Quantifying seasonal population fluxes driving rubella transmission dynamics using mobile phone data

Significance

Changing patterns of human mobility can drive seasonal outbreaks of infectious diseases, but limited data about travel behavior and population flux over time have made this idea difficult to quantify. Mobile phone data provide a unique source of information about human travel. Here we quantify seasonal travel patterns using mobile phone data from nearly 15 million anonymous subscribers in Kenya. Using a rich data source of rubella incidence, we show that patterns of population fluxes inferred from mobile phone data are predictive of disease transmission and improve significantly on standard school term time and weather covariates, showing for the first time to our knowledge that mobile phone data capture epidemiologically relevant patterns of movement.

Abstract

Changing patterns of human aggregation are thought to drive annual and multiannual outbreaks of infectious diseases, but the paucity of data about travel behavior and population flux over time has made this idea difficult to test quantitatively. Current measures of human mobility, especially in low-income settings, are often static, relying on approximate travel times, road networks, or cross-sectional surveys. Mobile phone data provide a unique source of information about human travel, but the power of these data to describe epidemiologically relevant changes in population density remains unclear. Here we quantify seasonal travel patterns using mobile phone data from nearly 15 million anonymous subscribers in Kenya. Using a rich data source of rubella incidence, we show that patterns of population travel (fluxes) inferred from mobile phone data are predictive of disease transmission and improve significantly on standard school term time and weather covariates. Further, combining seasonal and spatial data on travel from mobile phone data allows us to characterize seasonal fluctuations in risk across Kenya and produce dynamic importation risk maps for rubella. Mobile phone data therefore offer a valuable previously unidentified source of data for measuring key drivers of seasonal epidemics.

Seasonal variation in infectious disease incidence is a ubiquitous phenomenon observed for a range of pathogens such as malaria, measles, and influenza (1–7). Understanding and quantifying key mechanisms that drive seasonal variability such as climatic conditions (malaria and influenza) or patterns of human aggregation (measles and influenza) contribute to our fundamental understanding of epidemic dynamics; they also have important implications for evaluating public health measures that may reduce transmission such as vaccination and school closures (8–11).

The effectiveness of any public health measure designed to reduce seasonal transmission by modifying patterns of human aggregation and travel will depend on the degree to which transmission depends on population density and movement. Direct measures of population travel are rare (2, 4, 12, 13). As a result, proxy measures such as school terms and rainfall patterns have been used (1, 9, 13–15). Term time forcing, where school-driven aggregation leads to seasonal peaks of transmission for directly transmitted immunizing infections such as measles, mumps, and rubella, has been observed in many high-income countries (8, 16, 17) [England and Wales (8), Peru (15), and Denmark (17)]. On the other end of the spectrum in the low-income, predominantly agricultural context of Niger (13), analysis of night lights indicates that peaks in transmission reflect population changes resulting from annual mass migrations of individuals between agricultural areas to cities in the dry season (1). School terms and holidays versus agricultural movements likely represent the extremes in terms of density-related drivers of transmission in high- and low-income settings, respectively. Identifying where other low-income countries lie along this continuum will be important in order to plan public health measures and understand the dynamics of these infectious diseases.

Recently, the ubiquity of mobile phone ownership and use, particularly in low-income settings, has produced vast datasets on the individual movement patterns of millions of people (18–20). These data represent a potentially valuable previously unidentified resource for the direct observation of seasonal population dynamics on refined spatial scales that underlie disease transmission. Unlike other static measures of travel such as road networks, small-scale surveys, travel time surfaces, or census data, mobile phone data can provide a dynamic picture of mobility and population travel and changes over large geographic scales (1, 5, 12, 13, 21). However, their relevance to infectious disease dynamics has yet to be formally assessed, requiring parallel longitudinal estimates of phone use and transmission rates (19). For example, although we have previously estimated the rate of malaria importation across Kenya using spatially stratified prevalence estimates in combination with mobile phone data (20), because these estimates were static, the interaction between temporal dynamics in human mobility and malaria incidence was impossible to assess.

Here we analyze anonymous mobile phone call records including the location of the routing tower and timing of each call and short message service (SMS) communication between 14,816,512 subscribers during June 2008 to June 2009 (with February 2009 missing from the dataset) to quantify daily travel patterns (referred to as population fluxes) between provinces (Materials and Methods and Supporting Information). We combine this with a long-term and highly detailed dataset on rubella incidence to measure how key drivers of human aggregation are associated with disease transmission in this setting.

Results

Transmission and Mobile Phone-Derived Population Fluxes.

Unlike the classical two-peak seasonal pattern of many immunizing childhood infections, including rubella (e.g., in Peru, Mexico, Japan, South Africa, and Canada), rubella in Kenya exhibits three peaks of incidence each year (Fig. 1 A and B and Figs. S1 and S2) (15, 22–25). Similar patterns have been reported in other countries in East Africa, suggesting regional consistency (26). In the majority of provinces, transmission peaks in September and February (except Northeastern province, where inference is weak given paucity of data; Fig. S1). Epidemiological mechanisms driving this within-year triple peak in incidence are the occurrence of three yearly troughs in transmission (Fig. 1C) and the relatively low R₀ of this infection (Materials and Methods and Supporting Information).

Fig. 1.

The rubella patterns in Kenya. (A) Over the course of the rubella dataset (January 2008 to January 2012), the biweekly number of reported rubella cases is shown. (B) A map of Kenya with provinces outlined in red along with the rubella case data per province. (C) The monthly transmission (beta) estimates per province. In the majority of provinces, there are two pronounced peaks in transmission during September and January–March with a number of locations also peaking in May–June (see Central province in red, for example). The peaks in transmission varied geographically with the Nyanza province peaking in February, for example.

Fig. S1.

The trajectory estimates for each province. Simulations correspond to trajectory matches for each of the eight provinces; seasonality is as shown in Fig. 1C. Other parameters estimated include starting number of infected individuals (ranges from 155 to 3,215), starting proportion susceptible (0.18–30%), and reporting rate (7e-5 to 9e-4).

Fig. S2.

A simulated seasonal trajectory of incidence per province. Simulations correspond to underlying seasonality in transmission to that observed for rubella in Kenya but with the transmission rate set to 30 in every month to reflect more measles-like dynamics. Multiannual peaks in every year disappear, replaced by annual dynamics, in line with what has been observed for measles in an array of different contexts.

To measure the ecological and spatial mechanisms contributing to the three troughs in transmission, we turned to both previous proxy measures of movement and a previously unidentified measure extracted from anonymized mobile phone data. For the latter case, we constructed a daily location for each subscriber and calculated the number of trips from all subscribers between provinces (eight total provinces) per day (Materials and Methods, Fig. 2A, Supporting Information, and Fig. S3) (20). These subscriber locational time series were aggregated to create a province-level daily population flux that described the number of journeys originating from each province per day. This province-level time series was decomposed using a moving average, and the trend was analyzed (Materials and Methods and Supporting Information).

Fig. 2.

The relationship between population flux, rainfall, school terms, and rubella transmission per province. (A) The normalized population fluxes measured from the mobile phone data per month in each province with months ordered from the start of the dataset (June) until the following May. In nearly all provinces, travel peaked in December and July/August, although this varied by location. (B) Monthly mean values from provinces for transmission and the three covariates (rainfall, school terms, and population flux). The time series is shown highlighting the variability in these estimates over the course of the year. We would expect that transmission would decrease during school breaks (white area) and population fluxes would increase during these times (white area). (C) Using the province level covariates shown in B, we constructed a number of models using various subsets of the covariates to predict transmission values. The estimated (from the TSIR model) versus predicted values for transmission (to aid with comparison a black xy line is drawn) from the minimum adequate model (black, includes population flux and school terms as covariates) and a model based on only school terms (red) or rainfall (blue). The model based on movement and school terms (adjusted R² = 0.19, P < 0.001) provides the best estimates (only rainfall, adjusted R² = 0.03, P = 0.056; only school terms, adjusted R² = 0.09, P = 0.003). In comparison, the model based only on school terms only produces two transmission values, whereas the model based only on rainfall produces estimates over a smaller range than the model including population flux.

Fig. S3.

The population flux values for each province and relationship with rainfall and rubella transmission. (A) For each province, the population flux values over the course of a year. (B) The correlation between population fluxes with school terms and rainfall per province. Each province is colored according to the population density. School terms were negatively correlated with population fluxes, implying that there was more travel during school holidays (see main text). The relationship between rainfall and population fluxes was less clear with a number of provinces positively correlated.

As has been found in high-income settings, but in contrast to other African countries, rubella transmission was strongly positively related to school term times (t test, t = −3.6681, df = 80.505, P < 1e-3 for provinces excluding the Northeastern province where power for analysis was weak); transmission was not significantly correlated with rainfall (mean correlation coefficient, −0.13; 95% quantile interval, −0.34, 0.07, P > 0.2, excluding the Northeastern province; Fig. S3 and Table S1) (1, 13, 27, 28). There was also a strong positive relationship with province-level population flux in the previous month normalized for each province (mean correlation coefficient, 0.38; 95% quantile interval, 0.18, 0.55, P < 1e-3, excluding the Northeastern province). We further analyzed the relationship between these variables for districts (68 districts in Kenya), and although there exists heterogeneity between locations, we found the same broad general relationships (Fig. S4).

Table S1.

Relationship between population flux, rainfall, school terms, and rubella

Variables	Expected rel. with rubella transmission	General pattern	Rel. with population flux in the previous month	Rel. with rainfall	Rel. with school terms	Rel. with rubella
Population flux	Transmission increased with large population flux in the previous month	Large peak in December, smaller peaks in April and August		Positive in most provinces	Negative	Negative
Rainfall	Transmission decreased by high rainfall in concurrent month	Peak rainfall in May	Positive in most provinces		Negative	Negative
School terms	Transmission increased during months corresponding to term times	Breaks in April, August, and December	Negative	Negative		Negative
Rubella		Peak in September; smaller peaks in February and June	Positive	Negative, not significant	Positive

Rel., relationship.

Fig. S4.

The relationship between population flux and covariates on the district level. (A and B) For each province, we compared the population flux trends for districts located in that province such as Central or Eastern provinces. (C) In general, district-level trends were similar to province-level trends, although this varied geographically. (D) The relationship between district-level population flux and school terms and rainfall.

To explore the relative importance of the three drivers, we fit all three (rainfall, school terms, and population flux; Fig. 2B) as main effects in a linear regression with seasonal transmission as the response variable (excluding the Northeastern province and taking the square root of the response variable to normalize the errors). Including population flux significantly improved the model (F_1,82 = 19.59, R² = 0.19, P < 0.001; Table S2 and Fig. 2C), and further including either rainfall (F_1,81 = 0.40, P > 0.5) or school terms (F_1,81 = 3.41, P > 0.05) did not significantly improve the model fit (see Supporting Information for models including site effects; results remain qualitatively the same). To highlight the improved ability of population fluxes to predict transmission we also constructed two comparison models using either only rainfall or only school terms (Fig. 2C; also see Tables S2 and S3 and Fig. S5); these two models explained considerably less of the variance, with adjusted R² values of adjusted R² = 0.03 (P = 0.056) and adjusted R² = 0.09 (P = 0.003), respectively.

Table S2.

Model coefficients and statistics using the minimum adequate model (school terms and population flux) as well as models only using population flux, school terms, or rainfall

Model components	Minimum adequate	Only population flux	Only school	Only rainfall
Coefficients
Intercept	2.25***	2.25***	1.85***	2.5***
Population flux	0.33***	0.33***	—	—
School	—	—	0.53**	—
Rainfall	—	—	—	−0.0026
Model statistics
Adjusted R-squared	0.190	0.18	0.092	0.032
F-statistic	19.23	19.23	9.37	3.77
df	82	82	82	82
P value	3.40E-05	3.42E-05	0.003	0.056

Linear regression models were fit using a range of dependent variables to predict transmission values per province. Overall, the minimum adequate model where population flux is the significant variable has the best model performance. **P < 0.05; ***P < 0.01.

Table S3.

Model coefficients and statistics using the minimum adequate model obtained when also accounting for site

Model components	Minimum adequate model
Coefficients
Intercept	2.22***
Population flux	0.33**
School	—
Rainfall	—
Site 2	−0.13
Site 3	−0.01
Site 4	−0.26
Site 6	0.64*
Site 7	−0.03
Site 8	0.005
Model statistics
Adjusted R-squared	0.32
F-statistic	5.24
df	76
P value	6.4E-05

Because considerable variation remained unexplained in the previous analysis, we repeated it including site as a main effect. Qualitative results remain the same, and overall, the minimum adequate model where population flux is the significant variable has the best model performance. *P < 0.1; **P < 0.05; ***P < 0.01.

Fig. S5.

The relationship between transmission and population flux. The normalized population flux in the previous month is compared with the transmission rate for each province. Points representing months during which school terms are occurring (filled points) and not (empty points) showing that the population flux data are able to describe more variability in population dynamics than the binary school term measure.

Population-Scale Consequences of Seasonal and Spatial Population Fluxes.

With evidence that the mobile phone data captures epidemiologically relevant human movements for rubella in Kenya, we next used the mobile phone data to construct maps to characterize spatial and temporal patterns of risk of rubella introduction based on population fluxes across the country on scales finer than possible using only the rubella data (Fig. 3). We recalculated the population flux per district (Materials and Methods) and analyzed these finer spatial data. We identified both areas at a high risk for rubella introductions and how these locations and assessment of risk varied over the year. As suggested in Fig. 1, areas most at risk vary over the course of the year, although Nairobi District and districts in the Central province remain at high risk throughout the year (Fig. 3). During school terms, the risk decreases across the entire country, although the most noticeable differences are in western Kenya, where the risk during school breaks is relatively much higher than during the term. Given the variability in the amount of risk and the location of these risks over the course the year, spatially and temporally targeted control will be essential to maintaining gains that follow introduction of vaccination.

Fig. 3.

The seasonal variability in the risk of importation. We analyzed the average amount of population flux per district during (A) the major holiday and a school term break (December) and (B) during a school term (March). As highlighted in Fig. 1, there are large amounts of population flux and consequently the risk of importation during school breaks (A and B). In contrast, there is a decrease in the risk of importation during the school term. During the course of the year, the districts with the largest risks vary with higher risks to western Kenya during school breaks. However, Nairobi (shown in red in both maps) consistently remains at a high risk of importation from the large population fluxes.

Discussion

Our analysis of population fluxes from mobile phone data and rubella transmission dynamics shows that mobile phone data may be used to capture seasonal human movement patterns relevant for understanding childhood infection dynamics and significantly outperform previous proxies used in this context (1, 13). This suggests that mobile phone-derived data may represent an improvement on broadly used qualitative correlates of temporal variations in transmission (schools terms, measured as “on” or “off”; Fig. S5) or suspected phenomenological drivers (rainfall, where the strength of the relationship is likely to be highly spatially variable).

The power of population fluxes quantified by mobile phone data to describe patterns of transmission linked to childhood infections is somewhat surprising because previous work suggests that mobile phone ownerships is concentrated in adults and toward urban, more educated males (29, 30). However, this supports previous evidence that children rarely travel without adults and also underscores the importance of these population-scale movements for dynamics of infections like rubella (31). Although mobile phone data are inherently biased by ownership, there exist few data sources that can directly record daily movement patterns over the range of spatial (the dynamics of an entire country) and temporal (12 months of data) scale. We also analyzed the role of birth seasonality on rubella dynamics and did not find a strong association between transmission and seasonal birth rates (Supporting Information and Fig. S6). Moreover, a detailed age-structured simulation confirms that the average age of infection for rubella in Kenya makes the effect of susceptible births on the dynamics negligible (Supporting Information) (32).

Fig. S6.

Seasonal fluctuations in births in Kenya. (A) For each month and each province, total numbers of births for children born after 1990 reported by mothers from the 2008–2009 Kenya DHS survey. (B) The correlation between seasonal birth fluctuations and other variables explored here, indicating few significant relationships. (C) Simulation of age structured dynamics of rubella in a Kenya-like population. The pattern of contact over age is set to reflect POLYMOD (37); seasonality in transmission reflects estimates from Nairobi (e.g., as in Fig. 1, with R₀ = 4) with constant annual births (yellow), births fluctuating according to magnitude estimates from the DHS survey in Nairobi (orange), and the same pattern but with the magnitude tripled (red); fluctuations in births are depicted in E. The average age of infection is 6 y, resulting in annual dynamics with the expected three peaks every year. (D) Associated TSIR estimates of seasonal fluctuations in transmission, showing little effect, as expected given the relatively high average age of infection (27).

Rubella incidence is frequently underreported, as a result of the mild, even asymptomatic manifestation of the infection (15). Evidence that mobile phone data can capture population fluctuations that relate to rubella transmission provides grounds for optimism that patterns of incidence might be inferred indirectly. This is relevant not only to projecting timing of outbreaks but also, if epidemiologically relevant movement can be measured, to predicting patterns of increased congenital rubella syndrome (CRS) incidence stemming from metapopulation dynamics [local extinction of rubella followed by aging of susceptibles into childbearing ages means that subsequent introduction of rubella can result in CRS cases (15)]. Because introduction of rubella-containing vaccine is increasingly being considered across low-income countries (33), this could be used to help guide targeted vaccination efforts spatially and also to infer effects of geographic heterogeneities in vaccination coverage on the CRS burden (22), although more work would need to be conducted to fully understand the relationship between mobility measured via mobile phones and the populations of interest. Many of the same principles that apply to rubella also apply to measles, which is of increasing relevance because all WHO regions currently have measles elimination targets. As we move toward elimination goals for measles or other vaccine-preventable infections, mobile phone data offers enormous potential for quantifying daily movement patterns at particular spatial scales, which will be important in order to maintain elimination gains by indicating key areas to target to minimize reintroductions and ongoing spread. The resolutions of these data are variable, however, so the utility of this approach will need to be considered separately for different policy questions. In particular, mobile phone data can primarily describe within-country movement patterns on a relatively large spatial scale and so will be less relevant for public health planning when either international travel has large effects on disease dynamics or transmission is highly spatially localized.

Seasonality is a characteristic feature of many pathogens (6), thereby driving the time of interventions (e.g., influenza vaccination and seasonal malaria chemoprophylaxis). For immunizing infections like rubella, interannual fluctuations in transmission can result in complex multiannual dynamics (34), which may affect the outcome of vaccination programs (13). For vector-borne diseases, seasonality can be influenced by both environmental and behavioral conditions, making determining optimal timing for interventions dependent on being able to quantify both of these factors. Using mobile phone data we can measure both broad seasonal patterns (country-wide dynamics) as well as the variability in seasonal travel on smaller spatial scales that are unobtainable from many existing datasets (see Supporting Information for district-level analysis). A major result of our analysis, that mobile phone data capture epidemiologically relevant movement, indicates that this approach represents a powerful tool for quantifying critical drivers of epidemics on epidemiologically relevant spatial and temporal scales. Further investigations to calibrate the relevance of this effect across a broad array of systems will be an important direction for future research.

Materials and Methods

Mobile Phone Data.

The leading mobile phone operator in Kenya provided anonymous mobile phone call records that recorded the location of the routing tower and timing of each call and SMS communication between 14,816,512 subscribers during June 2008 to June 2009 (with February 2009 missing from the dataset) (4, 18). In total, over 12 billion mobile phone communications were recorded, including the communication’s location at one of 11,920 routing towers. The operator that provided the call data records had ∼92% market share at the time of data acquisition. All subscriber data were aggregated to either the province- or district-level scale to further preserve anonymity. These data were deidentified at the mobile phone operator, contain no personal information, and are considered nonhuman subject research.

Quantifying Population Fluxes.

From the mobile phone data the geographic location of the caller and receiver was approximated based on the unique longitude and latitude coordinates for each mobile phone tower. Using the data, a location for each subscriber every time they either made or received a call (or SMS) was obtained. For each day in the dataset, subscribers were assigned a single tower location. If the subscriber made at least one call on that day, then the location of the majority routing tower was assigned. If the subscriber had not made a call on that day, then the location of their most recent routing tower was assigned. This provided a 12-mo time series of tower locations for each subscriber on each day. As in previous studies, trips are calculated by observing when a subscriber’s tower location has changed from the previous day (4, 20). For the majority of the analysis, we aggregated towers to the province level based on the tower’s location. Thus, only trips between towers in different provinces were considered. We constructed a time series of outgoing travel/population flux for each province (Fig. S3). Incoming and outgoing travel/population fluxes were highly corrected (Pearson’s correlation coefficient: 0.997, P < 0.001). We decomposed each time series using a moving average and then analyzed the resulting trend. Although mobile phone data ownership is biased toward urban, more educated males, we have previously shown that this does not significantly bias mobility estimates (29, 30). We also aggregated towers to the district level based on the tower’s location and recalculated these flux values for travel from each district to all other districts.

Population Data.

Estimates of population sizes and numbers of live births for 2009 were obtained from the WorldPop project (www.worldpop.org.uk) using the spatial datasets that were constructed using the methods outlined by Tatem et al. (35) and Linard et al. (5). In brief, 2009 census data at sublocation level were matched to the relevant administrative boundaries and then combined with satellite-derived settlement and land cover data layers to disaggregate the counts to 100-m spatial resolution. Five-year age and sex groupings of population at sublocation level from the census were then used to adjust the output gridded population surface to create a set of 5-y age grouped surfaces that covered all women in the age range 15–49 (women of childbearing age). Subnational urban–rural age-specific fertility rates derived from the most recent demographic and health survey for Kenya (www.dhsprogram.com) were then used to convert these age-structured female count datasets into surfaces of estimates of numbers of live births per grid square.

Rubella Data and Dynamics.

Concerns about increases in the burden of congenital rubella syndrome have meant that vaccination against rubella has yet to be introduced in many Sub-Saharan African countries including Kenya, and rubella remains prevalent. Using over 9 y of data on rubella cases (n = 5,590) from each Kenyan province (Fig. 1 A and B, Materials and Methods, Fig. S1, and Supporting Information), we quantified seasonal fluctuations of transmission via a time series susceptible–infected–recovered model fitted using trajectory matching with a binomial observation model for case reporting. Seasonal estimates of transmission are shown in Fig. 1C; corresponding matched trajectories are in Fig. S1.

Quantifying Seasonal Fluctuations in Transmission for Rubella.

Rubella is a completely immunizing infection with a generation time (serial interval; approximately the latent plus infectious period) of ∼18 d (36). We therefore assumed that the time scale of the epidemic process was approximately 2 wk. The number of infected individuals observed after a 2-wk period, I_t+1, depends on I_t and the number of susceptible individuals S_t with expectation λ_t = β_sS_tI_t^m/N_t, where β_s is the transmission rate in every biweek in any particular location and the exponent m, usually a little less than 1, captures heterogeneities in mixing not directly modeled by the seasonality (8) and the effects of discretization of the underlying continuous time process. Dividing by N_t captures the fact that social contact networks tend to remain stable with population size. In the same time frame, the number of susceptible individuals will be depleted by this number of new infected individuals and augmented via births. We can therefore generate the full trajectory of susceptible and infected individuals through time as

$$\begin{array}{l}{I}_{t+1}={\beta }_s{S}_t{I}_t^m/N_t\\ S_{t+1}=S_t+B_t-I_t,\end{array}$$

where B_t is the number of births, β_s is seasonally varying transmission rates, and initial conditions are set by initial numbers of infected I₀ and susceptibles S₀. To infer the unknown parameters (β_s, I₀ and S₀, and m) we can link this to data by the relationship

$${I^{\left(r\right)}}_T=\text{Binomial}(I_t+I_{t+1},\rho ),$$

where ρ is the reporting rate and $I_T^{\left(r\right)}$ is the reported number of infected cases at a monthly time scale; the sum is taken over the previous 2 wk. We have previously found that low reporting rates result in strongly downward biased estimates of m, which result in unrealistic dynamics (15); this also proved to be the case here. For this analysis, we therefore fixed m at a consensus value of 0.97. Previous work (17) indicates that the exact value of m does not affect estimates of seasonal variation in transmission. We fit a different transmission parameter for every site in every month, to quantify how transmission varied throughout the year within each province, and then explored the degree to which the various proxies (including rainfall, school term times, and population flux quantified as above) performed as explanatory variables for fluctuations in transmission.

Rubella Data Source and Possible Biases

Rubella data were obtained via the system of general surveillance for measles. For all patients presenting with fever; generalized rash; and either cough, coryza, or conjunctivitis, a serum specimen was collected and subsequently tested using standard serological techniques. Samples that were determined to be measles IgM negative were tested for rubella IgM antibody.

Measles control has made great strides in Kenya over the last decade, and dynamics are typified by sporadic outbreaks (e.g., in 2005) rather than endemic fluctuations (35). This will reduce the risk of systematic year-on-year biases in rubella seasonality driven by measles seasonality. These sporadic dynamics also mean that the average age of measles infection is higher than in an endemic situation (around 9 y, rather than the more usual 5 y), and this greater overlap with rubella age of infection (here observed to be 7 y) may serve to reduce underreporting linked to focus on younger measles-relevant ages.

Nevertheless, reporting rates are estimated to be very low in our analysis of this data, consistent with previous analyses (15) and the known mildness of this infection in children. This precludes an analysis of metapopulation dynamics (15), but for investigation of seasonal transmission, this will only bias results if there is additionally seasonal variation in reporting. There is always the possibility that incidence amplifies reporting of incidence, leading to a positive feedback loop, and this may be particularly pernicious in contexts with very low reporting. It is very difficult to evaluate the magnitude of this issue, but consistency of seasonal patterns across provinces increased our confidence that this was not a major component of result obtained here because there is no reason to anticipate that the surveillance across provinces is behaving identically in this way.

Determinants of Unique Three Peaks of Rubella Incidence per Year

Three peaks in transmission in a year are rarely observed for immunizing childhood infections even when multiple troughs in transmission are observed within the year. For measles, the difference in resulting patterns of incidence can be explained by the larger R₀ of this infection, which has much more overcompensatory dynamics than rubella, driving annual or biennial dynamics that swamp the pattern of seasonal variation from human movement (Fig. S2). Because few infections are as transmissible as measles, our results are likely to be broadly relevant across other childhood infections where population fluxes may contribute to the disease dynamics [e.g., mumps, scarlet fever, and diphtheria (17)]. Furthermore, this supportive evidence for low transmission rates for rubella in Kenya is a positive indicator with regard to the introduction of rubella-containing-vaccine: the lower the estimate of transmission, the more positive the likely outcome of introduction of the vaccine (17).

Spatial Variation in Proxies of Seasonal Human Population Dynamics

The degree to which population fluxes revealed by mobile phone data relate to previously used proxies of human aggregation [rainfall and the timing of school terms on monthly scales (1, 13)] provides insights to the degree that these proxies might be expected to relate to epidemiologically relevant aggregation patterns. A priori, we would expect population fluxes to have a negative relationship with both rainfall and schools terms; during months of peak rainfall, nonpaved roads (∼93% of the roads in the country) may be impassable in very rural areas, reducing travel, and as in high-income countries, families may travel more frequently during school holidays (Table S1).

Population fluxes between provinces were negatively correlated with school terms, with greater amounts of interprovince travel occurring during school breaks (April, August, and December) including the largest peak of travel coinciding with major national holidays and a school break during December (Fig. 2A; mean correlation, −0.55; 95% quantile interval, −0.70 to −0.43). The relationship between rainfall and population flux was positive in all but three provinces (Fig. S3; mean correlation, 0.020; 95% quantile interval, −0.304–0.24). In general, provinces that had the strongest positive relationship with rainfall had the strongest negative relationship with school terms, unrelated to population density or the total amount of rainfall (correlation coefficient, −0.59, P = 0.1276; Fig. S3). This suggests that proxy measures of human aggregation are not equivalent.

Seasonal Birth Rates and Fluctuations in the Timing and Magnitude of Seasonal Peaks of Rubella

Season fluctuations in birth rates are observed across the globe, and may affect epidemiological dynamics (26, 27). We explored the role played by this here using data from the 2008–2009 Demographic Health Survey in Kenya (21) to characterize seasonal fluctuations in births by taking mother reports of birth dates of all children (Fig. S6A) and compared these to school terms, amount of rainfall, and rubella transmission. Seasonal fluctuations in birth broadly echo previous reports (26) with one peak in September and one in April–May, although there is considerable province-to-province variability. Over the time course considered, fluctuations are relatively mild, ranging between 17% and 21% of the mean (calculated by taking one-half the difference between the maxima and minima, measured as a percent of the annual mean, as in ref. 27). This range has been shown to be insufficient to generate major fluctuations in periodicity, although it may slightly modify amplitude in measles. Seasonal births are significantly correlated with the school term in the Central province and rainfall on the coast (Fig. S6B). There are no significant associations with transmission. We compared estimates of seasonal transmission obtained under different degrees of seasonal fluctuations in birth rate using a discrete time stochastic age-structured simulation following methods described in ref. 32, with monthly age classes up to age 15 and yearly thereafter, tracking movement through maternally immune, susceptible, infected, recovered, and vaccinated epidemiological classes. The model was specified to reflect Kenya-specific demography, and the observed pattern of transmission over the year estimated for Nairobi (Fig. 1), combined with either (i) flat, (ii) estimated seasonal fluctuations in birth rates from Nairobi, or (iii) the Nairobi pattern with amplitude tripled (Fig. S6C). This indicated no effect of seasonal fluctuations in birth rate on estimates of seasonal transmission for rubella-like infection parameters (Fig. S6D). As previously found (27), seasonality in birth does start to affect dynamics and consequently seasonal fluctuations in transmission for very high levels of R₀, but these are far beyond levels reported for rubella (R₀ > 40), so we did not consider this further here.

District-Level Analysis of Proxies of Seasonal Human Population Dynamics

A further strength of the mobile phone data is that they allow us to explore dynamics on much finer scales than is possible using the incidence data alone, given issues linked to underreporting. To examine the relationship between mobility on different spatial scales, we disaggregated district-level population flux from provinces and compared the two time series (district-level and the corresponding province-level population flux). In general, district population flux patterns were similar to the province pattern, although this relationship varied geographically.

Similar to the province-level results, district-level population flux was negatively correlated with school terms; that is, more population fluctuations occurred during school breaks (mean correlation coefficient, −0.45; 95% quantile interval, −0.65 to −0.18; Fig. S4). The strength of the negative relationship between population flux and school terms increased with population density (corr, −0.29; P = 0.01; Fig. S2). Nearly half of the districts were positively correlated with rainfall (32 total districts) with a wider range of the strength of relationships than in provinces (mean correlation coefficient, −0.018; 95% quantile interval, −0.58 to −0.49).