LAB #10
SIR Model of a Disease
Goal
: Model a disease and investigate its spread under certain conditions. Use graphs
generated by
pplane
(and its many options) to estimate various quantities.
Required tools
:
Matlab
routine
pplane
and its graphing options.
Discussion
The
SIR
model is a mathematical model of the spread of an infectious disease
satisfying the following assumptions:
(i) the disease is short lived and rarely fatal
(ii) the disease is spread by contact between individuals
(iii) individuals who recover develop immunity.
If
S
(
t
)
,I
(
t
)and
R
(
t
) represent the number of
S
usceptible,
I
nfected and
R
ecovered
individuals in a population, then it can be shown that with the above assumptions, the
system of equations modeling this disease satisﬁes:
dS
dt
=

aSI
dI
dt
=
aSI

bI
dR
dt
=
bI
(
*
)
where
a
and
b
are positive constants.
Because the total population
N
remains constant (at least in the short term), for small
values of
t
,wehave
N
=
S
(
t
)+
I
(
t
)+
R
(
t
)(
**
)
If we know
S
(
t
)and
I
(
t
), we also know
R
(
t
). Hence the 3
rd
equation in (
*
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 Spring '08
 CHO
 matlab

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