# MTH 202 Calculus in Practice – Modeling COVID 19 using S-I-R

## MTH 202 Calculus in Practice – Modeling COVID 19 using S-I-R

Instructor: Gelonia L. Dent, Ph.D Fall 2020 Medgar Evers College, CUNY

Utilize your understanding of calculus concepts to model the spread of the coronavirus spread in your

state.

In this task, you will attempt to build a simulation of the virus spread in Excel. Watch the SIR Model

video and take notes. This video explains the mathematical model that connects the susceptible, infected,

and recovered individuals within a population where an infectious disease begins to spread.

1. Modeling: The equations in the SIR model describe the changes in population of people who are

susceptible, infected or recovered during the spread of a disease throughout the population.

dS

dt = -aSI,

dI

dt = aSI -bI,

dR

dt = rI

a) Rewrite the left side of each equation using the definition of the derivative. For your data,

specify the values of the proportionality constants, a, b and r. Be sure you understand what these

constants mean in the model

b) Create a new sheet in your CIP datasheet, label it COVID Model. Create columns for each

population of the SIR model, and a Constants column for the proportionality constants.

c) Enter the equations that you derived in part (a), into Excel under each. Test that your formulas

give some output. If not, make corrections. Congratulations, you have just written a short

program!

i) Run the simulation for the same period of time, for which you collected data.

ii) Examine the data by visualizing the output. Does it make sense? If not, make corrections.

d) Create a combined graph of the simulated data for each quantity. Label the graphs.

2) Final Report: Write a summary report on the CIP project, include your results the model compared

to the real data. What does your model say about the near future trend of coronavirus in your state?

Submit your final report and the Excel spreadsheet.