Jonathan Dusho McMaster University Global Health Expert … · 2020. 6. 9. · What happens when we...

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Dynamical modeling of infectious diseases

Jonathan Dushoff

McMaster UniversityGlobal Health Expert Perspectives Webinar

May 2020

What is dynamical modeling?

1950 1955 1960 1965

Measles reports from England and Wales

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:

I Susceptible → Infectious → Recovered

I Individuals recover independently

I Individuals are infected by infectious people

Deterministic implementation

0 200 400 600 800 1000

Time (disease generations)

Deterministic

Individual-based implementation

0 200 400 600 800 1000

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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1990 2000 2010

R0 = 5.66

More detailed dynamics

Childs et al., http://covid-measures.stanford.edu/

Exponential growth

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Jan 13 Jan 20 Jan 27 Feb 03

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

1.0 homogeneous

Disease incidence tends to oscillate

0 200 400 600 800 1000

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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Jan 20 Jan 27 Feb 03date

e type

forecast

reported

Linking

0 50 100 1500

100200300400 R0 = 1.5

Days, t

0100200300400 R0 = 2.0

0100200300400 R0 = 2.5

0 200 400 600 800 1000 1200100

Days, t

Infected

R0 = 2.5R0 = 2.0R0 = 1.5

Coronavirus speed

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Jan 13 Jan 20 Jan 27 Feb 03

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

0 10 20 30 40 50

Generations and R

0 2 4 6 8

Time (weeks)

Reproduction number: 1.65

Generations and R

0 2 4 6 8

Time (weeks)

Reproduction number: 1.4

Propagating error for coronavirus

none µ̂r µG µκ all

Uncertainty type

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

Liberia

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1990 2000 2010

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

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?

Feb 01 Feb 15 Mar 01 Mar 15Date

A. Daegu

B. Seoul

(Daily traffic, 2020)/(M

ean daily traffic, 2017 − 2019)

C. Daegu

(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

0 50 100 150 200100

Weitz et al., https://github.com/jsweitz/covid19-git-plateaus

Modeling responses

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

number

ofreported

deaths C

ountries

USStates

Modeling responses

0 50 100 150 200 250 300 350 4000

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

Jonathan Dusho McMaster University Global Health Expert … · 2020. 6. 9. · What happens when we...

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