#FlattenTheCurve

• Author: Robert Dixon
• DOI: http://doi.org/10.1111/1467-8462.12380
• Published date: 01 September 2020
• Date: 01 September 2020

The Australian Economic Review, vol. 53, no. 3, pp. 450–458 DOI: 10.1111/1467-8462.12380

For the Student

#FlattenTheCurve

Robert Dixon*

Abstract

In this paper I adapt a common model used in

economics to study the diffusion of innova-

tions to model the transmission of a virus.

Emphasis is placed on the evolution of the

number of new infections and the cumulative

total number of infections over time and how

they might be influenced by different policies.

Although the model is very simple it does yield

some useful implications for public policy.

1. Introduction

The purpose of this article is to provide some

insights into a simple model of the way in

which a virus might spread within a popula-

tion. The model set out below is a slight

modification of one that is used widely in

economics and marketing to study the diffu-

sion of new innovations and the take‐up of

new consumer durables.

1

An advantage of

using a simple model is that it is relatively

easy to show some of the concepts and

methods that are used when models of the

time path of a variable of interest to us are

developed. While the model is very simple it

does yield some useful insights into public

policy to deal with an epidemic.

I begin by setting out some simple

assumptions about the very abstract world in

which the model is developed.

1.1 Some Assumptions and Notation

We assume that there is a given population of

a particular size and that in each period one

member of the population meets only one

other member of the population. We assume

that the (given) population is homogeneous in

the sense that all possible pairs of members of

the population have an equal chance of

meeting. We assume that meetings occur at

random and that the only way the virus can

spread is by close contact between people.

Let:

Y

t

be the total number of people in the

population who are infected with the virus by

the end of the current period—note that they

* Dixon: Department of Economics, University of

Melbourne, Victoria 3101, Australia. Corresponding

author: Robert Dixon, email: <r.dixon@unimelb.edu.au>

© 2020 The University of Melbourne, Melbourne Institute: Applied Economic & Social Research,

Faculty of Business and Economics

Published by John Wiley & Sons Australia, Ltd