Spatial patterns on the edge
of stability: measles in the
Sahel
• Great success in
measles eradication
•
Susceptible
Infected
Immune
Distribution of that
success has not been
equitable
• Poster child for nonlinear dynamics and
spatial epidemiology
Niger
• Culturally and
environmentally diverse
• Highest reported birthrate
in the world (51 per 1000)
• Low vaccine coverage in
Niger and surrounding
countries
Niamey • Relatively high case
fatality
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Measles Dynamics in Niger
All Niger
measles
Measles epidemic begin in the dry season
Aggregate measures can obscure local complexity
Local Dynamics: Niamey
• Timing is consistent with the national pattern
• High variability in outbreaks size
• Frequent local extinction
Estimating Seasonal
Transmission
Seasonal TSIR Model
   t St I t

Births
Susceptible
It 1 ~ neg binomial (It , )
St 1  St  It 1  births
Observational Model
Ot ~ binomial( It ,Pobs)

Infected
Pobs
Observed
Cases
Recovery rate
Immune
Fit state space model state using Bayesian MCMC methods
Estimated Seasonality
• Strong seasonality
in Niamey
• Related to the rainy
season
- Rural-urban
migration due to
agriculture?
• 3-fold greater seasonality
than pre-vaccine London
Seasonality Generates
Complex Epidemic Dynamics
• Stronger seasonality
leads to more episodic
dynamics at all
birthrates
• Potential for
deterministic chaos (!)
Niamey
Birth rate per 1000
London
Strength of seasonality
Deep Troughs Make
Stochastic Extinction Likely
• Stronger seasonality
leads to more episodic
dynamics at all
birthrates
• Potential for
deterministic chaos
• Stochastic extinction is
likely when there are
few cases
Niamey
Birth rate per 1000
London
Strength of seasonality
Dynamics set the stage for
spatial dynamics
Strong seasonality and high birth rates
give rise to locally instable dynamics
and erratic outbreaks that can vary in
size over orders of magnitude . . .
. . . public health strategies need to be
local and reactive.
2003-4 outbreak in Niamey
• Large outbreak
(>11,000 cases)
following 2 years of
few cases.
• In response a
collaborative effort
between MOH, WHO,
and MSF was
mobilized to vaccinate
Timing is Everything
Spatially implicit model showed that
campaign was unlikely to have had a great
impact on the course of the epidemic
Within Niamey Model
• > 9000 case
records
• 26 health districts
Within Niamey Model
• > 9000 case
records
• 26 health districts
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Within Niamey Model
• Spatially explicit
model of epidemic
spread in Niamey
Susceptibles
Infecteds
Ecases at i on day t    t Si,t1 (dij 1) I j

j
transmission rate
dij = distance between
location i and j
Within Niamey Model
data
simulation

rainfall
• Simulating the fitted model
replicates the aggregate
dynamics
• Seasonal transmission is
necessary to replicate timing
and extinction of outbreaks
• Weak spatial coupling is
required to slow spread
through entire city
Within Niamey Model
• Predict timescale for
vaccination response
• Prioritize spatial
surveillance

rainfall
= Epidemic size | index case
Regional Dynamics
Given that measles tends to go extinct
locally, even in the largest cities,
regional persistence must rely on
metapopulation dynamics.
Nita Bharti
5 years
Weekly reporting
County scale
health centers
Spatial and
temporal variation
in incidence
5 years
Weekly reporting
County scale
health centers
Spatial and
temporal variation
in incidence
QuickTime™ and a
Animation decompressor
are needed to see this picture.
Measles Persistence
Measles cases
Population size
• Measles persistence
scales with population
size
• Nowhere is measles
endemic
• Even above the classic
CCS
Regional Pattern
Measles cases
Population size
Spatial Metapopulation Model
Measles cases



E[It 1, j ]   t St, j 
I

d
 t, j  i, j It,i 


i j

Predicts Regional Pattern



E[It 1, j ]   t St, j 
I

d
 t, j  i, j It,i 


i j

• Spatial model captures regional
trend in persistence
• Effect of spatial arrangement
Guilt by association
• Predict that “well
connected” locations
have frequent
immigrants
• Districts with many
neighbors have short
periods of measles
extinction
Guilt by association
Trans-national
immigration
Districts with more frequent reintroductions than
expected are along the southern road network
A Natural Experiment
• Pulsed vaccination (Unicef, The Measles
Initiative)
– December 2004 > 80% coverage
– January 2008 > 90% coverage
• We can assume most 2005 and 2008 cases
are reintroductions
– 52 weeks from 2005
– 8 weeks from 2008
Isolating Reintroductions
Locations with > average cases per capita
2005 (1 yr)
2008 (8 wks)
2005 & 2008
Measles in Chad 2005
2004
2005
Measles in Nigeria
•
•
Measles killed more than 500 children
between January and mid-March in
Nigeria (WHO 2005)
Measles Outbreak Hits Northern
Nigerian State, over 3,000 cases
reported (VOA news March 2008)
A regional perspective
• Suggests that
understanding
measles persistence
(and conversely
eradication), requires
broadening the
regional perspective
beyond national
borders.
Goals at Multiple Scales
• Short term goals of
reducing measles
morbidity and mortality
require local response
and planning
• Long-term goals of
measles eradication
require large-scale
coordination that reflects
dynamics rather than
national boundaries
Acknowledgements
Nita Bharti, Ottar Bjornstad,
Bryan Grenfell
Andrew Conlan
Rebecca Grais,
Phillippe Guerin
Ministry of Health Niger
Ali Djibo