Operations Research for Public Health Preparedness

Jeffrey W. HerrmannAssociate ProfessorDept. of Mechanical Engineering& Institute for Systems ResearchA. James Clark School of EngineeringUniversity of Maryland

Rutgers UniversityJanuary 30, 2012

Focused Issue on Operations Engineering and Analysis

Homeland Security Department

IIE Transactions

2012 Industrial and Systems Engineering Research Conference

Hilton Bonnet Creek, Orlando, FloridaMay 19-23, 2012

The process of responding to a bioterrorism attack starts with detection and investigation.

Outbreak

EnvironmentalMonitoring

SyndromicSurveillance

ClinicalDiagnosis

Outbreak Investigation

Decision to respond

Distribution to PODsDispensing at PODs

Prepositioning

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Points of Dispensing (PODs) provide mass vaccination or dispensing of medication.

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The medication supply chain must move quickly to distribute medications.

StrategicNationalStockpile

LocalDepot(RSS)

POD

POD

POD

POD

residents

residents

residents

residents

POD residents

Planning Problems• What is the best way to preposition

medication?• How should medication be delivered to

points of dispensing (PODs)?• What is the best POD layout?• How many staff do we need?• How long will people wait in line?

Prepositioning medical countermeasures affects the mortality of an anthrax attack.

Exposed Prodromal Fulminant

Not exposed Potentialexposure

Prophylaxed Recovered

Dead

Potential exposure = someone will seek prophylaxis but cannot become ill.

1 2 3

4 5 6

7 8 109 1211

13 14

17

1615

22

18

19

20

21

23

24

25 26 27

28

28 compartments track the number of exposed, ill, recovered, and dead.

The compartment changes first after changing disease status and then after changing treatment status.

Scenario timeline.Time (hours) Event0 Attack occurs.48 Attack detected. PODs start opening.53 Local supplies become available.64 (or 76) Push pack supplies becomes available.84 Vendor-managed inventory becomes available.96 All PODs at maximum capacity.

Population size = 5,000,000.Number exposed = 50,000, 500,000, and 1,250,000.Percentage of non-exposed persons who will seek prophylaxis (potential exposures) = 1%, 10%, and 50%.Adherence rate = 65% and 90%.

Model output can estimate exposed population by condition over time.

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

0 48 96 144 192 240 288 336 384 432 480 528 576 624 672 720

Number

Time (hours)

Exposed Population by Condition

Incubation Prodromal Fulminant Adhering Recovered Dead

Deaths decrease as more medication is predispensed.

N = the number exposed.b = the fraction of non-exposed persons who will seek prophylaxis (potential exposures).alpha = prophylaxis adherence ratet = delay until push pack is available

Deaths as Medkits Distribution Increases (alpha = 90%, t = 24 hours)

0%

10%

20%

30%

40%

50%

60%

0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 5,000,000

Number of Medkits Distributed

Percen

tage

 of tho

se exposed

 who

 die N=1,250,000, b=0.5

N=1,250,000, b=0.1N=1,250,000, b=0.01N=500,000, b=0.5N=500,000, b=0.1N=500,000, b=0.01

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The last leg of medication distributionis from a local RSS to the PODs.

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PODs will receive batch deliveries, which must arrive before supplies are exhausted.

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0:00 6:00 12:00 18:00 24:00 30:00 36:00

Time from start (hh:mm)

Qua

ntity

(reg

imen

s)

DeliveredSlackDemand

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Inventory slack routing problem (ISRP) formulation maximizes minimum slack.

{ }1, , ; 1, ,

max minv

vjv V j rS s

= ==

… …

( ){ }1min /vj

vj vjk k vj vjkks T Q L t w

σ∈= + − +

( ), vjk

vjk abka b E

Q q∈

= ∑

( )( )

, : 1, , ; 1, ,

ab vj ab

abk vj va b t t k

q I t v V j rσ≤ ∈

≤ = =∑ ∑ … …

, 1 , 1 1, , ; 2, ,vj v j v j vt t y v V j r− −≥ + = =… …

vj

vjk vk

q Cσ∈

≤∑

( )2 11 1

1, ,vrV

vjk kv j

q T T L k n= =

= − =∑∑ …0vjt ≥

Patients wait in line for flu shots in Silver Spring, Maryland.

Waiting at a POD

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From Patient Flow …Arrival Triage Registration

Education

ScreeningVaccinationExit

Holding Room

Symptoms Room

Consultation

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…to Simulation Model• Simulation model created using Arena®.

Queueing Network Analysis

Queue Server

Workstation

Patient

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Performance Measures

i i i iCT w t W= + +

11

1 I

i ii

TCT rCTr =

= ∑

1

1, ,min i

i Ii i

m rRt r=

⎧ ⎫= ⎨ ⎬

⎩ ⎭…Clinic Capacity

Station utilization

Station cycle time

Total cycle time

i ii

i i

r tum k⋅

=⋅

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Clinic Planning Model Generator

Clinic Generator

spreadsheet Planning model

Clinic Template

User input

The Clinic Generator spreadsheet takes inputs from the user and modifies the Clinic Template file

to create a custom clinic planning model that the user can modify as desired.

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Comparing the approximations to simulation yielded mixed results.

30374451586572798693

100107114121128135142149156163170177184191198205212219226233240247254261268275282289296303310317

324331338345352359366373380

8.00

%

13.0

0%

18.0

0%

23.0

0%

28.0

0%

33.0

0%

38.0

0%

43.0

0%

48.0

0%

53.0

0%

58.0

0%

63.0

0%

68.0

0%

73.0

0%

78.0

0%

83.0

0%

88.0

0%

93.0

0%

98.0

0%

Resident arrival rate to clinic (percentage of clinic capacity)

Entit

y cy

cle

time

in c

linic

(min

)

Average of cycle time from simulation with lower and upperbound

Cycle time from formula

Cycle time from simulation (min) with lower and upper bound (confidence interval for 95%)

6

7

8

9

10

11

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20

15.0

0%

20.0

0%

25.0

0%

30.0

0%

35.0

0%

40.0

0%

45.0

0%

50.0

0%

55.0

0%

60.0

0%

65.0

0%

70.0

0%

75.0

0%

80.0

0%

85.0

0%

90.0

0%

95.0

0%

100.

00%

Resident arrival rate to clinic (percentage of clinic capacity)

Entit

y cy

cle

time

in c

linic

(min

)

Average of cycle time from simulationwith lower and upper bound

Cycle time from formula

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Public health emergency preparedness planners around the country are using CPMG.

Download: www.isr.umd.edu/Labs/CIM/projects/clinic

States whose health planners are using our software.

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Final Thoughts• Modeling should create a conversation,

not just answer a question.

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Acknowledgements• Centers for Disease Control and Prevention• National Association of County and City

Health Officers• Montgomery County Department of Health

and Human Services, Public Health Service– Kay Aaby– Rachel Abbey– Carol Jordan– Kathy Wood

… and the students:

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For more information• Visit the project web site at

http://www.isr.umd.edu/Labs/CIM/projects/clinic/• Download the Clinic Planning Model Generator at

http://www.isr.umd.edu/Labs/CIM/projects/clinic/cpmg.html

• Get publications about the work at http://www.isr.umd.edu/Labs/CIM/projects/clinic/publications.html

• Contact Jeffrey Herrmann at jwh2@umd.edu