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Human Mobility and Cholera Transmission
Insights from Mobile Phone Data from the D4D competition
Andrew Azman (with Justin Lessler)
io2012
highlight.js
tomorrow
mathjax
selfcontained

Motivation

  • What role do human mobility and local environmental conditions play in cholera transmission?
  • North American/European vs. African mobility patterns
  • Person-to-person vs. environmentally mediated transmission

Human Mobility Models

Human Mobility Models

  • Humans (may) follow simple reproducible patterns in their movements
  • Key predictors:
  • Population / population density
  • Distance between locations
  • Gravity Models $\left(pr( i \rightarrow j) \propto \frac{P_i^{\alpha}P_j^{\beta}}{f(d_{ij})}\right)$
  • Radiation Models (non-parametric)
  • Useful for understanding disease dynamics especially in the context of individual-based models

--- &twocol w1:50% w2:50%

D4D Data Set

  • 500,000 individuals observed over different two week periods
  • 55,319,911 calls made from ~1200 towers

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##      id      call.date.time call.tower
<<<<<<< HEAD
## 1833 20 2011-12-09 12:43:00        898
## 7723 72 2011-12-13 11:19:00        314
## 82    1 2011-12-13 21:15:00        264
## 2596 23 2011-12-09 13:55:00        863
## 3587 35 2011-12-16 20:25:00        544
## 9721 93 2011-12-18 19:51:00        491
=======
## 1652 20 2011-12-07 19:08:00        898
## 3930 39 2011-12-11 23:03:00        115
## 6654 57 2011-12-14 08:21:00        314
## 9098 90 2011-12-08 12:15:00       1025
## 84    1 2011-12-13 21:49:00        264
## 6589 57 2011-12-12 08:43:00        140
>>>>>>> gh-pages

--- &twocol w1:50% w2:50%

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--- &twocol w1:50% w2:50%

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Our (simple) Mobility Model

  • Person $k$ (given their home location $i$) will be seen in any other location at any point in time with probability $\nu_{i,j}$ [ \begin{align} logit(\nu_{i,j}) = \left{ \begin{array}{ll} \alpha_0 + \alpha_1 log(P_i) & \mbox{if } i = j \ \alpha_2 + \alpha_3 log(P_i) + \alpha_4 log(P_j) + \alpha_5 log(d_{ij}) & \mbox{if } i \neq j \end{array} \right. \end{align} ]
  • Challenges:
  • Depends on home location
  • Assumes trips always made from home to different locations

Model Fit

quantile $\alpha_0$ $\alpha_1$ $\alpha_2$ $\alpha_3$ $\alpha_4$ $\alpha_5$
2.5% 1.8704 -0.1603 -6.9926 0.0229 0.2897 -1.1270
50% 1.8791 -0.1594 -6.9815 0.0239 0.2905 -1.1266
97.5% 1.8876 -0.1584 -6.9707 0.0249 0.2913 -1.1262

Cholera Transmission Model

  • Discrete-time Susceptible Infectious Recovered (SIR) model
  • Country divided into 5-km grid cells
  • All infections mediated through environment
  • Cholera infected individuals shed vibrios into "environment"
  • People drink water with some concentration of vibrios from the environment
  • With some probability (dose-response) people get sick

Environmental Mediators of Transmission

Cholera Simulations

example simulation

Cholera Simulations

Future Directions

  • Improve movement model
    • How to learn about duration
    • Simulations to understand potential biases
  • Refine functional form of environmental modifiers
  • Fit to cholera data
  • Exploration of general epidemiologic connectivity of areas within country

Links