COVID-19 Contagion and Calculating a More Accurate Basic Reproductive Number (R0): Perspectives from a Patient in the Statler Hotel
Unfortunately, despite all of my best efforts to stay away from the current pandemic over the past nine months, I too became a statistic in the Tompkins County Health Department’s COVID-19 Dashboard. After coming back from Thanksgiving break, I quickly lost my senses of taste and smell. A day later, a positive test result led to a domino effect involving various phone calls and a request to check-in at the Statler Hotel for isolation. In the days following, I developed symptoms that were worse at first, but diminished faster than I had expected; I got lucky. But if it had not been for Cornell’s quick testing and action to ship me to the Statler, I could have infected many more people, and others I had been in contact with would have certainly done so. These truths are common knowledge considering that we have been dealing with this pandemic all year, but the recent course content regarding contagion got me thinking about the actual effectiveness of my isolation for the past two weeks in addition to the benefit that Ithaca’s community has received as a result of me being restricted to a hotel room.
In this blog post, I will be diving deeper into the SIR model and COVID-19’s proof of the limitations of R0, while also examining the effectiveness of the measures taken in my specific case of contracting COVID-19 and being placed into isolation. Firstly, it is important to recognize that COVID-19 is a virus unlike any we have seen (since the Spanish flu) in terms of contagiousness. For this reason, in conjunction with the cascading societal phenomena we have witnessed across the country over the past year, the study[1] I looked at included time-varying parameter estimation being considered alongside the traditional SIR model to create an adaptive SIR (aSIR) model. The study utilizes an “infection rate [that] is estimated using the reported cases for a seven-day window to obtain a continuous estimation of R𝑡.” R𝑡 is used here instead of R0 due to the prevalence of a key variable– time. In the study, the researchers prove that “the proposed adaptive SIR (aSIR) model can quickly adapt to an increase in the number of tests and associated increase in the reported cases of infections.” The SIR model, which can be seen in Figure 1, is a system of differential equations made up of S (# of people susceptible to the virus), I (# of people infected with the virus), R (# of people recovered and thus removed from the scenario), in addition to time-variant parameters β (the probability of infection during contact with an infectious individual * the average # of contacts per day), Îł (the rate at which those infected I are removed to the R compartment), and N (the population in a region of interest):
Figure 1
The time-variant R𝑡 can then be calculated as R𝑡(𝑡) = β(𝑡)/Îł. When R𝑡>1 the number of cases is expected to grow exponentially. The epidemic is contained when R𝑡 decreases and remains below 1. The researchers then went on to explain that this model is an accurate indication of the effects of efforts to halt COVID-19. Moreover, they also stated, “another measure to lower R𝑡 is to increase the removal rate 𝛾 by intensive testing and quarantine of individuals tested positive. This targeted intervention would strongly decrease the interaction between the infectious and susceptible individuals and keep R𝑡 <1 until a vaccine becomes available.”
Cornell’s handling of COVID-19 has taken into account this 𝛾 by making it a top priority to test students daily, and immediately quarantine individuals who have tested positive in a special environment where they will not feel the need to leave and expose the virus to others. Regarding the importance of time variance when analyzing the basic reproductive number of COVID-19, a key example can also be witnessed at this current moment. Most students have left campus for the winter and returned to their permanent homes. This leads to many fewer people to contact, but also allows for faster testing due to a lower volume of incoming patients and test samples. Thus, the generalizability of R0 without the consideration of time-variant parameters is problematic, because it leads to the possibility of overestimating or (worse) underestimating the threat at hand. In an example, Katarina Zimmer[2] writes, “because people responsible for super spreading events have an exceptionally high individual R, they can inflate estimates of R0—the mean of a population—early in an outbreak. This variation makes it impossible to project the overall spread of disease just from R0 alone.”
The research that has been conducted on this virus that has been up in everyone’s faces shapes many aspects of our current reality; much of that has to do with policies that are being enacted in order to contain the virus. This is why conducting accurate research is so important. Taking notes of variables as they change over time in order to estimate how to best respond to the virus, and when it is actually safe to resume normal daily activities– that is how we beat COVID-19. In my case, being moved into the Statler Hotel meant a lot more than I had initially thought. Cornell’s initiatives to take into account every potential source of an outbreak and mitigate the potential infection rate as much as possible (by tackling that 𝛾 variable I spoke of earlier) might just have saved someone’s life.
References:
[1] Shapiro, Mark & Karim, Fazle & Muscioni, Guido & Augustine, Abel. (2020). Are we there yet? An adaptive SIR model for continuous estimation of COVID-19 infection rate and reproduction number in the United States. 10.1101/2020.09.13.20193896. https://www.researchgate.net/publication/344982847_Are_we_there_yet_An_adaptive_SIR_model_for_continuous_estimation_of_COVID-19_infection_rate_and_reproduction_number_in_the_United_States
[2] Zimmer, Katarina. “Why R0 Is Problematic for Predicting COVID-19 Spread.” The Scientist Magazine®, 13 July 2020, www.the-scientist.com/features/why-r0-is-problematic-for-predicting-covid-19-spread-67690.