Learn practical skills, build real-world projects, and advance your career

Title: Pandemic Flu Spread

Group Members: Avi Dasgupta, Allison Madson, Lyttia McManus

Abstract

In this report, the epidemiological Susceptible-Infected-Recovered model (SIR) is used to simulate the spread of an infectious disease in a classroom. We calculated the transmission rate to gain insight on how quickly the disease infected the susceptible students via an analytical and simulation method. It was found that the pandemic may last as long as 25 days, with a vast majority of cases lasting less than 10-15 days. Due to the low infection rate of the flu, there are many cases in which no new children were infected on the first day, and the total expected infected never rose to above 2 during any day of our simulation. This model presents a bare-bones simulation in which the infection rate is known, constant, and is not affected by externalities. Of course, this fall short when considering sick children may now come into school if they are sick or may be isolated from the others. This model also assumes all children interact equally and thus are all equally likely to get infected, which is not always the case. Ultimately, we expect most pandemics to last less than a week with a majority of children not getting infected.

Background and Description of Problem

For our project, we will be modeling the spread of an infectious disease. Our problem is set up with the following scenario:

Consider a classroom of 21 elementary school kids. 20 of the kids are healthy (and susceptible to flu) on Day 1. Tommy (the 21st kid) walks in with the flu and starts interacting with his potential victims. To keep things simple, let’s suppose that Tommy comes to school every day (whether or not he’s sick) and will be infectious for 3 days. Thus, there are 3 chances for Tommy to infect the other kids — Days 1, 2, and 3. Suppose that the probability that he infects any individual susceptible kid on any of the three days is p= 0.02; and suppose that all kids and days are independent (so that you have i.i.d. Bern(p)trials). If a kid gets infected by Tommy, he will then become infectious for 3 days as well, starting on the next day.