Contagion, Vaccination, and An Updated SIR Model
On a recent episode of The Daily, a New York Times podcast hosted by Michael Barbaro, science and health reporter Donald G. McNeil Jr. discusses the implications of the U.S. emergency approval of Pfizer’s COVID-19 vaccine. Barbaro and McNeil take a look at the timeline for vaccinating different groups of Americans, and even explore potential vaccine mandates. McNeil knows it is “extremely unlikely” that the federal government will mandate nationwide vaccination. However, McNeil determines that some state governments, along with many entities, will take steps to require essential workers to get vaccinated once doses are available. Inevitably, Barbaro poses the question, “What does the government do with people in these various [essential] categories who don’t want the vaccine?” McNeil explores legal and scientific possibilities, ultimately saying loud and clear that “the problem is if you have enough people refusing the vaccine, your epidemic never ends.” Because there is an unavoidable number of people who are unable to get a vaccine due to other health concerns (e.g. immunocompromised people, cancer patients, severe allergies to previous vaccines, etc), there is risk of continuous contagion if eligible people choose to remain unvaccinated. While The Daily does not examine the process of contagion in depth, we can use the Branching Process model to represent the endless epidemic that McNeil describes if a large portion of people who can get the vaccine choose not to.
As discussed in class, the size/reach of the branching network, k, and the rate of infection, p, are crucial to predicting epidemic spread. According to National Geographic, the rate of infection of COVID-19 in indoor spaces can range from 30% to 80%, depending on factors such as air ventilation, distance, and mask effectiveness. While the Branching Process model uses a 50-50 coin flip to determine infection down the branched model, I have tailored the model to be more reflective of our knowledge of COVID-19 over time, which changed the likelihood of transmission from 50-50 (sometimes more likely than 50-50, sometimes less). The following model is definitely an oversimplification of COVID-19 transmission, but we can use it to understand the reality of an endless epidemic if enough people remain unvaccinated and still return to “normal”, unmasked, un-distanced life.
The transmission rate from Patient Zero down to the first wave of people reflects the small number of preventative measures we enacted at the beginning of the pandemic. From March through June, the pandemic ravaged through branched networks with a p infection rate much closer to ⅔ than ⅓. The first wave to the second wave reflects more effective control measures that lowered the p infection rate, including social distancing and being outside during the summer. The second wave to the third wave reflects our current state in which more people are spending time inside because of the cold weather and expressing exhaustion with the seemingly endless safety measures. Here, we return to a ⅔ transmission rate. Finally, the last branch I have drawn is a representation of the future explained by McNeil. In this case, the transmission rate may be much closer to 100%, because people will begin to return to normal life under the protection of the vaccine. If a significant portion of the population is unvaccinated and follows suit with the rest of society to return to normal, there is great risk of continued transmission for multiple reasons. One reason is the staggered rollout of vaccination, which will leave various populations waiting for vaccinations that could be jeopardized by those who refused vaccinations. More importantly, people who cannot safely receive vaccinations will be at perpetual risk for contracting and further spreading COVID-19 within their population. Finally, because there is so much unknown about COVID-19 and the vaccination, there is a real consideration of mutations and other unknowns that may put vaccinated individuals at risk if an unvaccinated person is contagious. Because of our progression of knowledge and the actions that will follow the rollout of vaccination, an unvaccinated portion of the population could perpetually spread the virus to people who have not been infected and potentially even to people who have been infected. Although the k branching value will decrease as more people receive the vaccine, it is likely the p infection rate will increase because safety measures will start to loosen under the assumption of vaccine immunity.
While we recognized in class that the Branching Process model is not fully accurate because it does not account for networks that close back in on themselves (e.g. friend networks, family networks), the SIR model (Susceptible Infected Removed) is also not necessarily applicable yet because there is still unknown information about COVID-19 reinfection. Instead, I thought it would be more interesting to examine a novel and complex SIR model developed in 2019. K. M. Ariful Kabirab and Jun Tanimoto published a paper in Communications in Nonlinear Science and Numerical Simulation about a vaccination strategy game that accounts for information buzz and SIR with vaccination. Admittedly, the modeling and explanations were a bit out of my understanding, but essentially, a more complex susceptible-infected-recovered/vaccinated (SIR/V) model uses relative information cost to see how the spread of disease can be mitigated. With information buzz, people who are unaware of the benefits of a vaccine can become more aware, but people who are aware of the benefits of a vaccine can become less aware with the spread of rumors or conspiracies. Considering that the COVID-19 vaccine is new and passed through clinical trials at a historically fast rate, the “cost” of information should be a consideration for public health messaging.
(Ariful Kabir & Tanimoto, 2019)
This diagram shows four outcomes that could result from the interaction of ignorance and consciousness in relation to a contagious disease. a and a* are rates of positive and negative information spread, respectively. Essentially, if a large portion of the population spreads positive information and a small portion of the population spreads negative information (i.e. rumors), the general reaction to a vaccine will be “impressed” and likely lead to more vaccinations. On the other hand, if a small portion of the population spreads positive information and a large portion of the population spreads negative information, the general reaction to a vaccine will be poor, which is “misleading” in the eyes of science (which assumes that the vaccine was tested properly and will be effective). This more recent complex take on the SIR model, which accounts for information costs, shows the importance of information spread as the COVID-19 vaccine becomes available worldwide. It would be interesting to consider this model in the context of timing and demographics, because currently the majority of people receiving vaccinations are essential healthcare workers and high-risk members of society. How will the delay in vaccination affect younger members of society who will have time to consider the effects of the vaccine before it is available to them? What information buzz will occur before then? These are all questions that should be considered, along with updated and complex mathematical modeling, as global governments and authorities grapple with vaccine distribution.
Sources:
https://www.sciencedirect.com/science/article/pii/S1007570419301042?casa_token=-fp5Xul-p5sAAAAA:fhUDLS5aE-PMOi0LDtL5xbFmuL9clfS0-c-vA67Dw4DLQMpXu59YWekt1RR9D0tY4tAP-1AmbQ
https://www.nationalgeographic.com/science/2020/08/how-to-measure-risk-airborne-coronavirus-your-office-classroom-bus-ride-cvd/