The appearance of the coronavirus (COVID-19) in late 2019 has dominated the news in the last few months as it developed into a pandemic. In many mathematics and physics classrooms, instructors are using the time series of the number of cases to show exponential growth of the infection. In this manuscript, we propose a simple diffusion process as the mode of spreading infections. This model is less sophisticated than other models in the literature, but it can capture the exponential growth and it can explain it in terms of mobility (diffusion constant), population density, and probability of transmission. Students can change the parameters and determine the growth rate and predict the total number of cases as a function of time. Students are also given the opportunity to add other factors that are not considered in the simple diffusion model.

1.
World Health Organization Director-General's
March 11,
2020
COVID-19 Media Briefing <https://www.who.int/dg/speeches/detail/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19—11-march-2020>
2.
The Wall Street Journal, “Coronavirus prompts colleges to send students home,” <https://www.wsj.com/articles/coronavirus-prompts-colleges-to-send-students-home-11583862936>.
3.
USA Today, “Coronavirus prompts colleges to send students home,” <https://www.usatoday.com/videos/news/2020/03/14/coronavirus-colleges-spring-break/5046501002/>.
4.
USA Today, “‘Stay home, stay healthy’: These states have ordered residents to avoid nonessential travel amid coronavirus,” <https://www.usatoday.com/story/news/nation/2020/03/21/coronavirus-lockdown-orders-shelter-place-stay-home-state-list/2891193001/>.
5.
Johns Hopkins: Coronavirus Resource Center, <https://coronavirus.jhu.edu/map.html>.
6.
World Health Organization, Coronavirus disease (COVID-2019) situation reports, <https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports>.
7.
Chicago: Coronavirus Response Center, <https://www.chicago.gov/city/en/sites/covid-19/home.html>.
8.
Spectrum News NY1, “Coronavirus in New York,” <https://www.ny1.com/nyc/all-boroughs/news/health-and-medicine/coronavirus-blog>.
9.
R.
Feynman
, “
The Brownian movement
,”
Feynman Lect. Phys.
I
,
41-1
41-18
(
1964
).
10.
VPython: 3D Programming for Ordinary Mortals, <https://vpython.org/>.
11.
F. A.
Williams
, “
Elementary derivation of the multicomponent diffusion equation
,”
Am. J. Phys.
26
,
467
469
(
1958
).
12.
D. C.
Kelly
, “
Diffusion: A relativistic appraisal
,”
Am. J. Phys.
36
,
585
591
(
1968
).
13.
Karmeshu
and
L. S.
Kothari
, “
Neutron diffusion as a random walk problem
,”
Am. J. Phys.
40
,
1264
1269
(
1972
).
14.
C.
Domb
and
E. L.
Offenbacher
, “
Random walks and diffusion
,”
Am. J. Phys.
46
,
49
56
(
1978
).
15.
J.
DArruda
and
E. W.
Larsen
, “
Simple derivation of the diffusion equation from the Fokker-Planck equation using perturbation methods
,”
Am. J. Phys.
46
,
392
393
(
1978
).
16.
A. M.
Albano
,
N. B.
Abraham
,
D. E.
Chyba
, and
M.
Martelli
, “
Bifurcations, propagating solutions, and phase transitions in a nonlinear chemical reaction with diffusion
,”
Am. J. Phys.
52
,
161
167
(
1984
).
17.
S.
Redner
and
P. L.
Krapivsky
, “
Capture of the lamb: Diffusing predators seeking a diffusing prey
,”
Am. J. Phys.
67
,
1277
1283
(
1999
).
18.
K.
Ghosh
,
K. A.
Dill
,
M. M.
Inamdar
,
E.
Seitaridou
, and
R.
Phillips
, “Teaching the principles of statistical dynamics,”
Am. J. Phys.
74
,
123–133
(
2006
).
19.
D. R.
Spiegel
and
S.
Tuli
, “
Transient diffraction grating measurements of molecular diffusion in the undergraduate laboratory
,”
Am. J. Phys.
79
,
747
751
(
2011
).
20.
T.
Pang
, “
Diffusion Monte Carlo: A powerful tool for studying quantum many-body systems
,”
Am. J. Phys.
82
,
980
988
(
2014
).
21.
NYC population: Current and projected populations
,” <www1.nyc.gov>. Accessed on May 2,
2019
.
23.
G.
Rossetti
,
L.
Milli
,
S.
Rinzivillo
,
A.
Sîrbu
,
D.
Pedreschi
, and
F.
Giannotti
, “
NDlib: A Python library to model and analyze diffusion processes over complex networks
,”
Int. J. Data Sci. Anal.
5
,
61
79
(
2018
).
25.
The code can be downloaded from <http://physics.neiu.edu/~acioli/research/viraldiffusion/Viral_Diffusion.py>. Instructors and students using the code should cite the present manuscript in any presentation or publication that uses this code as downloaded or modified.
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