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# A GLIMPSE AT SIR MODELING PART 1

AN “SIR” MODEL (as in S.I.R.) is a mathematical simulation of an epidemic. In full application, the model incorporates extremely detailed assessments of an epidemic’s factors. However, in “Susceptible, Infectious, Recovered,” London Review of Books, May 7, 2020, Paul Taylor offers the basics of SIR modeling. Here, in Parts 1 and 2 today and tomorrow, are tidbits on this for DIYers as well as for the rest of us wishing to get a sense of the epidemic modeler’s challenging task.

Paul Taylor is Professor of Health Informatics at University College London. He writes, “you can build a simple mathematical model of an epidemic in a spreadsheet, using three columns to represent the Susceptible, the Infectious, and the Recovered, and calculating daily totals to show how an imaginary population is affected.”

Paul Taylor is Professor of Health Informatics at UCL Institute of Health Informatics. He holds a BSc in Psychology, an MSc in Artificial Intelligence and a PhD in Medical Physics from UCL. His research interests have focused on the use of computer systems in clinical decisions, particularly in image interpretation, including mammography and chest radiography. Image from University College London.

Moving from Group to Group. The SIR model has two formulae, Taylor says. “These formulae tell us how many people to subtract each day from the Susceptible group and add to the Infectious group, and how many to subtract from the Infectious and add to the Recovered.”

From Susceptible to Infectious. In many such models, this first formula is the more complex one, Taylor cites three aspects: First is the daily “average number of contacts each individual has.” In the real world, population density obviously affects this; so do environmental aspects of office, entertainment, and public transportation. Social distancing offers obvious mitigation.

Second is “the likelihood that a contact is with an infected person.” In a real-world study, for example, health-care workers would have a higher likelihood than those of the general population.

Third is “the likelihood that such contact will lead to infection.” This is related to many things, including the virulence of the disease and the degree of any immunity, perhaps only temporary, granted to those recovered from or vaccinated against it.

From Infectious to Recovered. This second computation is a matter of epidemic bookkeeping. It’s each day’s number of infectious individuals multiplied by the average rate of recovery. This rate is obviously affected by medical intervention. It also reflects the population’s mortality rate.

Paul Taylor’s Straightforward SIR Model. Taylor says, “I generated the graph shown here from a spreadsheet set up in a way I have described. I took a population of 10,000 people and started with 9999 susceptible and one infectious person.”

Taylor’s SIR model: 10,000 individuals, one infected at day 0, progress of the epidemic over 100 days. Image from London Review of Books, May 7, 2020.

Taylor continues, “I set the number of contacts per person at 13 and the probability of an instance of contact resulting in disease transmission at 3 percent. I set the rate of recovery so that 15 percent of the infectious population recover each day.”

Tomorrow in Part 2, Taylor runs his model, comments on the resulting simulation, and concludes with some real-world considerations. ds