Mathematical Modelling in
Healthcare
John Frankish
John Frankish
C Grade, ‘O’ Level
Mathematics
1979
Everyone models...
to model:
to devise a
representation of a
phenomenon or system
Why model?
High level
process
Referral + Vetting
Registration
Booking
Scanning
Reporting
Patient
Sees Clinician
Clinician e.g. GP
Sends referral
Reception
Opens referral
letter
Phones
Booking for
appt
Receives letter
Receives OPA
confirmation
letter
Patient arriving
at reception
Changing room
Confirms ID
On Table
Count + log on
wall calendar in
office
Add validation
sheet
Place referral
letter in middle
tray
Request form
issue redesign
Prioritise &
justify letter
Open mail
Place in
bottom tray
Place forms
into basket
under
weekdays
Radiology Central
Booking
Rheumatology
Med Sec
Consultant
Rheumatologist
Rejected sent back
to referral with
letter or sent to
radiology
consultant for
advice
Check day
before: list
changes+paper
work present
Take Justified
forms to X-ray
Put/log &
scans form on
RADIS in date
order sends off
rejects
Radiology
Transport
Off table
Changing room
Gets result
from GP
Goes Home
Checks report
Date stamps
letter & puts in
top sheet tray
Check paper
work
Received on
RADIS
No Emergency
call
button/intercom
in scanning room
Paper work to
Scanning room
slot + ask
patient to
change
Need SOP
Radiographer
Close
c. 5 - 6 weeks
Estimated time
Place forms,
unfolded in A4
envelope & put
in internal mail
Porter collects
mail→General
Office→Van
etc
Porter
comes 2 x
day
Sorted by
Urgency, Date
Order U,R,FLS
Oncology
Check forms
missing details
previous scanssystem ?
PID for
Demand &
Capacity
Get a week list
ahead for
Dexa team
Takes mail to
general office,
picked up by
van etc
Update as
Reqd e.g.
missing paper,
printing worklist
Collect
Paperwork +
Patient
LMP,Identificati
on, ht & wt
details check
Do scan
Direct patient
to get changed
+ give info re
report
timescale
Generate/Print
paperwork
including DAP
No Batch Med
Sec
Add DAP to
RADIS + scan
form to
Synapse
Paperwork to
tray on filing
cabinet
Send Invite
letter to FLS
Place referrals
in filing cabinet
Booked
Send OPA +
questionaire to
patient
Paperwork into
drawer sorted
by consultant
Checks
MedSecs daily
for validated
letter
Print Report
Find paper
work in drawer
Post report to
referrer + ccs
as required
Paper work in date order
under desk
Digital
Dictation
Opportunity
Letter via
Porters To
General Office
for Post
Transport to
porters for
internal mail
Transport to
Porters
All others are
booked 6/52
ahead against
date order
Reported on
tape by Sue
Rice + sorted
for validation by
consultant
Booked pt
paperwork
returned in A4
env unfolded
weekly
Opportunity to send
to GPs
electronically with
CWS eClinical Letter
development
What is
contingency plan
in event of post
Types tapes to
MedSecs
Uncertain drafts
sent back to Sue
Checks &
validates
letter/report on
MedSecs
Cynefin model
http://everydaylean.info/2014/11/cynefin-ogre/ after Rob England
What is Operational Research?
Operations Research (OR) aims to
assist in solving complex problems
and making decisions, working to
achieve objectives in the best
possible way
Operational Research: Approaches
Hard OR
Soft OR
• Have data
• Uncertainties can be
quantified as
probabilities
• Mathematical
modelling of problems
• Expert analysis
• Poor or no data
• Uncertainties not
amenable to
quantification
• Visual modelling of
problems
• Facilitated guidance to
understand issues
Modelling Unit at ABUHB
• Part of ABCi
• Mathematical Modelling
• Maths support
• Knowledge & skills development
Knowledge escalator
Part-time MSc in
OR and Applied
Statistics
Geographic
Modelling
Problem
structuring
Introduction to
Modelling in
Healthcare
Essential
Statistics
in Healthcare
What graph,
when?
Excel Skills
Training
Courses
Foundation
Modules
Modelling Modules
The session
•
•
•
•
•
Forecasting – Dr Doris Behrens
Routing – Dr Soheil Davari
Queueing – Dr Izabela Komenda
Discrete Event Simulation – Dr Tracey England
System Dynamics/Problem Structuring – Dr Jennifer
Morgan
• Optimisation using Linear Programming – Geraint
Palmer
• 5 minutes each, time at end to go back for questions