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Dynamical modeling of infectious diseases Jonathan Dushoff McMaster University Global Health Expert Perspectives Webinar May 2020
Dynamical modeling of infectious diseases
Jonathan Dushoff
McMaster UniversityGlobal Health Expert Perspectives Webinar
May 2020
What is dynamical modeling?
1950 1955 1960 1965
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Measles reports from England and Wales
date
case
sI A way to connect scales
I Start with rules about how things change in short time stepsI Usually based on individuals
I Calculate results over longer time periodsI Usually about populations
Example: Post-death transmission and safe burial
I How much Ebola spread occursbefore vs. after death
I Highly context dependent
I Funeral practices, diseaseknowledge
I Weitz and Dushoff ScientificReports 5:8751.
Simple dynamical models use compartmentsDivide people into categories:
S I R
I Susceptible → Infectious → Recovered
I Individuals recover independently
I Individuals are infected by infectious people
Deterministic implementation
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cted
Time (disease generations)
Deterministic
Individual-based implementation
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ber
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cted
Time (disease generations)
SIR disease, N=100,000
StochasticDeterministic
Disease tends to grow exponentially at first
I I infect three people, theyeach infect 3 people . . .
I How fast does disease grow?
I How quickly do we need torespond?
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R0 = 5.66
YearH
IV p
reva
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More detailed dynamics
Childs et al., http://covid-measures.stanford.edu/
Exponential growth
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Mike Li, https://github.com/wzmli/corona
There are natural thresholds
I R is the number of new infectionsper infection
I A disease can invade a populationif and only if R > 1.
I The value of R in a naivepopulation is called R0
Non-linear response
I R = β/γ = βD = (cp)D
I c : Contact Rate
I p: Probability oftransmission(infectivity)
I D: Average duration ofinfection
0.1 0.5 2.0 5.0
endemic equilibrium
R0
Pro
port
ion
affe
cted
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1.0 homogeneous
Disease incidence tends to oscillate
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SIR disease, N=100,000
StochasticDeterministic
What is not dynamical modeling?
https://tinyurl.com/forbes-ihme
I Phenomenologicalmodeling uses historyand statistics
I Does not incorporatemechanistic processes
Coronavirus forecasting
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Inci
denc
e type
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forecast
reported
Linking
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100200300400 R0 = 1.5
I(t)
Days, t
0100200300400 R0 = 2.0
I(t)
0100200300400 R0 = 2.5
I(t)
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Days, t
Infected
,I(t)
R0 = 2.5R0 = 2.0R0 = 1.5
Coronavirus speed
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How long is a disease generation? (present)
Generation intervals
I Sort of the poor relations ofdisease-modeling world
I Ad hoc methods
I Error often not propagated
Generation intervals
I The generation distributionmeasures the time betweengenerations of the disease
I Interval between“index” infection andresulting infection
I Generation intervals providethe link between R and r
Approximate generation intervals
Generation interval (days)D
ensi
ty (
1/da
y)
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0.00
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0.08
Generations and R
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Time (weeks)
Wee
kly
inci
denc
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Reproduction number: 1.65
Generations and R
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Time (weeks)
Wee
kly
inci
denc
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Reproduction number: 1.4
Propagating error for coronavirus
2.6
3.0
3.4
none µ̂r µG µκ all
Uncertainty type
Basic
reproductivenumber
B. Reduced uncertainty in r
Growing epidemics
I Generation intervals look shorterat the beginning of an epidemic
I A disproportionate numberof people are infectious rightnow
I They haven’t finished all oftheir transmitting
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2014−01 2014−07 2015−01
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Liberia
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nce
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Backward intervals
Champredon and Dushoff, 2015. DOI:10.1098/rspb.2015.2026
Outbreak estimation
tracing based empirical individual based
contacttracing
populationcorrection
individualcorrection
empirical egocentric intrinsic2
4
8
Rep
rodu
ctiv
e nu
mbe
r
Serial intervals
Flattening the curve
Bolker and Dushoff, https://github.com/bbolker/bbmisc/
Flattening the curve
Bolker and Dushoff, https://github.com/bbolker/bbmisc/
What happens when we open?
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Rec
onst
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nce
A. Daegu
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B. Seoul
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Effe
ctiv
e re
prod
uctio
n nu
mbe
r
(Daily traffic, 2020)/(M
ean daily traffic, 2017 − 2019)
C. Daegu
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ctiv
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prod
uctio
n nu
mbe
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(Daily traffic, 2020)/(M
ean daily traffic, 2017 − 2019)
D. Seoul
Park et al., https://doi.org/10.1101/2020.03.27.20045815
Making use of immunity
Weitz et al., https://www.nature.com/articles/s41591-020-0895-3
Modeling responses
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103
Weitz et al., https://github.com/jsweitz/covid19-git-plateaus
Modeling responses
China
CA
Iran
WA
Italy
NY
UK
GA
USA
LA
Apr May Mar Apr May Apr May Apr May Apr May
Feb Mar Apr May Mar Apr May Mar Apr May Apr May Mar Apr May
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number
ofreported
deaths C
ountries
USStates
Weitz et al., https://github.com/jsweitz/covid19-git-plateaus
Modeling responses
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Weitz et al., https://github.com/jsweitz/covid19-git-plateaus
Going forward
I Statistical methods for inference and understandinguncertainty
I Work with policymakers to evaluate and tune strategies forgradual opening
Thanks
I Department
I CollaboratorsI Bolker, Champredon, Earn, Li, Ma, Park, Weitz, many others
I Funders: NSERC, CIHR
