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A GLIMPSE AT SIR MODELING PART 2

YESTERDAY IN PART 1, tidbits on epidemic modeling were offered, based on Paul Taylor’s “Susceptible, Infectious, Recovered,” London Review of Books, May 7, 2020. Today in Part 2, we see the model in operation.

Running the Model. “This model,” Paul Taylor notes, “has four parameters: 13, the average number of contacts per person per day; 3 percent, the probability that a contact will lead to transmission; 15 percent, the rate at which people recover; and 10,000, the size of the population.”

Taylor notes, “Dividing the product of the first two numbers by the third give the expected number of transmissions from a single case, also known as R0 or the basic reproduction rate. In this example, it is 13 x 3 / 15, which is 2.6; in other words, leading to an exponential increase in infections until the supply of non-infectious people begins to run out.”

He continues, “You can play with the numbers and see how quickly the epidemic spikes when R0 is 3 or 4, and how the combination of parameters affects the level of infection needed before the herd attains immunity: the more contagious a disease, the higher the percentage of people who need to be immune to it.”

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

Analyzing the Model’s Results. Taylor notes, “It shows the epidemic peaking at day 45, at which point 2068 people are infectious. By day 100, it is almost over. Not everyone has been affected—there are still 854 Susceptibles—but since day 45 the likelihood that any of their contacts will be in the Infectious group has been diminishing and is now getting close to zero.”

Day 45 displays the sought-after “flattening of the curve.” Day 100 is the desirable situation of R-nought approaching zero

“To put it another way,” Taylor says, “because the 9139 Recovered are no longer susceptible, their immunity is enough to guarantee the immunity of the herd.”

Real-World Modeling. The London School of Hygiene and Tropical Medicine’s SIR model suggests several of the complications in yielding accurate predictions. In the LSHTM model, Taylor notes, “Susceptible people pass through a latent phase between becoming infected and being infectious, and then either have a mild, or subclinical, version of the disease, or a more serous illness with both a pre-clinical phase and a clinical phase requiring a stay in the hospital. It is assumed that the mild cases are only half as infectious as the more severe cases.”

Also, the LSHTM model incorporates a multitude of values for the number of average contacts. Taylor says these are “calculated for every five-year age band in each of the 186 county-level administrative units in England, Wales, Scotland, and Northern Ireland.”

Epidemic modeling is not for the slipshod, nor for the faint of heart. ds

© Dennis Simanaitis, SimanaitisSays.com, 2020

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