Modelling the spread of disease Ken Eames, Adam Kucharski, Jenny Gage.
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Transcript of Modelling the spread of disease Ken Eames, Adam Kucharski, Jenny Gage.
![Page 1: Modelling the spread of disease Ken Eames, Adam Kucharski, Jenny Gage.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5514d08a550346b0478b4f5c/html5/thumbnails/1.jpg)
Modelling the spread of disease
Ken Eames, Adam Kucharski, Jenny Gage
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Person to person spread
Microbes
WormsBacteriaViruses
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Wealso share
microbes with animals…
WormsBacteriaViruses
Microbes
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The swine flu pandemic
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HIV/AIDSMeaslesInfluenza
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Jenny Gage
Who we are
Julia Gog
Andrew Conlan
Adam Kucharski
Ken Eames
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Want to understand, then we can control.
Microbes
Individuals
Populations
Social groups
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The Standing Disease
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• Everyone starts sitting down.• One person stands and is the first case.• They pick two others to infect.• Those two stand up and each pick two others.• The next generation stands up and each pick
two more… and so on.
• How many steps to infect everyone?• If time: try with three instead of two• What if your class were bigger?
The Standing Disease
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1 2 4
32
168
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12481632641282565121024
2048
4096
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16384
32768
65536
131072
262144
524288
1048576
2097152
33 steps!
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Swine flu, 2009
Early part of epidemic
Can plot as a graph
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Reproductive Ratio
Definition: Average number of people an infected person infects at the start of an epidemic.
R0 = 2R0 = ??
R0 R0
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R0 is a measure of how quickly an epidemic will take off…
R0 > 1
Cases increase each step
Reproductive RatioR0 R0
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So we can understand the start of an outbreak, but what happens next?
Make a mathematical model to explore…
• Is there no one left to infect?• Has the disease changed its nature?
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SusceptibleEveryone starts here: not yet infected
These people are unwell and can infect others
People recover & become immune to infection
Infected
Transmission
Recovered
Recovery
Need to know how people mix together.
Compartmental model
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The Network Disease
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• Like the standing disease but:• Before starting, everyone writes down the
names of 2 other people in the room.• The first case picks the 2 they’ve written
down to infect.• This next generation stands up and each
pick their 2 names… and so on.
The Network Disease
• How is this different from the standing disease?
• How many steps to infect everyone?• If time: challenge the model!
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Challenge the model
We’ve seen 2 disease models: the standing disease and the network disease.•Are the models realistic enough?•How might a real epidemic be different?•What other things should a model include?
R0
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Epidemics don’t happen everywhere at the same time.
Space
Earliest
Latest
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Metapopulation models
• Complicated word for something familiar.• Population patches: lots of infection within a
patch, less transmission between patches.
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The importance of schools
Schools are really important:•Lots of people close together in the same place.•Many susceptibles - ideal for an epidemic.
Summer holiday
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Explaining spatial spread
• Want to know how different patches are connected.
• Human movements can help explain disease spread.
• Most information is about regular adult movements (e.g. commuting, air travel).
• Very little is known about how younger people move.
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What:Measure movement patterns of school pupils:•Compare primary and secondary schools.•Compare holidays and term time.How:•Design a questionnaire for primary school pupils to measure their mixing patterns.•Apply survey in your school and local primary school.Note:This is brand new - we don’t know the answers!
Research project: your task
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Data collection - example
• Simple movement questionnaire.
Age: ______ School year: ______Furthest (in miles) from home each day last week:
Distance Mon Tues Wed Thur Fri Sat Sun
Home
<1
1-5
5-30
30-100
>100
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Data collection - example
Distance Mon Tues Wed Thur Fri Sat Sun
Home x x<1 x x x1-5
5-30 x30-100 x>100
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Reported distances travelled
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First thoughts?
• What’s good? What’s bad?• What problems might come up when you try
to use it?• Suggestions for changes?
Distance Mon Tues Wed Thur Fri Sat Sun
Home x x<1 x x x1-5
5-30 x30-100 x>100
![Page 30: Modelling the spread of disease Ken Eames, Adam Kucharski, Jenny Gage.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5514d08a550346b0478b4f5c/html5/thumbnails/30.jpg)
What:Measure movement patterns of school pupils:•Compare primary and secondary schools.•Compare holidays and term time.How:•Design a questionnaire for primary school pupils to measure their mixing patterns.•Apply survey in your school and local primary school.Note:This is brand new - we don’t know the answers!
Research project (recap)
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Assignment for next time
• Design a first version of a movement survey.• Use the example as a starting point, but feel
free to try out different ideas.• Test it in another class in your school.
• Tell us how it went in the next video conference.
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Any questions?