Tuesday, April 14, 2020

A happy thought on super-spreaders

From one of my super-smart colleagues.

The key is to get R0, the average number each infected person gives it to, below one. If that is done, the virus dies out.

R0 has a fat tail. Almost all spreading is done by a few super spreading people in super spreading events and activities. Cut those out and the problem is gone. Keeping the rest of us at home is a waste. (Latest, discovery by my wife. Dog groomers are shut down. One cutter, one dog, one store. No)

Happy thought: to the extent that super spreaders are super-spreading people, people with particularly bad habits, or people in particularly exposed jobs, they are most likely to get it and become immune. Thus, super-spreading naturally tails off on its own, and the average reproduction rate falls on its own. If the small herd of super-spreaders gets immunity, that helps the virus to die out.

This is one case I've heard of that heterogeneity in R0 rates affects the average that is tracked by most epidemic models.


  1. I think this article fails to distinguish the importance between super spreading people and super spreading events.

    Mary Mallon, aka Typhoid Mary, was an asymptomatic carrier of typhoid who unfortunately worked as a cook. She infected about 50 people. Was she a super spreader with a heightened propensity to infect people or just the wrong person in the wrong place, which would be a super spreader event.

    In other instances there seem to have been super spreader people. In the 1960s a study showed that 3 of 77 patients with cavitary TB accounted for 3/4 of the infectious burden. People do not develop immunity to TB after exposure and recovery. They can get it again. We're seeing reports of this from South Korea with COV-19. It would appear that not everyone develops antibodies.

    Resistance vs tolerance. The concept of super spreaders is not new, as evidenced by Typhoid Mary and the above mentioned TB study. Super spreaders have been identified for measles, SARS, cholera, and Ebola. One theory is that there are two possible ways for the body to react to infection. One is the classic concept that the immune system wages war on the invader, producing severe inflammatory responses and organ damage (resistance). The other is tolerance, a sort of peaceful coexistence whereby the body doesn't attack the pathogen and thus doesn't develop the inflammatory response. These might be the true super spreaders.

    Contrary to the theory that super spreaders will get immunity and stop being super spreaders it may be that the people who host COV-19 via tolerance may NEVER clear. They may become the modern day lepers.

    I can't address whether this is the first instance of heterogeneity of R0 affecting the average reported R0, but it seems to me that it should be obvious since we know from history that spread is multifactorial. On the Diamond Princess the initial R0 was about 15, falling to less than 2 after isolation precautions. No super spreaders were found and thrown overboard.

    Understanding the complexities of R0 illustrates that it's not as helpful a number as people might think.

    We also lack the capability to test everyone for active infection or post-infection antibodies or trace all cases.

    1. If super spreaders are symptomatic, then simply eliminating people with fever, headache, or cough from public would have been enough

  2. Re Typhoid Mary -
    Yes, she was a cook - but a private cook for wealthy NY families around the turn of the century. Wikipedia gives this version of her employment:

    "From 1900 to 1907, Mallon worked as a cook in the New York City area for seven families.[7] In 1900, she worked in Mamaroneck, New York, where, within two weeks of her employment, residents developed typhoid fever. In 1901, she moved to Manhattan, where members of the family for whom she worked developed fevers and diarrhea, and the laundress died. Mallon then went to work for a lawyer and left after seven of the eight people in that household became ill.[8]
    In August 1906, Mallon took a position in Oyster Bay, Long Island, and within two weeks 10 of the 11 family members were hospitalized with typhoid.[9] She changed jobs again, and similar occurrences happened in three more households.[8] She worked as a cook for the family of a wealthy New York banker, Charles Henry Warren. When the Warrens rented a house in Oyster Bay for the summer of 1906, Mallon went along, too. From August 27 to September 3, six of the 11 people in the family came down with typhoid fever. The disease at that time was "unusual" in Oyster Bay, according to three medical doctors who practiced there.[citation needed] Mallon was subsequently hired by other families, and outbreaks followed her.[8]"

    Given the small number of people she infected at repeated events, she'd be most accurately classified as a "super-spreader" and not a "super-spreading-event."

    1. Typhoid spreads through contaminated food and water. Mary was a cook. How many people would she have infected if she worked as a seamstress? She was an event - wrong person in the wrong place. Too bad she didn't wash her hands.

  3. A misapprehension appears in your writings. R(0), or "R0", is the reproduction number at the initiation of an epidemic. As time goes on the reproduction number, R(t), diminishes as the proportion of the population that is susceptible diminishes. Letting s represent the proportion of the population susceptible to the pathogen, r represent the transmissibility per contact between an infected person ("invective") and a susceptible individual, c the average number of such contacts per unit of time, and q represent the lapse rate of invectives per unit of time, then the reproduction rate R(t) = r•c•s(t)/q. At t=0, the reproduction number is at its maximum value R(0) = r•c/q. As the epidemic progresses, s(t) declines. When s(t) falls below q/(r•c), the growth rate of invectives as a proportion of the population becomes negative. This the point where the reproduction number, R(t), dips below unity. Let t* represent the point in time when R(t)=R(t*)=1.

    Various politicians (state governors, etc.) believe that their communities (states) have reached t*, or that they will soon reach t*, and will therefore be able to relax the various containment measures that have been imposed on their populations. This belief is based on the time rate of change in the apparent mortality figures published daily.

    The problem with that belief is that it fails to recognize that parameter c, average contacts per unit time, has two values -- c' and c", representing the value of c pre-'lockdown' and the value of c during the 'lockdown', respectively, where c'> c". When the 'lockdown' measures are lifted, the value of parameter c will either resort to c' or some value intermediate between c' and c", at which point the epidemic will resume with its initial force or somewhat diminished force, i.e., R(t)>1. And, back to square one we go.

    The various technical fixes proposed are merely postulated means of managing the consequences of the resumption of the epidemic progressing freely through the populace after 'lockdown' is lifted, until the next 'lockdown' is imposed. This is likely to be a cyclic phenomenon until the healthcare system collapses or the epidemic runs its full course, whichever is the earlier. We have not yet run the full length of the gauntlet; indeed, we have hardly begun the course.

  4. We have some math.
    R0 goes to zero from neighborhood to neighborhood. The public health officials have to adapt and discover the neighborhood size, then they set the hospital channel rate and the equilibrium for pandemic management is reached. It is a constant adaption method, neigborhood size adapted to the current situation. Quantization methodology, think of Fama and the information processor applied to hospitals value chain. In the end, the virus pops up randomly in a neigborhood and is ovewhlemed there by antibodies and cops/docs. This is all value chain math, we know how to do this model.

  5. If a virus is primarily due to super-shedders or super-spreader events, then it becomes easier to maintain since the network becomes something more like a power-law distribution and the probability of epidemics declines dramatically even for R>1.

    There is a note about R<1 that's important though - that assumes the susceptible population is fixed. Unless the virus has died out globally, it would imply we need immigration & travel restrictions until herd immunity is reached.


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