Prevalence, Transmission and Cases

There has been a lot of discussion during the epidemic of R, the supposed reproductive rate; transmission speed, infectiousness, prevalence and related topics.  I want to see if in my own inadequate way I can point people to some useful background and make some observations that help think about these concepts and what they tell us about current and future features of the epidemic.  I have been astounded at the mis-statements by people who are supposedly guiding our response, like the infectious disease head in Minnesota, regarding this notion.

I would encourage you to read this article, published by the CDC in 2019, before the epidemic, on the misunderstandings and misuse of R.  (CDC Article)   You can also read some of the articles cited as references in that article and if you know what PubMed is, you can go there and look for more recent articles that cite this one.  The article gives you an excellent historical perspective on the development of the R concept.  This number was supposed to identify how many persons in a completely unexposed population the original case might infect, or how many additional persons might be infected by each of a set of cases early in an epidemic.  And that number was supposed to tell you something about how infectious the pathogen was–how easily would it spread through the population.  R does not have a time component and R naught (I don’t know how to do subscripts in WordPress but this R with a little zero at the bottom) which is most commonly cited, would reflect that number of secondary cases from the very first case.  Any later R number, sometimes seen as R with a subscript t, supposedly would reflect how many secondary cases there are from one index case at that point of the epidemic.  It is pretty obvious that R (t) will continually decline during the epidemic, unless no one ever develops any adaptive immunity to the pathogen.

The fact that R contains no time component is perhaps the most misunderstood aspect of the concept.  Here is an example.   Imagine that a pathogen infects the first person.  That person is going to infect 8 others.  That is a high R and seems scary.  It would be if those secondary infections occurred in an average of two days from the index case, and so on for the tertiary cases and each branching of cases.  But what if it takes two weeks for those secondary cases to arise.  That is obviously a substantially slower spread, with implications for resource use and other management aspects of the epidemic.  R doesn’t tell you anything about that.   You have to figure out that time component, which is very critical, in other ways.

As the article points out, R also is not a description of some characteristic of the pathogen.  Aspects of the pathogen do have an impact on infectiousness or rate of spread.  If it is aerosolized, transmitted on surfaces, could penetrate skin, down-regulates immune responses, has a variety of receptor targets, has a very high binding capability, is very small, and so on, it would inherently be more transmissible, but R doesn’t specifically reflect that.  Nor does it specifically reflect the variability in the population that affects infectiousness.  This includes all aspects of a person’s health status, including immune defenses, contact patterns, and as the epidemic proceeds, changes in behavior.  And it doesn’t directly reflect environmental factors like temperature, humidity, amount and intensity of sunlight, and others.  Or the actual interaction between an infected and uninfected human, such as infectious dose and viral load.  All these factors go into influencing how fast a pathogen can move through a population.

So measuring R is complex and given all the variables, it may be best to think of it as a range, depending on those variables.  And it likely isn’t the same across different populations.  If you want to measure it directly you would have to contact trace each and every infection, a difficult task at best and almost impossible when, as appears to be the case with CV-19, there are so many asymptomatic and presymptomatic cases.  If you could do that, you would know exactly how many other people each person infected and in what time frame and could gather information on other variables affecting transmission.  This is why even the inadequate contact tracing studies we have can be very useful.  And genetic sequencing adds another dimension which can help verify pathogen spread patterns.   So the alternative to the contact tracing approach to ascertaining this fundamental parameter we want to understand– how quickly and easily is a pathogen spreading or capable of spreading through a population–and which depends on a huge number of factors, is our old favorite; modeling.  Those factors in many cases are not easily measured, so people build models which just make assumptions or create distributions around a value for the factors.  I don’t put a lot of faith in the models for the obvious reasons stated in the CDC article.  There is too much uncertainty to generate accurate answers.  We can forget the Minnesota Model that even under a significant mitigation of spread regime said almost all Minnesotans would be infected and the epidemic would be over by early September.

So is there any practical way to get a sense of how fast the pathogen is spreading without building an elaborate model?  The best thing I can think of is try to track daily or weekly prevalence and look at changes in those.  You can do that in Minnesota by taking total cases, which are reported every day, and subtracting the no longer needing isolation number and the deaths number.  That is effectively active cases–which might be roughly equivalent to those who are infectious (and that is what really accounts for epidemic management–how many people are infectious).  The state is just rolling people off after 14 days as a case, which likely means many aren’t still infectious before that period ends, but on the other side, you have people who are infectious but haven’t yet been tested.  And I am ignoring the whole issue of how many undetected cases there are and how that might change over time.  You can track that active case number over time and it gives you current prevalence but you can also compare that number to how fast new cases are growing and make some rough assumptions about how quickly the epidemic is moving and how many people on average an active case is infecting.  Current prevalence in Minnesota is growing rapidly over the last few weeks, but is still low.  Daily new cases are also growing as a percent of active cases.  As best I can estimate, each active case or infectious person in Minnesota is infecting between 1 and 2 other people, in about a one week time frame.  Our doubling time on total cases looks to be about 30 days or more.  Our doubling time on active cases is around two to three weeks.  Eventually I will find time to finish my actual table and graphs in this area.  Several of you before provided me with your own work in this area, which I am incorporating and I appreciate additional thoughts.