Examining Biological Contagion with COVID-19
One class topic I found particularly interesting this year was the idea of epidemic/disease contagion, the rate of transmission across a certain in-contact network, and how it is measured/estimated that a disease will die out after a finite number of steps or spread indefinitely. I wanted to see if this same theory could be applied to the context of diseases in the world that I’ve actually interacted with and see if the model is an accurate predictor of the disease’s probability of living on.
Each disease is assigned some value R0, otherwise known as the Basic Reproductive Number, which is an epidemiological parameter that measures the transmission potential of a disease in a certain population. It is defined as a product product of k, the number of people an infected person meets in a population, and p, the probability that this person infects the number of people they meet independently. If a disease’s R0<1, then the disease isn’t ‘replenishing’ itself and will die out in a finite number of steps with probability 1. If a disease’s R0>1, then the disease is more than ‘replenishing’ itself and will spread indefinitely with probability greater than 0. If you want to reduce R0, you can take measures to reduce p and/or k by reducing the likelihood that the disease can spread or the amount of interaction in the pandemic. To measure this, I will look at a disease that could represent an indefinite epidemic or represent an epidemic that dies out after a certain number of waves. Let’s look at the example of COVID-19, which is an infectious disease caused by the SARS-CoV-2 virus that was discovered in 2019.
Based on an article “Probability of COVID-19 infection by cough of a normal person and a super-spreader” published by Amit Agrawala and Rajneesh Bhardwaj in 2021 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7976050/), the probability of infecting someone with COVID-19 depends on a number of factors including distance and the use of protective equipment like masks. In the situation that we are trying to model, we want to look at the original R0 of COVID-19 without preventative measures (like introducing masks), so assuming that an infected person on our model comes within a distance of 0.5 meters of another person, p=0.5. Let’s also assume that we’re trying to model the transmission potential of COVID-19 in a high school of about 500 people, where an infected person would be likely to come into contact with 100 of these people while sick, thus making k 100. In this situation, the model predicts that R0 = (0.5)(100) = 50, which is greater than 1 and therefore the disease would continue to spread indefinitely.
Now imagine that preventative measures are introduced to stop the spread of the disease in two ways: 1) by introducing protective equipment like masks and 2) by implementing a home-quarantine for students (which is consistent with the response that was taken to COVID-19 epidemic in real life.) In this case, the probability of transmission at a distance of 0.5 meters with a surgical mask is 0.1. During an at home quarantine, we can assume that the average number of people that an infected person could interact with is 3, which is our k. In this situation, the R0 = (0.1)(3) = 0.3, which is less than 1 and, therefore, contains the spread of the disease and reduces the epidemic to a finite number of waves. Contextually, this model is consistent with the spread of COVID-19 in real life before and after the introduction of preventive measures.