have the disease. These infected people are locked up with the uninfected in giant dorms, see below. In rooms like this, most of the uninfected will become infected. And, since the disease is deadly, many people try to hide their exposure to avoid being rounded up. In over 80% of COVID cases the symptoms are mild, and somewhat over 1% are asymptomatic, so a lot of people will be able to hide. The more people do this, the poorer the chance that the quarantine will work. Given this, I believe that over 10% of Hubei province is already infected, some 1.5 million people, not the 79,000 that China reports.

Wuhan quarantine “living room”. It’s guaranteed to spread the disease as much as it protects the neighbors.

Also making me think that quarantine will not work as well here as with SARS, there is a big difference in R°, the transmission rate. SARS infected some 2000 people over the first 120 days, Dec. 1 to April 1. Assuming a typical infection time of 15 days, that’s 8 cycles. We calculate R° for this stage as the 8th root of 2000, 8√2000 = 2.58. This is, more or less the number in the literature, and it is not that far above 1. To be successful, the SARS quarantine had to reduce the person’s contacts by a factor of 3. With COVID-19, it’s clear that the transmission rate is higher. Assuming the first case was December 1, we see that there were 73,437 cases in only 80. R° is calculated as the 5 1/3 root of 73,437. Based on this, R° = 8.17. It will take a far higher level of quarantine to decrease R° below 1. The only good news here is that COVID-19 appears to be less deadly than SARS. Based on Chinese numbers the death rate appears to be about 2000/73,437, or about 3%, varying with age (see table), but these numbers are overly high. I believe there are a lot more cases. Meanwhile the death rate for SARS was over 9%. For most people infected with COVID-19, the symptoms are mild, like a cold; for another 18% it’s like the flu. A better estimate for the death rate of COVID-19 is 0.5-1%, less deadly than the Spanish flu of 1918. The death rate on the Diamond Princess was 3/600 = 0.5%, with 24% infected.

The elderly are particularly vulnerable. It’s not clear why.

Backing up my value of R°, consider the case of the first Briton to contact the disease. As reported by CNN, he got it at conference in Singapore in late January. He left the conference, asymptomatic on January 24, and spent the next 4 days at a French ski resort where he infected one person, a child. On January 28, he flew to England where he infected 8 more before checking himself into a hospital with mild symptoms. That’s nine people infected over 3 weeks. We can expect that schools, factories, and prisons will be even more hospitable to transmission since everyone sits together and eats together. As a worst case extrapolation, assume that 20% of the world population gets this disease. That’s 1.5 billion people including 70 million Americans. A 1% death rate suggests we’ll see 700,000 US deaths, and 15 million world-wide this year. That’s almost as bad as the Spanish flu of 1918. I don’t think things will be that bad, but it might be. The again, it could be worse.

If COVID-19 follows the 1918 flu model, the disease will go into semi-remission in the summer, and will re-emerge in the fall to kill another few hundred thousand Americans in the next fall and winter, and the next after that. Woodrow Wilson got the Spanish Flu in the fall of 1918, after it had passed through much of the US, and it nearly killed him. COVID-19 could continue to rampage every year until a sufficient fraction of the population is immune or a vaccine is developed. In this scenario, quarantine will have no long-term effect. My sense is that quarantine and vaccine will work enough in the US to reduce the effect of COVID-19 to that of the Hong Kong flu (1968), so that the death rate will be only 0.1 – 0.2%. In this scenario, the one I think most likely, the US will experience some 100,000 deaths, that is 0.15% of 20% of the population, mostly among the elderly. Without good quarantine or vaccines, China will lose at least 1% of 20% = about 3 million people. In terms of economics, I expect a slowdown in the US and a major problem in China, North Korea, and related closed societies.

Robert Buxbaum, February 18, 2020. (Updated, Feb. 23, I raised the US death totals, and lowered the totals for China).

Disease, atom bombs, and R-naught

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A key indicator of the speed and likelihood of a major disease outbreak is the number of people that each infected person is likely to infect. This infection number is called R-naught, or Ro; it is shown in the table below for several major plague diseases.

R-naught - communicability for several contagious diseases, CDC.

R-naught – infect-ability for several contagious diseases, CDC.

Of the diseases shown, measles is the most communicable, with an Ro of 12 to 18. In an unvaccinated population, one measles-infected person will infect 12- 18 others: his/her whole family and/ or most of his/her friends. After two weeks or so of incubation, each of the newly infected will infect another 12-18. Traveling this way, measles wiped out swaths of the American Indian population in just a few months. It was one of the major plagues that made America white.

While Measles is virtually gone today, Ebola, SARS, HIV, and Leprosy remain. They are far less communicable, and far less deadly, but there is no vaccine. Because they have a low Ro, outbreaks of these diseases move only slowly through a population with outbreaks that can last for years or decades.

To estimate of the total number of people infected, you can use R-naught and the incubation-transmission time as follows:

Ni = Row/wt

where Ni is the total number of people infected at any time after the initial outbreak, w is the number of weeks since the outbreak began, and wt is the average infection to transmission time in weeks.

For measles, wt is approximately 2 weeks. In the days before vaccine, Ro was about 15, as on the table, and

Ni = 15w/2.

In 2 weeks, there will be 15 measles infected people, in 4 weeks there will be 152, or 225, and in 6 generations, or 12 weeks, you’d expect to have 11.39 million. This is a real plague. The spread of measles would slow somewhat after a few weeks, as the infected more and more run into folks who are already infected or already immune. But even when the measles slowed, it still infected quite a lot faster than HIV, Leprosy, or SARS (SARS is a form of Influenza). Leprosy is particularly slow, having a low R-naught, and an infection-transmission time of about 20 years (10 years without symptoms!).

In America, more or less everyone is vaccinated for measles. Measles vaccine works, even if the benefits are oversold, mainly by reducing the effective value of Ro. The measles vaccine is claimed to be 93% effective, suggesting that only 7% of the people that an infected person meets are not immune. If the original value of Ro is 15, as above, the effect of immunization is to reduce the value Ro in the US today to effectively 15 x 0.07 = 1.05. We can still  have measles outbreaks, but only on a small-scale, with slow-moving outbreaks going through pockets of the less-immunized. The average measles-infected person will infect only one other person, if that. The expectation is that an outbreak will be captured by the CDC before it can do much harm.

Short of a vaccine, the best we can do to stop droplet-spread diseases, like SARS, Leprosy, or Ebola is by way of a face mask. Those are worn in Hong Kong and Singapore, but have yet to become acceptable in the USA. It is a low-tech way to reduce Ro to a value below 1.0, — if R-naught is below 1.0, the disease dies out on its own. With HIV, the main way the spread was stopped was by condoms — the same, low tech solution, applied to sexually transmitted disease.

Image from VCE Physics, https://sites.google.com/site/coyleysvcephysics/home/unit-2/optional-studies/26-how-do-fusion-and-fission-compare-as-viable-nuclear-energy-power-sources/fission-and-fusion---lesson-2/chain-reactions-with-dominoes

Progress of an Atom bomb going off. Image from VCE Physics, visit here

As it happens, the explosion of an atom bomb follows the same path as the spread of disease. One neutron appears out of somewhere, and splits a uranium or plutonium atom. Each atom produces two or three more neutrons, so that we might think that R-naught = 2.5, approximately. For a bomb, Ro is found to be a bit lower because we are only interested in fast-released neutrons, and because some neutrons are lost. For a well-designed bomb, it’s OK to say that Ro is about 2.

The progress of a bomb going off will follow the same math as above:

Nn = Rot/nt

where Nn is the total number of neutrons at any time, t is the average number of nanoseconds since the first neutron hit, and nt is the transmission time — the time it takes between when a neuron is given off and absorbed, in nanoseconds.

Assuming an average neutron speed of 13 million m/s, and an average travel distance for neutrons of about 0.1 m, the time between interactions comes out to about 8 billionths of a second — 8 ns. From this, we find the number of neutrons is:

Nn = 2t/8, where t is time measured in nanoseconds (billionths of a second). Since 1 kg of uranium contains about 2 x 1024 atoms, a well-designed A-bomb that contains 1 kg, should take about 83 generations (283 = 1024). If each generation is 8 ns, as above, the explosion should take about 0.664 milliseconds to consume 100% of the fuel. The fission power of each Uranium atom is about 210 MeV, suggesting that this 1 kg bomb could release 16 billion Kcal, or as much explosive energy as 16 kTons of TNT, about the explosive power of the Nagasaki bomb (There are about 38 x10-24 Kcal/eV).

As with disease, this calculation is a bit misleading about the ease of designing a working atomic bomb. Ro starts to get lower after a significant faction of the atoms are split. The atoms begin to move away from each other, and some of the atoms become immune. Once split, the daughter nuclei continue to absorb neutrons without giving off either neutrons or energy. The net result is that an increased fraction of neutrons that are lost to space, and the explosion dies off long before the full power is released.

Computers are very helpful in the analysis of bombs and plagues, as are smart people. The Manhattan project scientists got it right on the first try. They had only rudimentary computers but lots of smart people. Even so, they seem to have gotten an efficiency of about 15%. The North Koreans, with better computers and fewer smart people took 5 tries to reach this level of competence (analyzed here). They are now in the process of developing germ-warfare — directed plagues. As a warning to them, just as it’s very hard to get things right with A-bombs, it’s very hard to get it right with disease; people might start wearing masks, or drinking bottled water, or the CDC could develop a vaccine. The danger, if you get it wrong is the same as with atom bombs: the US will not take this sort of attack lying down.

Robert Buxbaum, January 18, 2019. One of my favorite authors, Issac Asimov, died of AIDS; a slow-moving plague that he contacted from a transfusion. I benefitted vastly from Isaac Asimov’s science and science fiction, but he wrote on virtually every topic. My aim is essays that are sort-of like his, but more mathematical.