A previous post noted that the parameter which was denoted there by r is the ratio of a day's new cases to the number of active cases. It diverges from the observed ratio of daily new cases-to-total cases because the number of daily cases diverges from the number of active cases as people either die or recover from their infection.It was also mentioned that r can be thought of as a measure of how easily the virus spreads; large values for r represent a highly contagious virus that spreads easily, and low values represent the opposite.
The value of r cannot be observed directly, because there is no current reliable way to determine which patients who survive the disease are no longer infectious on a day-to-day basis. We can use the relationship observed from modeling to estimate it however. We can also make some generalized observations about r.
First, as has been mentioned previously, r can be manipulated somewhat by measures meant to inhibit spread of the virus. This is obvious from the nature of r as a measure of how easily the virus, or alternatively how much resistance there is to the spread of the virus.
Secondly, the value of r steadily declines as a virus spreads; the greater the total number of infections, assuming that those infected develop immunity, the harder it is for the virus to spread. This is the basis of herd immunity, and is true even if everyone in a population had the same susceptibility to infection. As argued previously however, everyone does not have the same susceptibility to infection, and the the more highly susceptible people are infected, the virus must spread through more resistant populations and r will decrease. This is easily seen in the daily new cases and daily death profiles from places like South Korea and Italy.
Thirdly, r cannot be driven to zero, except perhaps in the case of a 100% effective vaccine. Universally effective precautions against spread of the virus are not possible. People will interact for necessary daily activities, they will encounter each other or come into contact with something that has previously come into contact with something else. This accounts for the persistent tail seen in the daily new case profile from South Korea, and the number of new cases in places like Taiwan.
Fourth, r is made up a different types of components. The simplest way to think about them is to classify exposure by the risk such exposure entails and the frequency of each type of exposure. The highest risk exposures are probably those that involve inoculating the virus into the oral pharynx; e.g. sharing a beverage container with someone without washing it, or using a community serving spoon at a large gathering then eating something with hands without washing in between. Low risk exposures would be like entering a room after someone infected with the virus has passed through without touching anything. there are other examples between these. Looking at infection rates and considering some "super spreaders," and anomalous scenarios like the choir group in Washington state, we can surmise that the high risk exposures are low frequency in general, but are dramatic when they occur in the right setting. If averaged over a large number of persons , the average risk from typical activities seems to be relatively low, which gives r values in the range of approximately 0.7 to 1.4 early in an epidemic.
Fifth, r seems to be sensitive to the type of environment. The experience in Washington state does not translate easily to New York, nor New York to California, nor South Korea to Italy.
Sixth, we can estimate the effect of relaxing mitigation efforts at different points in the course of the virus, specifically when the number of new cases has declined a given percentage of the peak value, by increasing the value of r. This will be discussed subsequently.
No comments:
Post a Comment