-
Notifications
You must be signed in to change notification settings - Fork 0
/
index.Rmd
169 lines (122 loc) · 4.53 KB
/
index.Rmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
---
title : Human Mobility and Cholera Transmission
subtitle : Insights from Mobile Phone Data from the D4D competition
author : Andrew Azman (with Justin Lessler)
job : http://scottyaz.github.io/d4d_pres/
framework : io2012 # {io2012, html5slides, shower, dzslides, ...}
highlighter : highlight.js # {highlight.js, prettify, highlight}
hitheme : tomorrow #
widgets : [mathjax] # {mathjax, quiz, bootstrap}
mode : selfcontained # {standalone, draft}
---
<img class="center" src=figures/d4dscreen.png height="600" width="900">
---
## 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
<img class="center" src=figures/zipf_and_newton.jpg height="315" width="500">
---
## 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
*** left
```{r echo=FALSE,tidy=TRUE}
dat <- read.table("/Users/aazman/Documents/D4D/trunk/data/POS_SAMPLE_0.TSV",sep="\t",nrows=10000)
dat <- dat[-which(dat[,3] == -1),]
colnames(dat) <- c("id","call.date.time","call.tower")
head(dat[sample(nrow(dat),10),])
```
---
<img class="center" src=figures/towers_tesselation.png height="550" width="600">
--- &twocol w1:50% w2:50%
*** left
<p></p>
<p></p>
<p></p>
<img class="center" src=figures/calls_per_person.png height="500" width="500">
*** right
<p></p>
<p></p>
<p></p>
<img class="center" src=figures/time_between_calls50.png height="500" width="500">
--- &twocol w1:50% w2:50%
*** left
<p></p>
<p></p>
<p></p>
<img class="center" src=figures/disp_hist_no_zeros_freq.png height="500" width="500">
*** right
<p></p>
<p></p>
<p></p>
<img class="center" src=figures/home_disp_ecdf.png height="500" width="500">
---
## 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
<img class="center" src=figures/prob_at_home_simple_model_fit.png height="400" width="400">
---
## 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
<img class="center" src=figures/four_env_plot.png height="500" width="500">
---
## Cholera Simulations
<img class="center" src=figures/run5_3.png height="500" width="600">
<h4><a href="http://andrewazman.com/D4D/movies/run3">example simulation</a></h4>
---
## Cholera Simulations
<img class="center" src=figures/arrival_time_run2.png height="500" width="400">
---
## 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
* [netmob](http://perso.uclouvain.be/vincent.blondel/netmob/2013/)
* [kaggle](http://www.kaggle.com/)
* [d4d](http://www.d4d.orange.com)