Thursday, March 26, 2020

Coronavirus: A couple of thoughts on the model that limits infections in a non-immune population

The model described in previous posts, in which the portion of an exposed population that contracts an infection is dependent on the distribution of susceptibility and exposures, may benefit from a couple of points:

1.) While it may be the case that no one is completely immune, i.e. that they will not contract an infection regardless of their exposure, most people are relatively immune, i.e. they are more or less likely to contract an infection for a given exposure than someone else. Thus, as a theoretical matter, everyone can get the infection (although even if everyone were completely susceptible herd immunity would limit exposures) as a practical matter, for a given outbreak, the dynamics of how the disease spreads from more susceptible to less susceptible populations limits the extent of the epidemic.

2.) As per 1.) above, the uninfected population remains susceptible to infection given the right environment. Thus, a new epidemic, for example in the fall, is entirely possible, although it would likely have to start with a different set of dynamics. This distinguishes epidemics that are limited because a majority of the population has already been exposed from one in which the susceptibility to infection varies. Another distinguishing factor is that, in the latter population, a low level of infections continues, as for example occurred in Diamond Princess passengers.

3.) A population that has varying susceptibilities to infections appears somewhat abstract, and even though it makes sense to assume that not everyone has the same risk of infection given the same level of exposure, such differences seem far-fetched in real-world modeling. This is one way in which it might come about:

Assume that there are three dominant modes of exposure that transmit an infection: inhaling infected droplets, inoculating the oral or nasal pharynx directly, or by coming into contact with infected blood. The exposures representing the first type vary widely in the degree of associated risk. Passing through a room and breathing the air in the same room as someone with the infection is one degree of risk, but likely at a very low, almost negligible level. An intimate, hour long conversation within a foot of each each other a higher risk of the same type of spread, but one would assume that if a virus spreads easily just by breathing in infected air, is would be almost certain to infect the population to the level of herd immunity. Furthermore, we may assume that an individual's susceptibility to infection depends on personal factors: the type of viral receptors a person may have in his nasopharynx, which may in turn be affected by smoking status, medications, genetics, etc. It may be affected by anatomy or the quality of mucus or chronic inflammation. Regardless, we may consider that the population that is susceptible to infection by this route comprises the left hand side of the exposure-population curve. they are infected most easily and would be expected to contract the infection earliest in the epidemic.

The second group of people is relatively resistant to contracting infection just by breathing in. Although possible, the disease is unlikely to spread widely in this population simple by inhaling infected aerosol droplets. However, this group is susceptible to directly inoculating themselves by delivering virus directly into their oral pharynx, and especially their tongue, with virus they pick up on their fingers. A simple act of eating food with their unwashed fingers may be sufficient. Thus, while this group is more resistant than the previous one, it is still susceptible, and importantly, a large part of this susceptibility is behavioral.

The third group is very unlikely to contract infection by inhaling infected aerosols, and exhibit limited behaviors that predispose to direct inoculation from one's own hand. they are unlikely to become infected unless they come into significant contact with the infected bodily fluid; blood, sputum, urine etc. These people may be infected, but are very unlikely to do so.

Varying susceptibility to infection may be genetic, or come from partial immunity due to exposure to similar pathogens in the past, or because of co-infections that interfere with the new pathogen's ability to infect the host. Some people may simply have a better immune system.

Regardless of the case, if the first group of people, i.e. those who can be infected easily through aerosol spread is relatively small, and there is significant difference in the ability of the virus to establish infections between the two groups, the infection will spread widely in first group and begin to die out before it can establish a large enough presence in the more resistant populations to continue to spread.

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