This GitHub repository contains source code to build the `mobility`

R package which provides tools for analyzing human mobility data, including functions for parsing travel data, fitting mobility models using Bayesian inference, and simulating mobility patterns. This package is currently in development and maintained by John Giles (@gilesjohnr) and Amy Wesolowski.

Recently there has been a surge in research that incorporates human mobility data into epidemiological models. Depending on the context, mobility data can be derived from multiple sources such as GPS tracking studies, travel surveys, call data records, or mobile phone applications with location services. In addition, widespread social distancing measures that have been implemented to slow COVID-19 transmission have spurred several technology companies in the private sector to make data collected by mobile phone applications publicly available. A particular advantage lended by these data is that they offer real-time or near-real-time measures of human mobility at a high spatial resolution, leading to an increased interest in incorporating real-time data on human mobility into spatial models of disease transmission. Given the multitude of mobility data types now available and the impetus to use them in disease models, we developed the R package `mobility`

which provides tools to help public health researchers fit and simulate mobility models using different sources of human mobility data. The package will undergo continued development as methods evolve to meet current demand.

Although the initial format of each data type may be different, there are general challenges regarding data sparsity, spatial scale, and statistical uncertainty that make direct use of mobility data in modeling pipelines challenging:

**Data sparsity**occurs when observations for some routes of travel are missing, making it difficult to generalize observed mobility patterns for routes of travel that are unobserved. We address data sparsity by fitting mobility models to the data that are observed and then inferring travel for unobserved routes based on estimated model parameters.The

**spatial scale**of the mobility data is often different from that needed by the epidemiological model. Functions in this package account for differences in spatial scale by aggregating travel patterns to a larger spatial scale or extrapolating them to a smaller one using covariates such as distance and population size.**Statistical uncertainty**in the travel patterns found in human mobility data results from the variance in a naturally stochastic process. Depending on the method used to collect the mobility data and the subset of the population represented, measurement error and observation bias also have an impact. To facilitate integration of mobilty model uncertainty into disease models, we provide model fitting and simulation tools that allow researchers to simulate the mobility process according to the distribution of estimated model parameters.

To help facilitate modeling studies that wish to use mobility data and address the challenges above, we have developed a suite of tools that can be used to do some of the heavy lifting required to fit and simulate mobility models. Sections below show the general work-flow, see the package vignettes for more detailed examples.

There are many sources of travel data that researchers wish to fit models to. So, we have designed a generalized data frame template to standardize travel data from various sources into a longform format that is compatible with the modeling and simulation tools in this package. This data template can be populated by starting with the `travel_data_template`

object and adding rows.

Utility functions take mobility data from the generalized long-form format and build data matrices that are used to fit models.

```
mobility_data <- cbind(mobility_data, get_unique_ids(mobility_data, adm_start=2))
# Sparse matrix containing trip counts
M <- get_mob_matrix(orig=mobility_data$orig_id,
dest=mobility_data$dest_id,
value=mobility_data$trips)
# Distance matrix containing distances among all locations
xy <- get_unique_coords(mobility_data)
D <- get_distance_matrix(x=xy[,1],
y=xy[,2],
id=xy[,3])
# Unique population sizes for all locations
N <- get_pop_vec(mobility_data)
```

Alternatively, you can create mobility data matrices from your own data source. See the `mobility_matrices`

data object for an example of data structure.

```
str(mobility_matrices)
3
List of $ M: num [1:10, 1:10] 4559 NA 25 1964 NA ...
- attr(*, "dimnames")=List of 2
..$ origin : chr [1:10] "A" "B" "C" "D" ...
.. ..$ destination: chr [1:10] "A" "B" "C" "D" ...
.. ..$ D: num [1:10, 1:10] 0 671 1023 521 796 ...
- attr(*, "dimnames")=List of 2
..$ origin : chr [1:10] "A" "B" "C" "D" ...
.. ..$ destination: chr [1:10] "A" "B" "C" "D" ...
.. ..$ N: Named num [1:10] 9868 9511 5561 9596 12741 ...
- attr(*, "names")= chr [1:10] "A" "B" "C" "D" ... ..
```

```
# Fit a mobility model to data matrices
<- mobility(data=mobility_matrices, model='gravity', type='power_norm', DIC=TRUE)
mod
summary(mod) # Summary statistics of parameter estimates
.5 Q97.5 Rhat n.eff AC5 AC10
mean sd Q21.951844e-01 0.0006248893 1.939529e-01 1.964152e-01 1.00 919 0.02 0.01
gamma 5.695785e-04 0.0005556265 1.924751e-05 2.087491e-03 1.03 378 0.01 0.02
omega 9.953428e-01 0.0040059916 9.873916e-01 1.003462e+00 1.00 1000 0.01 0.02
theta 4.424932e+04 2.8947540122 4.424574e+04 4.425680e+04 1.00 659 -0.05 -0.01
DIC 4.424504e+04 2.8947540122 4.424146e+04 4.425251e+04 1.00 659 -0.05 -0.01
deviance 2.141799e+00 NA NA NA NA NA NA NA
pD
check(mod) # Check goodness of fit
$DIC
1] 44249.32
[
$RMSE
1] 1046.458
[
$MAPE
1] 5.578757
[
$R2
1] 0.712208 [
```

```
# Predict the expected mean number of trips using fitted mobility model parameters
<- predict(mod)
pred 1:5,1:5]
pred[
destination
origin A B C D E5819.4341 424.1779 390.5899 445.6444 410.3822
A 405.2726 5559.8336 456.8372 362.2968 439.9313
B 224.5727 274.9148 3343.7435 207.3500 259.8844
C 453.4775 385.8624 366.9740 5921.5336 382.2572
D 532.6940 597.6884 586.7235 487.6157 7556.0780 E
```

```
<- predict(mod, nsim=3, seed=123)
sim 1:5,1:5,]
sim[
1
, ,
A B C D E5819.2934 426.1649 392.4692 447.6925 412.3339
A 407.1690 5559.6542 458.8656 364.0649 441.9293
B 225.6655 276.1520 3343.6948 208.3886 261.0833
C 455.5835 387.7662 368.8098 5921.6621 384.1542
D 535.2219 600.3998 589.3920 490.0069 7555.9685
E
2
, ,
A B C D E5785.3651 422.5080 389.0609 443.8742 408.7853
A 403.6777 5527.2621 454.9804 360.9001 438.1816
B 223.7098 273.8168 3324.1344 206.5649 258.8627
C 451.6861 384.3829 365.5662 5886.9730 380.8022
D 530.6073 595.2950 584.3594 485.7362 7511.9216
E
3
, ,
A B C D E5833.9490 419.7001 386.1108 441.0524 406.0959
A 401.0265 5573.7552 452.0747 358.2909 435.6061
B 222.1749 272.2446 3351.0992 205.0489 257.3595
C 448.7633 381.5303 362.5781 5935.4389 378.0528
D 526.9251 591.5347 580.3331 482.1094 7575.6664 E
```

Please see package vignettes to explore each step in more detail.

The model fitting functions in the package perform parameter estimation using the Bayesian MCMC (Markov Chain Monte Carlo) algorithm called JAGS (Just Another Gibbs Sampler), which requires the JAGS library version >= 4.3.0 to be installed.

- If you do not have the JAGS 4.3.0 library installed, download HERE.
- If you already have an installation of the JAGS library, check that the version is >= 4.3.0 by opening your console and typing
`jags`

which should give you the following message:

```
user@computer:~$ jags
Welcome to JAGS 4.3.0 on Fri May 1 16:05:10 2020
JAGS is free software and comes with ABSOLUTELY NO WARRANTY
Loading module: basemod: ok
Loading module: bugs: ok
.
```

`mobility`

from GithubUse the `devtools`

package to install the development version of `mobility`

from the COVID-19-Mobility-Data-Network GitHub repository. The source code and its dependencies should be backwards compatible with previous R versions, but we recommend R version >= 3.6.2.

```
install.packages('devtools')
devtools::install_github('COVID-19-Mobility-Data-Network/mobility')
```

For general questions, contact John Giles (jrgiles@uw.edu) and/or Amy Wesolowski (awesolowski@jhu.edu). For technical questions, contact package maintainer John Giles (jrgiles@uw.edu). To report bugs or problems with code or documentation, please go to the Issues page associated with this GitHub page and click *new issue*.