Human mobility patterns are a reflection of behaviors, ranging from routine (e.g., commuting daily for work or school, traveling for holidays and religious gatherings, or seeking seasonal work opportunities) to irregular (e.g., relocating due to environmental changes or crises or social distancing due to a pandemic) (Charaudeau et al., 2014; Haberfeld et al., 1999; International Organization for Migration, 2019; Lessler et al., 2014; Lu et al., 2012; Pullano et al., 2020). Consequently, characterizing human mobility patterns is important for a wide range of applications, including predicting the spread of infectious diseases, traffic forecasting, designing intervention strategies, assessing health service accessibility, planning natural disaster relief efforts, and estimating migratory flows to estimate changes in population demographics (Charaudeau et al., 2014; Dotse-Gborgbortsi et al., 2020; Findlater and Bogoch, 2018; Finger et al., 2016; Gilbert et al., 2020; Lu et al., 2012; Mari et al., 2017; Palchykov et al., 2014; Stoddard et al., 2009; Wesolowski et al., 2012). Depending on the spatial and temporal resolution of travel relevant to the question of interest, there are many data sources that can quantify travel, such as national censuses, traffic or commuting data, travel surveys, or mobile phone data (Tatem, 2014). However, when mobility data are limited or unavailable, spatial interaction models are often used to estimate mobility patterns. One of the most commonly used models is the gravity model (Wesolowski et al., 2015b), which assumes the number of trips between an origin and destination over a fixed time period will increase as a function of the destination and origin population sizes and decrease with distance. While the gravity model was originally developed to describe commuting in a high-income setting (Zipf, 1946), it has been used to model travel in low- and middle-income countries (LMICs) when data are limited or unavailable (Stone et al., 2019; Wells et al., 2019; Wesolowski et al., 2015b). In high-income settings, the standard gravity model has been shown to perform well when predicting commuter movement between cities (Masucci et al., 2013) and perform poorly when predicting movement across areas with heterogeneity in demographics and population density or in rural areas (Truscott and Ferguson, 2012; Xia et al., 2004). However, the degree to which geographic, sociodemographic, and infrastructure differences may impact the ability for models to capture travel patterns in LMICs, particularly in more rural settings, remains to be determined.

Increasing mobile phone ownership (over 67% of the global population in 2019) and the mobility patterns that can be extracted from these data provide a valuable resource for evaluating how well spatial interaction models can capture human mobility patterns in low- and middle-income settings (GSM Association, 2020; Wesolowski et al., 2016). However, the challenge of procuring mobile phone datasets has resulted in relatively few studies that fit mobility models to relevant travel data from LMICs. Of these, a few studies have explored model adjustments and show that predictions can be improved by adjusting the gravity model to account for factors such as education levels, economic opportunities, gender, environmental factors, trip duration, contiguity of origin and destination, and proportion of population living in urban areas (Garcia et al., 2015; Henry et al., 2003; Wesolowski et al., 2015b). Typically, studies assume that these factors impact all trips homogeneously, thus fitting a single set of parameters for all trips is a sufficient adjustment. Yet, even with such adjustments, gravity models may still fail to accurately capture mobility patterns in LMICs, particularly in rural areas (Henry et al., 2003; Wesolowski et al., 2015b), suggesting that models which account for regional heterogeneity in travel may improve their estimates in these settings.

Here, we examine the impact that regional heterogeneity and urbanicity has on travel patterns as well as how well spatial interaction models can reproduce travel patterns in LMICs by examining four countries in Sub-Saharan Africa: Namibia, Kenya, Burkina Faso, and Zambia (Figure 1A–D). These countries capture a range of levels of urbanization, population distribution, and importantly include large rural areas common in many LMICs. Using mobile phone data, we first characterized human mobility patterns from these four countries and determined which features were not well captured by basic gravity models. Next, we conducted an analysis of six variations of the basic gravity model, including variations that account for regional travel and urbanicity, as well as a basic radiation model to determine which provided the best trip estimates for each country (Simini et al., 2012). Finally, we compared the different model fits across the four countries to evaluate if the adjustments produced similar improvements for all countries. To our knowledge, no other models have captured these mobility features, been tested consistently against mobility data from multiple LMICs, and provided clear guidance on which model to use and when. This study provides further insight on the mobility patterns in LMICs and highlights where mobility model estimates may deviate when applied in other similar settings, ultimately improving our understanding of topics such as disease spread, migratory flows, and intervention efficacy in LMICs.

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We analyzed the average number of daily trips, defined here as the number of subscribers moving from one district (administrative level 2) to another, per month extracted from each mobile phone dataset (see Materials and methods). Similar to other studies, we found that the average number of monthly trips between districts from Namibia, Kenya, Burkina Faso, and Zambia generally decreased with trip distance and there were more trips from and to more populated areas (Figure 1E–H, Figure 1—figure supplements 1–8). Trips were concentrated between districts within the same region (administrative level 1) to varying degrees (intra-regional trips made up 30% of all trips in Burkina Faso, 45% in Kenya, 62% in Namibia, and 72% in Zambia) and to a few common destinations, including the district where the capital was located (Figure 1I–L, Supplementary file 1A). Although Namibia, Burkina Faso, and Zambia each consisted of ~95% predominantly rural districts, the distribution of monthly trips between urban and rural districts varied across countries. The majority of Namibia’s and Burkina Faso’s trips were between rural locations (62% and 70.5% of all trips, respectively), while Zambia’s trips were split between rural locations (53%) or rural and urban locations (46%). Kenya, with 56% predominantly urban districts, had the largest proportion of monthly trips between urban locations (70%). As a basic model, we first estimated trip counts using a basic gravity model (single parameter set fitted for all trips), which is based on the population sizes of the origin and destination and the distance between locations, with two variants on the distance kernel (power or exponential decay) (Equation 1). Estimates from this basic model overestimated trip counts and missed important features of the data, such as higher trip counts in short-distance and within-region trips, relative to long-distance and between-region trips (Figure 1E–L, Figure 1—figure supplements 1–8). Travel involving predominantly rural locations tended to be overestimated and these results were largely observed for both distance kernels and for all countries.

Given how the basic model’s estimates of urbanicity and regional movement deviated from the call data records, we tested six additional variations of a gravity model that allowed for parameters to capture increasingly complex features in the data (Equations 2–9). These included fitting parameters for the origin and destination population sizes and trip distance to: (1) trips defined by origin and destination population density (urbanicity model: higher population density = predominantly urban, lower population density = predominantly rural), (2) trips within- and between-regions (regional model), and (3) trips defined by both region and urbanicity (regional-urbanicity model) (Figure 2). Each model variation was tested with two distance kernels (power and exponential decay). We also evaluated a basic radiation model (Equation 11; Masucci et al., 2013; Simini et al., 2012).

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Table of model parameter values fit for each country, both distance kernels, and all trip types.

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All parameterized gravity models outperformed the basic model. Allowing for parameters to be fit by urbanicity or region improved model fit to varying degrees, depending on the country (Table 1, Supplementary file 2A). Accounting for urbanicity provided a larger improvement in model fit than region for all countries; however, this improvement was larger in Kenya and Burkina Faso than Namibia and was only observed for Zambia if the lower urbanicity threshold (10%) was implemented. In these models, the degree to which the parameters varied increased with model complexity, with the distance parameter varying the most, allowing for different weights to be applied based on the trip type (Figure 2—figure supplements 1–2). Overall, the most complex model, the regional-urbanicity model, had the best fit for all countries (the power variant reduced the basic model’s deviance information criterion (DIC) by 41% for Namibia, 30% for Kenya, 28% for Burkina Faso, and 16% for Zambia) (Table 1, Supplementary file 2A). Its flexibility allowed for the importance of origin and destination population sizes to vary by trip type, distinguished differences in the relative importance of distance by trip type, was able to better distinguish between inter- and intra-regional trip estimates, and adjusted for the lower trip counts between rural locations, relative to other trip types (Figure 3A, Figure 3—figure supplements 1–4). This was true regardless of the distance decay function assumed, although the best fitting decay function did vary by country (Supplementary file 2A). Interestingly, the radiation model had the most variable performance of all models, where it was the poorest performing in Namibia, Burkina Faso, and Zambia, but outperformed the basic gravity model (exponential form) in Kenya. Differences in the population distribution (more heterogenous in Namibia, Burkina Faso, and Zambia than Kenya) and locations of more populated areas may be the cause of these conflicting findings across countries (Figure 1—figure supplement 9; Linard et al., 2012; Masucci et al., 2013). These results were consistent across a range of administrative levels (1-3), suggesting that including locations’ urbanicity and/or region in a model will generally improve model fit across spatial scales (Supplementary file 2B).

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Overall model fit may not accurately describe how well each model can estimate certain trip types which may be relevant for particular questions. We further evaluated how close model estimates were to the observed trip count using the ratio of predicted to observed trip counts (Figure 3B, Figure 3—figure supplements 5–7). Unsurprisingly, the regional-urbanicity model (with either the exponential or power decay) produced some of the most accurate model estimates ( ± 10% of the observed trip counts) for most trip types in Namibia (11/14 trip categories), Kenya (7/14 trip categories), and Burkina Faso (6/9 trip categories) (Supplementary file 3A); however, the regional model produced the most accurate estimates for a range of trips in Zambia (5/13). The proportion of trips estimated within the 10% margin of error was lowest for Kenya, with the most accurate models only well estimating 3–7% of trips, and highest for Namibia, with some models estimating >30% of certain trip types. Depending on the type of trip and country, simpler models may provide more accurate trip estimates than the more complex regional-urbanicity model. We found that just accounting for region may be sufficient for best capturing rural-to-rural as well as general or specific inter-regional travel in Namibia. Further, a wide range of trip types was well estimated by the radiation model in Kenya and by a basic model (exponential decay) in Zambia.

To date, there have been limited evaluations of mobility patterns in Sub-Saharan African countries and how the geographic, demographic, and economic differences in many LMICs impact the validity of modeling assumptions to estimate travel. By comparing and evaluating a range of gravity models in four Sub-Saharan African countries, we identified clear patterns of travel that were not well approximated using a basic gravity model. By allowing these models to accommodate differences in travel between predominantly rural and/or urban areas and within- versus between-regions, we found that the best fitting model allowed for the greatest flexibility for estimating different trip types. However, there were differences in which model was best able to estimate particular types of travel, the importance of distance and population, and the overall fit of all models to the data by country. Therefore, selecting a model that adjusts for the trip type and context of interest is important for improving estimates.

If a given application is focused on estimating specific trip types (e.g., urban residents traveling to rural areas for work), these findings may be informative for model selection in similar settings. If a country is sparsely populated with a single predominantly urban district (e.g., capital district), like Burkina Faso, then the regional-urbanicity model would be recommended, as it maximizes the proportion of trips reasonably estimated for most trip types. If specifically considering trips between predominantly rural and urban locations in a sparsely populated country with a few predominantly urban districts, like Namibia, then the regional model would provide the best estimates in these settings. Alternatively, if a country is more homogeneously populated, like Kenya, the radiation model may provide the best estimates for most specific trip types. If data are limited or unavailable, then the parameters fit to these four exemplar countries may serve as a proxy.

Moving forward, the need to select a single model could be mitigated and estimates of mobility patterns could be improved by developing an ensemble model. Recently, an ensemble model outperformed individual models in estimating human mobility patterns in Australia, combining different mobility models as well as data types to optimize mobility estimates across different spatial scales (McCulloch et al., 2021). Using this approach, additional individual level information (e.g., gender, age, occupation) collected from other data sources could be incorporated to study their impact on model fit. Future work could also evaluate the models tested here in other countries, both within and outside of Sub-Saharan Africa. Model estimates of travel patterns in high-income countries may also benefit from accounting for urbanicity and regionality (Truscott and Ferguson, 2012; Xia et al., 2004). The increasing availability of mobility data has enabled the comparison of global human mobility patterns and revealed that (a) longer distance trip ( > 20 km) patterns are similar across low- and high-income settings (Kraemer et al., 2020) and (b) that mobility patterns in rural (sparsely populated) areas differ from those in urban (densely populated) areas (Liu et al., 2015). This suggests that our findings based on trips aggregated to the region or district level will be generalizable to other countries from a range of income settings. However, mobility patterns at smaller spatial scales appear to be different for low- and high-income settings (Kraemer et al., 2020), and requires further investigation.

There are a number of caveats to be noted in this study. Mobile phone data has inherent owner, user, and coverage biases, especially in LMICs where mobility data tend to be concentrated around urban areas and roads (Kraemer et al., 2020; Wesolowski et al., 2013). Furthermore, the dataset from Burkina Faso was limited to 100,000 randomly selected subscribers (1.4% of Burkina Faso’s Telecel Faso subscribers). This smaller sample size may have resulted in the models overestimating routes that were missed in the actual dataset due to relatively small trip counts. Regardless, mobile phone data remain one of the most direct ways to gather information on a large population in LMICs. Alternative human mobility data sources that have recently become more available, such as Google Mobility or Facebook Data for Good (Kissler et al., 2020; Ojal, 2020), could verify these observations in future studies; however, smart phones are also associated with ownership biases and are currently less pervasive than general mobile phone ownership (GSM Association, 2020). It should be noted that models parameterized by different mobility data sources have produced different outcomes (Panigutti et al., 2017). Thus, the generalizability of the results ascertained from these four LMICs should continue to be evaluated and expanded upon as more mobility datasets from other settings become available. Similarly, the ability of other spatial interaction models to better estimate human mobility should be explored. We opted to focus on the gravity model because it has been the most commonly used spatial interactions model; however, one of its shortfalls is that it does not address the competition or synergism that often occurs between potential destinations (Bjørnstad et al., 2019). While this is addressed by the radiation model, the degree to which accounting for region and urbanicity can improve its estimates remains to be considered in the future (Bjørnstad et al., 2019). Another shortfall of the gravity and radiation models is their inability to capture the temporally dynamic nature of human mobility. Here, we focused on one definition and measurement of human mobility patterns; however, seasonal mobility patterns, such as those driven by seasonal work or societal factors (Buckee et al., 2017; Wesolowski et al., 2015a), and irregular migration, such as those driven by political or natural crises and environmental changes (International Organization for Migration, 2019), are ubiquitous. Mobile phone data could also be used to quantify these movements and improve estimates of population distribution and movement over time (Facebook data for good, 2021; Finger et al., 2016; Wesolowski et al., 2015a). Finally, the modifiable areal unit problem (MAUP) is a source of bias in the spatial distribution and aggregation of both CDRs (and other movement data) and population that impacts the results of models dependent on these inputs (Fotheringham and Wong, 2016). Although the general trends in model fits were preserved across a range of administrative levels, the generalization of the results to movement aggregated at finer spatial scales or for different geographical boundaries remains to be determined.

Ultimately, gaining a more complete understanding of travel in diverse geographies will help inform applications in the health, economic, social, and transportation sciences. While incorporating urbanicity and region did improve the gravity model fit to various degrees for different countries, this study highlights the need to continue honing a model framework that can better capture mobility patterns and behavioral nuances in LMICs.

Due to data sharing agreements with the mobile phone companies, the call data records used in this study are not directly available. However, the Burkina Faso data sharing agreement allows for a jittered dataset of monthly aggregated trips between administrative 2 units, which can be found on Dryad as "Burkina Faso mobility data with some noise" (https://doi.org/10.5061/dryad.fn2z34tt6). A different form of the datasets from Kenya and Namibia that were negotiated in a prior negation are available as supplements of (Ruktanonchai et al., 2016) and (Wesolowski et al., 2015b). Individuals interested in the dataset from Zambia may contact the authors with requests. The code used to analyze the mobile phone data and run the models can be found on github at https://github.com/hrmeredith12/Rural-mobility-models.git (copy archived at https://archive.softwareheritage.org/swh:1:rev:cfc77221c574dad23c3204cd6c5d5fadcb1ce385).

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Acceptance summary:

This paper presents a comparison of several mathematical models of human mobility in low and middle income settings, fitted to mobile phone usage data. This article is of particular interest to researchers within the field of human mobility studies, in addition it is also of potential interest to a broader audience with interests in the application of human movement patterns such as the spread of infectious diseases, health service access and utilization, logistics and more.

Decision letter after peer review:

Thank you for submitting your article "Characterizing human mobility patterns in rural settings of Sub-Saharan Africa" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, including Jennifer Flegg as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Aleksandra Walczak as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Francois Rerolle (Reviewer #3).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

1) Is there data across more countries in Africa? If so, it would be great to see the applicability of the recommendations of models to similar settings.

2) Can the authors be clearer about how they select which model was most appropriate for different contexts eg the interplay between model fit and model complexity?

3) Can the authors comment on the likely suitability of the recommendations outside of Africa?

4) Why were only 1.4% of randomly selected subscribers from the Burkina Faso provider included? Was this the only data provided to authors or was this the percentage of subscribers left once the authors excluded local movement within the district?

5) Line 138 of the manuscript reads "By comparing and evaluating a wide range of models…" This statement is too broad and potentially misleading given that all models (except the radiation model) utilised in this study are variations of the gravity model.

6) Have the authors considered deriving an ensemble model as part of their future work? If they were to pursue this idea, it would be interesting to see the results from other interaction models first such as an intervening opportunities model.

7) It would also be great to see something similar done for LMICs on a different continent, although I note this is beyond the scope of the current manuscript.

8) Given the differences in time frame for call data records (provided in the supporting information) used for each country, this should be discussed in the Materials and methods section of the manuscript.

9) The rationale behind the choice of the target interval of 0.5-2 times the observed trip counts determined to be appropriate for the percentage of estimated trips should be included.

10) From the title, I was expecting a bit more description/characterization of what the human travel looks like on these settings. I believe the article needs to describe the overall patterns of human mobility highlighted in the data collected rather than focus too much on model performance. How many trips are there per inhabitants per year? How much does it depend on distance (simple interpretation of decay function: trips decreased by X% every 100km or something like that), population density (there are Y times as many trips to urban areas compared to rural areas). And how it varied across the 3 countries.

11) The analysis ends up suggesting a variation of basic models with more parameters, adapted to the rural settings of sub-saharan Africa. Shouldn't the introduction provide more background on the performances of the basic models and their more parametrized variations in settings where they have been developed (high-income countries)? One would expect the basic model not to perform as well across all mobility settings of high-income countries. Similar adjustment for regionality and urbanicity may be needed (and previously evaluated) in more studied settings of rural America for instance?

12) Figure 1 J-L: For those type of plots, it would be worth spending a sentence or two to describe interpretations. For the axis, I know there is a reference to supplementary materials but it took me a while to understand that these were just numbered locations? Same comment with respect to the coloring, what proportion is that referencing to? Within a destination? Overall? Why categorize the coloring and not use a continuous nuanced color palette? Breaking by log values seems arbitral and the bluest categories contains a very wide range of proportion (0.1 to 1). Also, have you considered sorting the locations by population density? It might convincingly demonstrate the limitations of the basic model.

13) The introduction mentions other studies in LMIC that have adjusted basic models with individual levels factors such as education, SES, gender,etc and improved the fit. In this study, the authors propose a different and higher-level type of adjustment (regionality and urbanicity of trips' origin/destination). Are the authors also able to adjust for those individual level factors or are they absent from the mobile phone data? The comparison with previous work and improvements suggested in the article would be more convincing if both type of adjustment are done and combined on the same datasets. Otherwise we can't really compare the 2 approaches and advocate in favor of one or the other, can we?

14) Stratifying models by features (urbanicity and regionality) limits generalizability to other settings important features and/or where cut points (e.g, between rural and urban) may need to be different. Thanks to Bayesian analysis, have the authors considered modeling parameters of the gravity models as continuous functions of population density instead? Although it would decrease interpretability of the results, it would improve generalizability of the work and potentially result in significant fit improvements.

15) The authors compare models' performance based on % change in DIC. I am not as familiar with DIC, but I thought absolute changes (for AIC) were more relevant. Can the authors please clarify?

16) Lines 275: The selected interval (1/2; 2) seems both arbitral and pretty wide. Could the authors elaborate a bit more on it?

17) Figure 3B: Out of the gravity models, the bell curve for the basic model seems to be the closest to the 1:1 ratio except for the rural-rural trips. Doesn't this mean it is well performing?

18) At first, it is a bit confusing to use similar notation for functions used in the equations to denote exponential/power decay f() and stratification of parameters f(all trips), f(urbanicity),…. Can the authors please revise the notation?

Essential revisions:

1) Is there data across more countries in Africa? If so, it would be great to see the applicability of the recommendations of models to similar settings.

While the manuscript was under review, we gained access to a new mobile phone dataset from Zambia. We have updated the analysis to include this additional country. While data sharing was not part of the original agreement we have with the regulator, we are working with them to make some of the aggregated data available. In the meantime, individuals may contact us with data requests.

One of the biggest limitations of mobile phone data is its accessibility, and we are unable to include data from more countries across Africa at this time. A few data sets, including those from Senegal (https://doi.org/10.4081/gh.2016.408) and Cote d’Ivoire (https://doi.org/10.1038/srep02923), have been published, we did not currently have access to these data for this work.

2) Can the authors be clearer about how they select which model was most appropriate for different contexts eg the interplay between model fit and model complexity?

The model that best predicted all trips was selected based on the Deviance Information Criterion (DIC). This criterion incorporates the trade-off between model fit and model complexity. We have updated the text to provide a clearer description of what the DIC is and how it should be interpreted:

“Models were compared using the Deviance Information Criterion (DIC), a criterion designed for MCMC outputs that assesses a model’s trade-off between goodness of fit and complexity (Shriner and Yi, 2009; Spiegelhalter et al., 2002). Models fit to the same datasets (e.g., from the same country) were compared and those with the lowest DIC were selected as the best model.” (Lines 309-312)

The DIC is best for assessing how well the model fit the entire dataset, not specific trip contexts (e.g., Rural-rural or inter-regional). To evaluate a model in a specific context, we focused on predictive accuracy. Oftentimes metrics such as mean squared error are used to assess model accuracy. However, we wanted to be able to better illustrate not just the accuracy of the estimate, but also if these estimates were likely to be over- or under- estimated for a particular trip. Thus, we used the ratio of modeled:observed trips to evaluate model accuracy for each origin-destination pair. (Lines 312-316)

3) Can the authors comment on the likely suitability of the recommendations outside of Africa?

While this remains to be studied, we surmise that our findings will likely apply to similar settings outside of Africa. Differences geographically and more urban settings (as opposed to many settings in Sub-Saharan Africa) may change which model is the best fitting, however we believe this approach could be used more generally to investigate mobility models. We have incorporated this point in the discussion.

“Future work could also evaluate the models tested here in other countries, both within and outside of Sub-Saharan Africa. The increasing availability of mobility data has enabled the comparison of global human mobility patterns and revealed that (a) longer distance trip (> 20 km) patterns are similar across low- and high-income settings (Kraemer et al., 2020) and (b) that mobility patterns in rural (sparsely populated) areas differ from those in urban (densely populated) areas (Liu et al., 2015). This suggests that our findings based on trips aggregated to the region or district level will be generalizable to other countries from a range of income settings. However, mobility patterns at smaller spatial scales appear to be different for low- and high-income settings (Kraemer et al., 2020), and requires further investigation.” (Lines 177-186)

4) Why were only 1.4% of randomly selected subscribers from the Burkina Faso provider included? Was this the only data provided to authors or was this the percentage of subscribers left once the authors excluded local movement within the district?

Telecel only provided a subset of their subscribers for analysis. We have clarified the methods to better reflect this limitation.

“The Burkina Faso provider shared CDRs from a subset of randomly selected subscribers (100,000, ~1.4% of subscribers), as opposed to the other countries’ providers that shared CDRs from all of their subscribers” (Lines 237-239)

5) Line 138 of the manuscript reads "By comparing and evaluating a wide range of models…" This statement is too broad and potentially misleading given that all models (except the radiation model) utilised in this study are variations of the gravity model.

We have updated the statement to: “By comparing and evaluating a range of gravity models…” (Line 155)

6) Have the authors considered deriving an ensemble model as part of their future work? If they were to pursue this idea, it would be interesting to see the results from other interaction models first such as an intervening opportunities model.

The reviewer makes a good point. An ensemble model would be an interesting approach to explore in future studies. A recent study has shown that an ensemble model has improved estimates of mobility patterns in Australia. We have included this point in the discussion:

“Moving forward, the need to select a single model could be mitigated and estimates of mobility patterns could be improved by developing an ensemble model. Recently, an ensemble model outperformed individual models in estimating human mobility patterns in Australia, combining different mobility models as well as data types to optimize mobility estimates across different spatial scales (McCulloch et al., 2021).” (Lines 172-175)

7) It would also be great to see something similar done for LMICs on a different continent, although I note this is beyond the scope of the current manuscript.

We thank the reviewer for the suggestion. Indeed, this would be interesting, but is outside the scope of this study. We have addressed this in our response to comment #3 above and are also making our code available on github to facilitate testing datasets from other settings.

8) Given the differences in time frame for call data records (provided in the supporting information) used for each country, this should be discussed in the Materials and methods section of the manuscript.

We have updated the methods section to include the time frames for the CDRs:

“The duration of and year(s) covered by the CDR datasets varied by country, defined by relevant data sharing agreements: Namibia’s ran October 2, 2010 – April 30, 2014; Kenya’s ran June 1, 2008 – July 3, 2009 (excluding the month of February, 2009); Burkina Faso’s ran January 1, 2016 – December 31, 2016; and Zambia’s ran August 1, 2020 – December 30, 2020.” (Lines 239-242)

9) The rationale behind the choice of the target interval of 0.5-2 times the observed trip counts determined to be appropriate for the percentage of estimated trips should be included.

To assess the accuracy of each model’s estimates, we considered how much each model over- or under-estimated trips of a given category. Given that the ratio of predicted to observed trip counts ranged orders of magnitude (1E-03 to 1E+06), we selected an interval that would represent a reasonable degree of over/under-estimation. In response to a comment below, we have reduced the target interval to be ± 10% the observed trip counts.

“To determine the distribution of trips that were over- or under-estimated for a given model, the ratio of estimated to observed trip counts for each route was calculated. Given that the distribution of ratios ranged nine orders of magnitude, the general accuracy of model estimates for specific trip types was evaluated by comparing the proportion of trips with model estimates that fell within ±10% of the observed trips.” (Lines 312-316)

10) From the title, I was expecting a bit more description/characterization of what the human travel looks like on these settings. I believe the article needs to describe the overall patterns of human mobility highlighted in the data collected rather than focus too much on model performance. How many trips are there per inhabitants per year? How much does it depend on distance (simple interpretation of decay function: trips decreased by X% every 100km or something like that), population density (there are Y times as many trips to urban areas compared to rural areas). And how it varied across the 3 countries.

We thank the reviewer for the suggestion. While the call data records are aggregated spatially such that individual level trends cannot be analyzed, we have expanded upon the population level description of the trips. For instance, the distribution of trips between rural and/or urban locations and within or between regions differed for each country.

“Trips were concentrated between districts within the same region (administrative level 1) to varying degrees (30% in Burkina Faso, 45% in Kenya, 62% in Namibia, and 72% in Zambia-62% of trips, depending on the country) and to a few common destinations, including the district where the capital was located (Figure 1JI-L, Supplementary file 1A). Although Namibia, Burkina Faso, and Zambia each consisted of ~95% predominantly rural districts, the distribution of monthly trips between urban and rural districts varied across countries. The majority of Namibia’s and Burkina Faso’s trips were between rural locations (62% and 70.5% of all trips, respectively), while Zambia’s trips were split between rural locations (53%) or rural and urban locations (46%). Kenya, with 56% predominantly urban districts, had the largest proportion of monthly trips between urban locations (70%).” (Lines 94-102)

11) The analysis ends up suggesting a variation of basic models with more parameters, adapted to the rural settings of sub-saharan Africa. Shouldn't the introduction provide more background on the performances of the basic models and their more parametrized variations in settings where they have been developed (high-income countries)? One would expect the basic model not to perform as well across all mobility settings of high-income countries. Similar adjustment for regionality and urbanicity may be needed (and previously evaluated) in more studied settings of rural America for instance?

We thank the reviewers for the chance to provide more background on how the gravity model performs in high income settings. We have updated the introduction with the following:

“In high income settings, the standard gravity model has been shown to perform well when predicting commuter movement between cities (Masucci et al., 2013) and perform poorly when predicting movement across areas with heterogeneity in demographics and population density or in rural areas (Truscott and Ferguson, 2012; Xia et al., 2004).” (Lines 57-60)

We have also mentioned in the discussion that these model adjustments may also help improve trip estimates in high income countries.

“Model estimates of travel patterns in high income countries may also benefit from accounting for urbanicity and regionality (Truscott and Ferguson, 2012; Xia et al., 2004).” (Lines 178-180)

12) Figure 1 J-L: For those type of plots, it would be worth spending a sentence or two to describe interpretations. For the axis, I know there is a reference to supplementary materials but it took me a while to understand that these were just numbered locations? Same comment with respect to the coloring, what proportion is that referencing to? Within a destination? Overall? Why categorize the coloring and not use a continuous nuanced color palette? Breaking by log values seems arbitral and the bluest categories contains a very wide range of proportion (0.1 to 1). Also, have you considered sorting the locations by population density? It might convincingly demonstrate the limitations of the basic model.

We thank the reviewers for the opportunity to clarify the OD matrices. We have updated the legend to further explain the coloring scheme and axis tics.

“The columns and rows of the OD matrix are ordered by district ID, the order of which is typically assigned by shapefiles or mobile phone operators. The capital district is indicated by the black arrow on the x- and y-axes. The colors indicate the proportion of an origin’s trips made to each destination (with light blue representing destinations visited infrequently and dark blue representing destinations visited most frequently). ” (Figure 1 caption, Lines 365-369)

The trip colors were categorized into bins to help better visualize patterns. Relatively few destinations made up > 10% of an origin’s trips, which is lost when using a continuous color scale. We also believe it is easier to interpret the plot with fewer colors (e.g., uncommon destination: < 0. 1% of all trips <-> common destination: 10-100% of all trips)

We considered sorting by urbanicity (a proxy for density; Author response image 1 middle panel) and population size (right panel); however, the clearest trends were observed when sorting by district ID (left).

Author response image 1

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13) The introduction mentions other studies in LMIC that have adjusted basic models with individual levels factors such as education, SES, gender,etc and improved the fit. In this study, the authors propose a different and higher-level type of adjustment (regionality and urbanicity of trips' origin/destination). Are the authors also able to adjust for those individual level factors or are they absent from the mobile phone data? The comparison with previous work and improvements suggested in the article would be more convincing if both type of adjustment are done and combined on the same datasets. Otherwise we can't really compare the 2 approaches and advocate in favor of one or the other, can we?

While it would be interesting to see how accounting for urbanicity and regionality impacts the fit of models with individual level factors, our datasets were de-identified by the mobile phone operators and aggregated to a spatial and temporal level such that we could not analyze individual level factors. To investigate this in the future, perhaps different datasets, such as travel surveys, census data, or data collected from mobile phone apps, could be incorporated into an ensemble model. We have incorporated this into the discussion:

“Using this approach, additional individual level information (e.g., gender, age, occupation) collected from other data sources could be incorporated to study their impact on model fit.” (Lines 175-177)

14) Stratifying models by features (urbanicity and regionality) limits generalizability to other settings important features and/or where cut points (e.g, between rural and urban) may need to be different. Thanks to Bayesian analysis, have the authors considered odelling parameters of the gravity models as continuous functions of population density instead? Although it would decrease interpretability of the results, it would improve generalizability of the work and potentially result in significant fit improvements.

We appreciate the reviewer’s suggestion to make the models more generalizable. Population density can be approximated by urbanicity (proportion of the administrative unit that falls within a region with a population density above a standard/generalizable threshold established by WorldPop). As a test, we considered fitting the parameters as functions of population density for Namibia, however the model fit was not significantly improved (see Author response table 1). Furthermore, fitting by population density/urbanicity did not allow for the parameters to vary as much as the regional-urbanicity model, making the model less flexible. As such, we decided not to run this model variation for the other countries and did not include it in the manuscript.

15) The authors compare models' performance based on % change in DIC. I am not as familiar with DIC, but I thought absolute changes (for AIC) were more relevant. Can the authors please clarify?

Both the AIC and DIC aim at balancing goodness of model fit to data and model complexity and are used in the same way to compare and select “best” models. The difference is that the DIC estimates model complexity as a function of the posterior in a Bayesian setup, whereas the AIC is computed as a function of the maximum likelihood estimate. Thus, calculating the AIC is more appropriate for approaches based on maximum likelihood whereas the DIC is more appropriate for approaches based on MCMC. In response to reviewer comment #2, we have expanded the text to clarify our choice of DIC for model selection and how it should be interpreted.

16) Lines 275: The selected interval (1/2; 2) seems both arbitral and pretty wide. Could the authors elaborate a bit more on it?

We thank the reviewer for their comment. We have reduced the selected interval to ± 10% the observed trip counts and have further elaborated on its selection. Please see our full response answer to the similar question/comment (#9) above.

17) Figure 3B: Out of the gravity models, the bell curve for the basic model seems to be the closest to the 1:1 ratio except for the rural-rural trips. Doesn't this mean it is well performing?

The reviewer’s interpretation is correct – the closer the distribution’s mean is to 1 and the tighter the spread, the better that model is at predicting those trips. However, in Figure 3B, the only trip type the Basic Model is best at predicting is the Urban-Urban trips. For Rural-Urban and Urban-Rural trips, the Regional model’s mean was closer to 1 than the Basic model’s. For Rural-Rural trips, the Radiation model’s mean was closer to 1 than the Basic model’s. We have changed the lines indicating the 1:1 ratio as well as the boundaries of the selected interval (now white) to be more distinguishable from the line of the mean ratio (black).

18) At first, it is a bit confusing to use similar notation for functions used in the equations to denote exponential/power decay f() and stratification of parameters f(all trips), f(urbanicity),…. Can the authors please revise the notation?

The notation has been revised to the following (see Lines 272-278):${\displaystyle {\hat{T}}_{i,j}=\theta \frac{P_i^{{\alpha }_k}{P}_j^{{\beta }_k}}{d_{i,j}^{{\gamma }_k}}\{\begin{array}{c}k=1\text{if urbanicit}{y}_i=rural\text{AND}{\text{urbanicity}}_j=\text{rural }\\ k=2\text{if}\text{urbanicit}{y}_i=rural\text{AND}{\text{urbanicity}}_j=\text{urban}\\ k=3\text{if}\text{urbanicit}{y}_i=urban\text{AND}{\text{urbanicity}}_j=\text{rural}\\ k=4\text{if}\text{urbanicit}{y}_i=urban\text{AND}{\text{urbanicity}}_j=\text{urban}\end{array}}$

Author details

1. Hannah R Meredith

   Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, United States

   Contribution

   Conceptualization, Formal analysis, Investigation, Methodology, Writing - original draft, Writing – review and editing

   For correspondence

   hmeredi4@jhu.edu

   Competing interests

   none

   "This ORCID iD identifies the author of this article:" 0000-0002-5315-7568

2. John R Giles

   Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, United States

   Contribution

   Software, Writing – review and editing

   Competing interests

   none

3. Javier Perez-Saez

   Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, United States

   Contribution

   Data curation, Validation, Writing – review and editing

   Competing interests

   none

4. Théophile Mande

   Bureau d'Etudes Scientifiques et Techniques - Eau, Energie, Environnement (BEST-3E), Ouagadougou, Burkina Faso

   Contribution

   Resources

   Competing interests

   none

5. Andrea Rinaldo

   1. Dipartimento di Ingegneria Civile Edile ed Ambientale, Università di Padova, Padova, Italy
   2. Laboratory of Ecohydrology, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

   Contribution

   Data curation, Funding acquisition, Resources, Writing – review and editing

   Competing interests

   none

6. Simon Mutembo

   1. Department of International Health, International Vaccine Access Center, Johns Hopkins Bloomberg School of Public Health, Baltimore, United States
   2. Macha Research Trust, Choma, Zambia

   Contribution

   Data curation

   Competing interests

   none

7. Elliot N Kabalo

   Zambia Information and Communications Technology Authority, Lusaka, Zambia

   Contribution

   Data curation

   Competing interests

   none

8. Kabondo Makungo

   Zamtel, Lusaka, Zambia

   Contribution

   Data curation

   Competing interests

   none

9. Caroline O Buckee

   Department of Epidemiology and the Center for Communicable Disease Dynamics, Harvard TH Chan School of Public Health, Boston, United States

   Contribution

   Resources

   Competing interests

   None

   "This ORCID iD identifies the author of this article:" 0000-0002-8386-5899

10. Andrew J Tatem

    WorldPop, School of Geography and Environmental Science, University of Southampton, Southampton, United Kingdom

    Contribution

    Resources, Writing – review and editing

    Competing interests

    none

11. C Jessica E Metcalf

    Department of Ecology and Evolutionary Biology and the Princeton School of Public and International Affairs, Princeton University, Princeton, United States

    Contribution

    Resources, Writing – review and editing

    Competing interests

    none

    "This ORCID iD identifies the author of this article:" 0000-0003-3166-7521

12. Amy Wesolowski

    Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, United States

    Contribution

    Conceptualization, Data curation, Funding acquisition, Resources, Supervision, Writing – review and editing

    For correspondence

    awesolowski@jhu.edu

    Competing interests

    Reviewing editor, eLife

    "This ORCID iD identifies the author of this article:" 0000-0001-6320-3575

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