Climate variability and the population dynamics of diarrheal - - PDF document

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Climate variability and the population dynamics of diarrheal - - PDF document

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5/11/2017 Climate variability and the population dynamics of diarrheal diseases Mercedes Pascual University of Chicago and The Santa Fe Institute 1 5/11/2017 London, 1854 Bangladesh, 2000 Cholera cases Time courtesy ICDDR, B 2

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5/11/2017 1 Mercedes Pascual

Climate variability and the population dynamics

  • f diarrheal diseases

University of Chicago and The Santa Fe Institute

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courtesy ICDDR, B Bangladesh, 2000 London, 1854

Time Cholera cases

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From National Geographic web site

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5/11/2017 6 Matlab

SST data: HadSST1: Rayner et al. 2003

El Tor Cholera Dhaka

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5/11/2017 7 – Observed precipitation enhanced following El Niño – Model captures much of the

  • bserved empirical signal

Link between cholera and ENSO

Cash, Rodo and Kinter ,

  • J. Climate 2008
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5/11/2017 8 Climate variability Spatial heterogeneity in vulnerability (in large urban environments of the developing world) feedbacks within the disease system itself (epidemiological processes that depend on the current or past state of the system  immunity; control measures) forecasting

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Limitation of temporal ‘correlative’ approaches:

1 – Spatial (and other forms) of population heterogeneity 2 – Nonlinear responses to environmental forcing 3 – Everything is seasonal… explanations for seasonality are hard

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Motivation

  • Spatial effects have not been considered before in the

response of cholera to climate variability. We may expect global climate drivers such as ENSO to operate at regional scales.

  • We still have a poor understanding of proximal mechanisms

that mediate the effect of global climate drivers in urban environments

  • Statistical models in the literature cannot be used effectively

for prediction because of their short lead times (ranging from 0 to 1 months )

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Movie

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5/11/2017 14 Reiner et al., PNAS 2012

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5/11/2017 16 Probabilistic model ( discrete state Markov chain model): probabilities a function

  • f group , season, neighbors’ states, and climate covariates.
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) (

anom

SST f

anom

SST

)] ( 1 [ * ) , ( ) , (

anom ENSO

SST f j i P j i P  

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  • Spatial heterogeneity: the dynamics between groups are significantly

different (p-value=0.0001)

  • Local effect: the state of neighboring districts matters (p-value =0.01) but

a weaker effect

  • Interaction between spatial structure and climate forcing: the parameters

governing the effect of ENSO are significantly different between the groups (p-value= 0.03); and similarly for flooding (p-value= 0.015) > ENSO is a significant covariate (p=value < 0.0001); lag

  • f 11 months for the spring months and 9 months for

the fall ones. > Flooding is also significant (p-value < 0.0001) > Flooding still significant when tested in the presence

  • f ENSO (p-value = 0.008) and vice-versa (p-value <

0.0001) Reiner et al. (PNAS 2012))

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Socio-economic conditions

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  • Cholera outbreaks in Dhaka (and Bangladesh) are driven by

climate variability (ENSO and flooding). The effect of El Niño is partly through precipitation and associated flooding.

  • Population susceptibility shows pronounced geographic

variation within Dhaka, with a part of the city acting as a susceptible core , in a way that highlights the key role of sanitary and associated socio-economic conditions.

Summary so far:

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Perez et al. Advances in Water Resources 2017

A remote-sensing view of the city

water urban rural

Population density Zooming out

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Bayesian approach to classify districts based on a dynamical model and time series data: Baskerville EB, Bedford T, Reiner RC, Pascual M (2013) Nonparametric Bayesian grouping methods for spatial time-series data. arXiv:1306.5202.

Search algorithms to identify ‘groups ‘ of locations with similar dynamics …

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5/11/2017 28 ‘ Longer-term weather cycles such as ENSO have been invoked to ‘explain’ outbreaks of malaria and other

  • diseases. … none of these analyses allows an alternative

explanation involving intrinsic cycles.’ (Rogers et al., 2002) NATURE INSIGHT – MALARIA REVIEW

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when two cycles interact…

0.2 0.4 0.6 0.8 1

  • 1
  • 0.5

0.5 1

Seasonal transmission Natural cycles of the disease Annual cycles Biennial cycles

  • r cycles of

longer period Multiple coexisting cycles Chaos

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I

Intrinsic dynamics

Model + statistical inference methods

Extrinsic drivers

NL

Climate variable Cases

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Model

ENSO No ENSO PARAMETER ESTIMATION Sequential Monte Carlo method

MODEL COMPARISON

Based on likelihood

Parameters were estimated with a method that maximizes the likelihood and allows for the inclusion of both measurement and process noise , as well as hidden variables

Ionides et al. PNAS 2006, King et al. Statistical inference for partially observed Markov processes (R package) http://pomp.r-forge.r-project.org

Parameter inference and model comparison

www.keywordpictures.com

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Model diagram

Reported cases

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 : seasonality and ENSO

𝛾 = exp[ ෍

1 6

𝑏𝑗𝑡𝑓𝑏𝑡𝑝𝑜𝑗 + 𝑐. 𝑡𝑓𝑏𝑡𝑝𝑜5. 𝐹𝑂𝑇𝑃 𝐾𝑏𝑜𝑣𝑏𝑠𝑧 ]

Time B-splines (1 to 6)

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Force of infection

‘secondary’ transmission

‘primary’ transmission

noise

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Inference method:

King AA, N D, Ionides EL. Statistical Inference for Partially Observed Markov Processes via the R Package pomp. J Stat Softw. 2016; 69(1): 1–43. Likelihood maximization by iterated filtering (based

  • n sequential Monte Carlo

methods --- particle filters) can accommodate:

  • flexible model formulations ; continuous time
  • unobserved variables (e.g. susceptibles)
  • stochasticity , trends
  • measurement error (under-reporting)

See Laneri et al (PloS Comp. Biol. 2010) for inclusion of covariates and pseudo-code in a malaria example

From Z. Chen 2009

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Fig 2. Comparison of simulated and predicted monthly cases with those reported for Dhaka, Bangladesh.

Martinez PP, Reiner RC Jr, Cash BA, Rodó X, Shahjahan Mondal M, et al. (2017) Cholera forecast for Dhaka, Bangladesh, with the 2015-2016 El Niño: Lessons learned. PLOS ONE 12(3): e0172355. https://doi.org/10.1371/journal.pone.0172355 http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0172355

‘Out-of-fit’ data

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Water level and rainfall in Dhaka

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Some conclusions

  • Model with ENSO better explains the retrospective data

including the large epidemic of 1998

  • It also predicts the low incidence of ‘out-of-fit’ data

during non-EL Nino years

  • It overpredicts the response to the 2015-16 event.
  • This appears to reflect a decrease susceptibility to

flooding in the city, and perhaps a decadal change in rainfall conditions

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Rotavirus: segmented RNA virus

Transmission electron micrograph of rotavirus particles

http://pathmicro.med.sc.edu/virol/rotaviruses.htm http://www.babymed.com/infections/rotavirus

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Rotavirus: empirical patterns

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Core Periphery

us

Transmission model

Martinez et al., PNAS 2016

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Transmission rate

seasonality flooding process noise

(interannual variation)

Force of Infection α = coupling (0 ≤ α ≤ 1)

Month

𝑡4 Fourth spline 𝒕𝟓

Model

Transmission model

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Results

Martinez et al., PNAS 2016.

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>> Higher force of infection in the core >> Especially, during the monsoons >> Transmission in the core continues outside the two main seasons (no deep troughs)

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Some general implications

  • Dense urban areas can enhance transmission and facilitate

more endemic dynamics

  • In these areas, enhanced responses to climate forcing may

be seen even in infections that are not considered climate sensitive to begin with

  • These responses are reflected primarily in changes to the

seasonality

  • More epidemic behavior, in areas where disease persistence

throughout the year is more marginal, will exhibit responses to climate forcing at multiannual rather than seasonal scales

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Climate variables and seasonality

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Seasonality of rainfall and temp

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The model

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Seasonality: Model and data

The historical Bengal region encompasses all the seasonal patterns observed worldwide Monthly data: 1891-1941

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Rainfall and ‘hydrology’

Dhaka Patna drainage rainfall

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Interannual variability

Dhaka Patna

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Gracias

Ben Cash: COLA (Center for Ocean Land and Atmosphere Studies) Xavier Rodó (IC3 Barcelona) Aaron King, UM

Md Yunus ICDDR, B

Robert Reiner, UW Pamela Martinez, UC Theo Baracchini , EPFL Menno J. Bouma, LSHTM, UK

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James S. McDonnell Foundation NOAA, Oceans and Health Program NSF-NIH, Ecology of Infectious Diseases Graham Environmental Sustainability Institute (GESI, UM)

Gracias

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Conclusions and Implications

  • Cholera epidemics appear primarily limited by the local depletion of

susceptibles

  • Explicit ‘space’ matters (the dynamics are distributed in space or in a

network)

  • Stochasticity (demographic noise) might be essential to the epidemic

dynamics of infectious diseases, beyond the recognized effect of small population size on extinction.

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5/11/2017 56 NOAA, Oceans and Health Howard Hughes Medical Institute Graham Environmental Sustainability Institute (GESI, UM)