#
1
2
3
4 t
1
Time t
0
= t t t
1
2
0
+x
Disease Stage
Outbreak/attack with disease in geographical location G
End of Disease Incubation period x
Detection phase of epidemic
Enter Containment Phase
I
Model Requirements
Ascertain :
N
G
= the population of Area ‘G’
S t
= the number of susceptible individuals in the population of area ‘G’ at time t
0
I t
= the number of infected individuals in the population of
‘G’ at time t
0
R t
= the number of recovered individuals in the population at time t
0 s
t0
= S t0
/N
G
the susceptible fraction of the population i t0
= I t0
/N
G the infected fraction of the population r t0
= R t0
/N
G
the recovered fraction of the population
Comments
When it all begins s
t0 will depend upon number of people in the population that have been previously inoculated. i t0
& r
t0 will be assumed to be zero
S t1
=
I t1
= By applying
R t1
= SIR equations
Modify inputs to SIR
S
R t1 t1 t1
=
=
=
S
I t1 t1
R
+ E
G t1
Obtain new populations
S t2
=
I t2
= By applying
R t2
= SIR equations
V t2
= vaccination dosage available to area G
β
1
used for SIR calculations will be number of transmission possible in the undetected phase
κ
1
will fraction that miraculously recover at this stage (zero ideally)
E
G
= Net emigration and births in geographical location G.
New susceptible population
We need to obtain plausible values for E
G.
β
2 =
β
1 + some factor reflecting the effect of quarantine
[ We need to develop an equation for this ]
κ
2
will be modeled to represent the following:

#
5
6
7
Time t
2 t
3
….t
t n+1 n
Disease Stage
Begin Containment Phase
Intermediate Containment phases
End of Simulation (after a specific time)
Model Requirements Comments
1 ) fraction that recover because of the availability of the vaccine at time t
2, i.e
V t2
2) fraction of population that are considered as recovered (treated, died, emigrated)
[We need to develop an equation to derive this]
Provide a report of conditions that exist :
1) CareGiver/Emergengy
Responder allocation strategy
2) Dosage Shipment inventory management
3) Quarantine guidelines
4) Evacuation guidelines for area ‘G’
S tn
=
I tn
= By applying
R tn
= SIR equations
Allow sensitivity analysis by modifying β n and κ n
The model should indicate how successful our manipulation of
β n &
κ n
in getting the Infected population I tn
to zero or some threshold
.
β n,
κ n
will effectively reflect our Quarantine and
Vaccination strategy
[Essentially this stage is a repetition of stages 3,4,5]