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.SIRModel
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The SIR Model of Infectious Disease
John Sterman (1999) Business Dynamics. Irwin/McGrawHill
Copyright (c) 1999 John Sterman
This is the classic SIR (SusceptibleInfectiousRecovered) model of infectious \
disease. Infectious individuals remain infectious for a constant average
period, then recover. Chapter 9.
It is initialized with a population of 10000.

Infectious Population I= INTEG (
Infection RateRecovery Rate,
Initial Infectious Population)
~ People
~ The infectious population accumulates the infection rate less the recovery \
rate.

Initial Infectious Population=
1
~ People
~ The initial number of infectious people.

Contact Rate c=
6
~ 1/Day
~ People in the community interact at a certain rate (the Contact Rate, c, \
measured in people contacted per person per time period, or 1/time \
periods).

Total Population N=
10000
~ People
~ The total population is constant

Infection Rate=
Contact Rate c*Infectivity i*Susceptible Population S*Infectious Population I/Total Population N
~ People/Day
~ The infection rate is the total number of encounters Sc multiplied by the \
probability that any of those encounters is with an infectious individual \
I/N, and finally multiplied by the probability that an encounter with an \
infectious person results in infection i.

Average Duration of Illness d=
2
~ Day
~ The average length of time that a person is infectious.

Recovered Population R= INTEG (
Recovery Rate,
0)
~ People
~ The recovered population R accumulates the recovery rate

Recovery Rate=
Infectious Population I/Average Duration of Illness d
~ People/Day
~ The rate at which the infected population recover and become immune.

Infectivity i=
0.25
~ Dimensionless
~ The infectivity (i) of the disease is the probability that a person will \
become infected after exposure to someone with the disease.

Susceptible Population S= INTEG (
Infection Rate,
Total Population N  Infectious Population I  Recovered Population R)
~ People
~ The susceptible population, as in the simple logistic epidemic model, is \
reduced by the infection rate. The initial susceptible population is the \
total population less the initial number of infectives and any initially \
recovered individuals.

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.Control
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Simulation Control Paramaters

FINAL TIME = 30
~ Day
~ The final time for the simulation.

INITIAL TIME = 0
~ Day
~ The initial time for the simulation.

SAVEPER =
TIME STEP
~ Day
~ The frequency with which output is stored.

TIME STEP = 0.125
~ Day
~ The time step for the simulation.

\\\/// Sketch information  do not modify anything except names
V300 Do not put anything below this section  it will be ignored
*View 1
$192192192,0,Helvetica10B0000000001111110,0
10,1,Susceptible Population S,75,296,50,25,67,3,0,8,0,0,0,0,000,000,10B000
10,2,Infectious Population I,408,294,50,25,3,3,0,8,0,0,0,0,000,000,10B000
1,3,5,2,4,0,0,22,0,0,0,111,,1(302,295)
1,4,5,1,100,0,0,22,0,0,0,111,,1(180,295)
11,5,220,241,295,6,8,34,3,0,0,1,0,0,0
10,6,Infection Rate,241,334,34,31,40,3,0,8,1,0,0,0,000,000,10B000
1,7,1,6,1,0,43,0,8,64,0,111,10B000,1(140,380)
1,8,2,6,1,0,43,0,8,64,0,111,10B000,1(359,376)
10,9,Infectivity i,365,464,53,13,8,3,0,8,0,0,0,0,000,000,10B000
10,10,Contact Rate c,83,431,49,17,8,3,0,8,0,0,0,0,000,000,10B000
1,11,10,6,1,0,43,0,8,192,0,111,10B000,1(209,394)
1,12,9,6,1,0,43,0,8,64,0,111,10B000,1(264,391)
12,13,0,163,329,15,15,5,4,0,8,1,0,0,0,000,000,10B000
B
12,14,0,329,326,15,15,4,4,0,8,1,0,0,0,000,000,10B000
R
10,15,Recovered Population R,713,294,50,25,3,3,0,8,0,0,0,0,000,000,10B000
1,16,18,15,4,0,0,22,0,0,0,111,,1(614,294)
1,17,18,2,100,0,0,22,0,0,0,111,,1(506,294)
11,18,412,560,294,6,8,34,3,0,0,1,0,0,0
10,19,Recovery Rate,560,333,33,23,40,3,0,8,1,0,0,0,000,000,10B000
1,20,2,19,1,0,43,0,8,192,0,111,10B000,1(478,376)
10,21,Average Duration of Illness d,586,451,53,26,8,3,0,8,0,0,0,0,000,000,10B000
1,22,21,19,1,0,45,0,8,192,0,111,10B000,1(614,386)
12,23,0,489,321,15,15,5,4,0,8,1,0,0,0,000,000,10B000
B
10,24,Total Population N,194,463,53,19,8,3,0,8,0,0,0,0,000,000,10B000
1,25,24,6,1,0,45,0,8,192,0,111,10B000,1(238,403)
12,26,0,160,354,39,9,8,4,0,8,1,0,0,0,000,000,8B000
Depletion
12,27,0,329,356,42,9,8,4,0,8,1,0,0,0,000,000,8B000
Contagion
12,28,0,493,350,42,6,8,4,0,8,1,0,0,0,000,000,8B000
Recovery
10,29,Initial Infectious Population,406,200,50,25,8,3,0,0,0,0,0,0
///\\\
:GRAPH POPULATIONS
:TITLE Populations
:XAXIS time
:SCALE
:VAR Susceptible Population S
:VAR Infectious Population I
:VAR Recovered Population R
:GRAPH RATES
:TITLE Rates
:XAXIS time
:SCALE
:VAR Infection Rate
:VAR Recovery Rate
:L<%^E!@
1:current.vdf
1:E:\My Stuff\Cairo Univ_Work\SD_Course\Business Dynamics Book CD\VENSIM\VENSIMMO\CHAP09VE\current.vdf
9:current
15:0,0,0,0,0,0
19:100,0
27:2,
4:Time
5:Susceptible Population S
24:0
25:30
26:30