Incubation Periods Impact the Spatial Predictability of Cholera and Ebola Outbreaks in Sierra Leone

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Incubation periods impact the spatial predictability of cholera and Ebola outbreaks in Sierra Leone

Rebecca Kahna,1, Corey M. Peaka,1, Juan Fernández-Graciaa,b, Alexandra Hillc, Amara Jambaid, Louisa Gandae, Marcia C. Castrof, and Caroline O. Buckeea,2

aCenter for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA 02115; bInstitute for Cross-Disciplinary Physics and Complex Systems, Universitat de les Illes Balears - Consell Superior d’Investigacions Científiques, E-07122 Palma de Mallorca, Spain; cDisease Control in Humanitarian Emergencies, World Health Organization, CH-1211 Geneva 27, Switzerland; dDisease Control and Prevention, Sierra Leone Ministry of Health and Sanitation, Freetown, Sierra Leone FPGG+89; eCountry Office, World Health Organization, Freetown, Sierra Leone FPGG+89; and fDepartment of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, MA 02115

Edited by Burton H. Singer, University of Florida, Gainesville, FL, and approved January 22, 2020 (received for review July 29, 2019) Forecasting the spatiotemporal spread of infectious diseases during total number of secondary infections by an infectious individual in an outbreak is an important component of epidemic response. a completely susceptible population (i.e., R0) (13, 14). Indeed, the However, it remains challenging both methodologically and with basis of contact tracing protocols during an outbreak reflects the respect to data requirements, as disease spread is influenced by need to identify and contain individuals during the incubation numerous factors, including the pathogen’s underlying transmission period, and the relative effectiveness of interventions such as parameters and epidemiological dynamics, social networks and pop- symptom monitoring or quarantine significantly depends on the ulation connectivity, and environmental conditions. Here, using data relationship between infectiousness and symptoms (14). Additional from Sierra Leone, we analyze the spatiotemporal dynamics of re- related metrics, the generation interval (i.e., the time between in- cent cholera and Ebola outbreaks and compare and contrast the fection of an infector−infectee pair) and the serial interval (i.e., the spread of these two pathogens in the same population. We develop time between symptom onset of an infector−infectee pair), as well a simulation model of the spatial spread of an epidemic in order to as their variances, can further impact the growth rate and total examine the impact of a pathogen’s incubation period on the dy- number of infections during an epidemic (15). The incubation namics of spread and the predictability of outbreaks. We find that period is also likely to play a particularly important role in de-

differences in the incubation period alone can determine the limits of termining the spatial spread of an epidemic, because one’stypical POPULATION BIOLOGY predictability for diseases with different natural history, both empir- travel may continue prior to symptom onset, whereas travel be- ically and in our simulations. Our results show that diseases with havior may change or stop altogether during illness (16), particu- longer incubation periods, such as Ebola, where infected individuals larly when symptoms are severe or immobilizing; even if symptoms can travel farther before becoming infectious, result in more long- are mild, if one knows they are infected, behavior may also change, distance sparking events and less predictable disease trajectories, as impacting transmission. compared to the more predictable wave-like spread of diseases with Back-to-back epidemics of cholera (2012−2013) and Ebola shorter incubation periods, such as cholera. (2014−2015) in Sierra Leone present a unique opportunity to compare the spatial dynamics of two epidemics in the same cholera | Ebola | epidemics | modeling | predictability Significance pidemics of emerging infectious diseases such as Ebola and EZika underscore the need to improve global capacity for Understanding how infectious diseases spread is critical for surveillance and response (1–3). Forecasting the spatiotemporal preventing and containing outbreaks. While advances have spread of infectious diseases during an outbreak can enable re- been made in forecasting epidemics, much is still unknown. sponders to stay ahead of an epidemic. However, it remains Here we show that the incubation period, the time between challenging both methodologically and with respect to data re- exposure to a pathogen and onset of symptoms, is an impor- quirements (4, 5), as disease spread is influenced by multiple tant factor in predicting spatiotemporal spread of disease and factors, including the pathogen’s underlying transmission pa- provides one explanation for the different trajectories of re- rameters and epidemiological dynamics, social networks and cent Ebola and cholera outbreaks in Sierra Leone. We find that population connectivity, and environmental conditions (6–9). outbreaks of pathogens with longer incubation periods, such Previous forecasting efforts have had varying levels of success in as Ebola, tend to have less predictable spread, whereas path- predicting the total number of cases and spatiotemporal spread of ogens with shorter incubation periods, such as cholera, spread outbreaks like Ebola, and few have actually been used in real time in a more predictable, wavelike pattern. These findings have in the midst of an epidemic (7). Efforts to understand the likely implications for the scale and timing of reactive interventions, performance of forecasts have shown that heterogeneity in contact such as vaccination campaigns. structure and number of secondary infections can pose challenges, but reasonable predictions can be made in some cases, depending Author contributions: R.K., C.M.P., J.F.-G., A.H., A.J., L.G., M.C.C., and C.O.B. designed on disease-specific parameters (6). However, the epidemiological research; R.K., C.M.P., and J.F.-G. performed research; R.K., C.M.P., J.F.-G., and M.C.C. attributes that determine predictability remain uncertain in real- analyzed data; and R.K., C.M.P., J.F.-G., L.G., and C.O.B. wrote the paper. world settings (10–12). The authors declare no competing interest. The time from when individuals are infected to when they be- This article is a PNAS Direct Submission. come infectious (the latent period) and to when they become Published under the PNAS license. symptomatic (the incubation period), and the relationship between Data deposition: Code and data are available on Github, https://github.com/rek160/Sierra- the two, have been shown to play a large role in the epidemic Leone-Cholera-Ebola. potential of diseases (9, 13, 14). In particular, transmission that 1R.K. and C.M.P. contributed equally to this work. occurs during the incubation period before an individual develops 2To whom correspondence may be addressed. Email: [email protected]. symptoms can contribute to rapid disease spread. When the latent This article contains supporting information online at https://www.pnas.org/lookup/suppl/ period is shorter than the incubation period for an infectious in- doi:10.1073/pnas.1913052117/-/DCSupplemental. dividual, presymptomatic transmission can be a strong driver of the First published February 13, 2020.

www.pnas.org/cgi/doi/10.1073/pnas.1913052117 PNAS | March 3, 2020 | vol. 117 | no. 9 | 5067–5073 Downloaded by guest on September 26, 2021 predictable disease trajectories, as compared to the more predictable wave-like spread of diseases with shorter incubation periods, such as cholera. Results We first summarize the cholera and Ebola epidemics in terms of their dynamics in time and space. More cases were reported during the cholera epidemic (22,691) than during the Ebola epidemic (11,903); however, far fewer cholera cases were fatal (324 vs. 3,956). Both epidemics lasted for similar periods of time, with cholera (January 7, 2012 to May 14, 2013) occurring 2 y prior to Ebola (May 18, 2014 to September 12, 2015). Data for both outbreaks were reported at the chiefdom level, the third- level administrative units. The times between the onset of an outbreak and when half or all of its cases were reported were longer when outbreaks were aggregated by district (second-level administrative units, comprised of chiefdoms) instead of chiefdom (Fig. 1), which has implications for the optimal scale for surveillance and response measures. The median time for a chiefdom cholera outbreak to report half of its case total was 3.9 wk, and median outbreak duration was 11.3 wk. The median time for Fig. 1. The proportion of cholera and Ebola cases reported over time dif- district outbreaks to report half of their cholera cases was 7.9 wk, fered between district and chiefdom levels. The times between the onset of and the median outbreak duration was 43.7 wk. Analysis of an outbreak and when half or all of its cases were reported were longer Ebola revealed similar trends, with chiefdoms reporting half of when outbreaks were aggregated by district instead of chiefdom, which has their cases at a median of 13.9 wk and median outbreak duration implications for the optimal scale for surveillance and response measures. of 43.3 wk, and districts reporting half of their cases at a median The median time for a chiefdom cholera outbreak to report half of its case total was 3.9 wk, and a median of 7.9 wk for district cholera outbreaks. For of 23.5 wk and median outbreak duration of 64.1 wk. Ebola, chiefdoms reported half of their cases at a median of 13.9 wk, and Both the cholera and Ebola epidemics were widespread, each districts reported at a median of 23.5 wk. reaching more than 75% of the country’s chiefdoms. However,

population caused by pathogens with notable similarities in both the drivers of outbreaks and the interventions used to curtail them, including oral rehydration (17, 18). Both are transmitted through contact with contaminated diarrhea or vomitus (plus other bodily fluids for Ebola), and the basic reproductive number (R0) for both diseases is thought to be between 1 and 3 (19, 20). Both diseases can cause immobilizing gastrointestinal symptoms of diarrhea and vomiting, and, untreated, their case fatality rates can exceed 50% (21, 22). Cultural factors and rituals, such as traditional funeral practices, are known to influence the spread of both cholera (23) and Ebola (24), while water, sanitation, and hygiene programs are often used to slow the spread of each (25). Both epidemics occurred against a backdrop of an immunologi- cally naïve population. Although it seems likely that travel patterns and the density and distribution of people were broadly similar over the time period in question, regular movements may have been more impacted during the Ebola epidemic than during the cholera epidemic due to travel restrictions, particularly during the multiday lockdowns (26). One critical difference between the dynamics of these diseases, however, is the incubation period, which is estimated at a median of 8 d to 12 d between infection and onset of symptoms for Ebola (1) and only 1 d to 2 d for cholera (27). We hypothesize that the disease incubation period may be a particularly influential driver of different patterns of disease spread through space and time. We analyze the spatiotemporal dynamics of a cholera outbreak and an Ebola outbreak in Sierra Leone, both of which occurred over a similar time period. We develop a simulation model of the spatial spread of an epidemic Fig. 2. Spatial trend contours of disease spread and chiefdom attack rates and examine the impact of the incubation period on the dy- highlight similarities and differences between the two epidemics. Spatial namics of spread and the predictability of outbreaks. We find trend contours of cholera (A) and Ebola (B) chiefdom case onset dates spread that differences in the incubation period alone can determine the from areas in dark red to light orange; thicker lines (A and B) show monthly increments, and thinner lines (B) show 2-wk increments. Each line of the limits of predictability for these diseases with different natural same color represents the same timescale. Larger spacing between lines history, both empirically and in our simulations. Our results show represents faster spread. Thick black lines denote regions, and thin black that diseases with longer incubation periods, such as Ebola, lines denote districts. Chiefdom attack rate quartiles for cholera (C)and where infected individuals can travel farther before becoming Ebola (D) vary over space and regions. Colored boundaries denote regions, infectious, result in more long-distance sparking events and less followed by bold black borders for districts and thin borders for chiefdoms.

5068 | www.pnas.org/cgi/doi/10.1073/pnas.1913052117 Kahn et al. Downloaded by guest on September 26, 2021 their trajectories differed. The spread of cholera from the north- Simulations. To examine the role of the incubation period in the west followed a radial spatial dispersion gradually in all directions spread of disease, we simulated outbreaks characterized by varying for the first 6 mo, while Ebola spread from the southeast for 2 mo incubation periods among agents distributed evenly on a spatial before rapid expansion to the northwest which sparked the na- lattice, with movement between populations in the lattice based on tional epidemic (Fig. 2 A and B and Movie S1). These findings a gravity model. These simulations show a systematic relationship were statistically supported by space−time analysis of each epi- between the incubation period and spatiotemporal patterns of demic, which revealed clusters of high case reporting of both disease spread. As expected, simulated epidemic curves of diseases diseases in western Sierra Leone and unique clusters of cholera in with shorter incubation periods were more acute, while diseases the south and Ebola in the east (SI Appendix,Fig.S1). The wave with longer incubation periods peaked later (Fig. 4A). Although front of chiefdom cholera outbreak onset progressed more slowly epidemics tend to last longer for diseases with longer incubation and gradually than for Ebola, which exhibited faster and more periods, the spread of the disease to more distant locations can discontinuous expansion, as shown by the larger spacing between progress more quickly, causing a discontinuous and more rapidly monthly contour lines (Fig. 2 A and B). Despite their different spreading wave front (Fig. 4 C and D). In the first 50 d of our trajectories, the geography of the epidemics largely overlapped, simulations, locations farther from the origin of the epidemic ex- with clusters of high cumulative attack rates of cholera and Ebola perienced cases earlier, on average, in simulations with longer in- observed in the north and west regions of Sierra Leone (Fig. 2 C cubation periods compared to those with shorter incubation and D) and confirmed through Local Moran’sImethods(SI periods, likely due to long-distance sparking events from infected Appendix,Fig.S2). agents traveling during the incubation period (Fig. 4B). The dis- As a daily estimate of transmission intensity, we recorded the persion kernel Kx(d), the probability that an agent will end up at a effective reproductive number on day t (Rt) and its variation over position separated a distance d from the initial position after x days, time nationally and by region (Fig. 3). While some areas sus- is more homogeneously spread and has nonvanishing probabilities tained transmission (i.e., Rt > 1) of both cholera and Ebola for at greater distances the higher the incubation period (x), explaining many days (e.g., Freetown in the west and Kenema Town in the the enhancement in sparking events (SI Appendix,Fig.S5). east), 75% of chiefdoms during the cholera outbreak and 44% of Simulations on a lattice with relative population size based on chiefdoms during the Ebola outbreak recorded either zero cases Sierra Leone’s chiefdom census data (as opposed to the evenly or zero days with Rt > 1(SI Appendix, Fig. S3). As expected, distributed populations in the original lattice simulations) support transmission intensity of both diseases was positively correlated the finding that the duration of epidemics is longer on a district in chiefdoms near each other (SI Appendix, Fig. S4). Correlation (i.e., group of lattice points) rather than chiefdom (i.e., individual decayed with distance, consistent with local disease spread, and lattice point) scale, with duration lengthening with increasing in- POPULATION BIOLOGY interchiefdom distances of over 100 km eliminated any evidence cubation periods (Fig. 5A). of positive correlation of disease presence, chiefdom outbreak Consistent with the correlation analysis comparing Sierra time, case count, and cumulative attack rate (SI Appendix, Fig. Leone’s cholera and Ebola outbreaks, time series from simulated S4). These metrics appear more highly correlated in space for outbreaks with shorter incubation periods were more highly cholera than for Ebola, although the confidence intervals overlap correlated than those from simulations with longer incubation (SI Appendix, Fig. S4). periods, with correlation decaying as distance between locations

Fig. 3. Weekly case counts show outbreak trajectory in the four regions of the country. The bars in A and B indicate the weekly case count on independent y

axes of cholera and Ebola, respectively. Black lines show maximum likelihood estimates of Rt of cholera and Ebola epidemics nationally (A and B, respectively) and in each region (C and D, respectively).

Kahn et al. PNAS | March 3, 2020 | vol. 117 | no. 9 | 5069 Downloaded by guest on September 26, 2021 Fig. 4. Results of 700 simulations of 14 different incubation periods show the impact of incubation period on disease spread. Epidemics with shorter incubation periods are more acute than epidemics with longer incubation periods (A). The average start time of epidemics at all locations over the first 50 d of outbreak is later for shorter incubation periods than for longer ones (B). Spatial trend contours of the first 50 d of simulated outbreaks with shorter incubation period (2 d) (C) and longer incubation period (10 d) (D), spreading from areas in dark red to light red, show that shorter incubation periods result in a more wave-like spread, and longer incubation periods result in more long-distance sparking events; numbers show average start day relative to start of the outbreak.

on the lattice increased (Fig. 5 B and C). Higher correlation suggests places, making sparking events more probable given the same increased predictability, which the results of the overlap function number of transmission events. support (Fig. 6). As the incubation period lengthened, the average Similar results were also obtained when infectious agents did predictability during the beginning of the outbreak decreased as the not decrease mobility when ill, suggesting that travel during the epidemics spread via unpredictable sparking patterns. Predictability incubation period has more influence on correlation and pre- plateaued as the outbreaks became widespread. dictability than travel during the infectious period. While many other factors will influence wave speed, continuity, and epidemic Discussion synchrony, our simulations showed that small changes in the in- Analysis of the cholera and Ebola epidemics revealed commonal- cubation period can powerfully influence epidemic dynamics. For ities and differences in the way these pathogens spread throughout example, environmental persistence of Vibrio cholerae in a local Sierra Leone, and our simulations suggest the differences in the water source can potentially lead to a longer serial interval for incubation period reproduce these differences. Spatial diffusion of local transmission (29) and a fatter right tail in offspring distri- Ebola occurred more quickly than cholera, as evidenced by the bution via superspreading. Following the dynamics of cholera and wave front contour lines and further supported by statistical tests Ebola, our models assumed that the incubation and latent periods considering a subset excluding cholera cases before the brief respite were equal; however, presymptomatic infectiousness may be an in June (SI Appendix,Fig.S6). Additionally, cholera metrics were important factor increasing spatial heterogeneity of onward trans- more correlated in space than Ebola metrics. Our model simula- mission, especially in the context of decreasing mobility when ill. For tions suggest that these findings are potentially due to the coun- a disease with presymptomatic infectiousness, we would expect to terintuitive role of the longer incubation period for Ebola as continue to see a positive correlation between long-range sparking compared to cholera. Travel during the incubation period will be a events and the incubation period, as well as a greater likelihood of key driver of geographic disease dispersion and predictability, es- intermediate-range sparking events as infectiousness increasingly pecially in a population of individuals who decrease mobility when precedes symptom onset and travelers transmit en route. ill. Consequently, diseases with longer incubation periods will tend The incubation period has already been recognized as an im- to have more long-distance sparking events caused by infected, but portant component for understanding epidemics and control healthy, individuals traveling during the incubation period. This will (13), with the conventional knowledge that long incubation pe- result in faster epidemic dispersion to distant, unpredictable loca- riods allow more time for responders to scale up interventions tions. These findings are in line with Marvel et al.’s(28)results, against the overall epidemic and are therefore advantageous for which found epidemic wave fronts are less likely to occur for mo- disease control efforts. Here we demonstrated a counterintuitive bility kernels that decay more slowly; when the incubation period mechanism whereby a longer incubation period may, in fact, is longer, the effective mobility kernel can span to more distant hinder a response by decreasing the predictability of outbreaks

5070 | www.pnas.org/cgi/doi/10.1073/pnas.1913052117 Kahn et al. Downloaded by guest on September 26, 2021 the dataset, thereby excluding missing cases and asymptomatic transmitters. However, this method has been shown to be robust to cases missing at random, and we furthermore expect the role of asymptomatic transmission to be limited for both diseases, due to the strong correlation between pathogen load, symptoms, and infectiousness (33, 34). Further, we assume no changes to the serial interval for either cholera or Ebola during the course of the epidemics. For cholera, specifically, waterborne transmission could potentially lead to a heavy right tail in serial intervals or change the distribution as pathogen accumulates or clears from a drinking source. Household data in Bangladesh, where the role of water contamination is expected to be large, suggest few serial intervals beyond 7 d (35). The geographic spread of cholera in Sierra Leone from the northwest and south toward the center of the country was not consistent with the direction of key waterways in the country, which primarily run from the eastern highlands to the western shores, suggesting population density and human-to-human contact likely played a larger role than water sources in this outbreak. Finally, our simulation model provides a proof-of-concept test of the hypothesis of the impact of the incubation period on disease spread and makes several simplifying assumptions. These assumptions could be relaxed in future work, including the complete overlap of symptoms and infectiousness and constant or structured diffusion of agents, for example, without increased probability of “ ” Fig. 5. The incubation period impacts the timing of outbreaks and, as a returning home, which could decrease the overall distance ex- result, the correlation. As the incubation period increases, the proportion of posed agents travel and therefore lower the probability of longer- cases reported by 10 wk, when a reactive vaccination campaign might begin, range sparking events. One could use other models for the mo- POPULATION BIOLOGY decreases in simulated epidemics (A). As the incubation period increases, the bility of the agents, such as the one by Song et al. (36) which in- average correlation overall (B) and by distance from origin of simulated cludes probabilities for returning to already visited places, as well outbreaks (C) decreases. as for exploration of locations not previously visited. In general, complex travel patterns are difficult to measure in real populations and increasing their geographic scope as well as of the needs of and are highly context-specific, interacting in critical ways with the surveillance and response. We use simulations to reproduce the epidemiological drivers of epidemics examined here. double-edged sword of the influence of the disease incubation The threat of cholera and Ebola reemergence in Sierra Leone period on reactive interventions. remains a concern (37). We have shown that differences in incu- Reactive vaccination strategies exist for both cholera and Ebola bation period alone are a powerful driver of geographic dispersion outbreaks, and a better understanding of spatiotemporal spread and merit further study. Although this study only examines one can facilitate locally preemptive vaccination to target locations at epidemic from each disease, the size of these epidemics, com- high risk of introduction (30–32). Reactive vaccination campaigns bined with simulation results from our model, can lend infor- must consider both the expected duration of an outbreak at a mation toward a better understanding of each disease and our given spatial scale and the predictability of its spread. We found ability to predict disease spread. This work can inform develop- that both epidemics lasted longer at the district level than chief- ment of international preparedness and response strategies and dom level, likely due to the larger spatial scale of the districts. For ensure timely and effective interventions. cholera, we showed that chiefdom outbreaks tended to report half of their cases within ∼4 wk, suggesting that reactive vaccination of a chiefdom triggered by detection of a case may not be early enough to avert an outbreak, and, instead, intervening at a wider scale, such as districts, might provide more favorable timing for intervention targeting. We posit, for future study, that regional ring vaccination strategies may be better suited to diseases with short incubation periods, while contact ring vaccination strategies may be better suited to diseases with longer incubation periods, due to their regional unpredictability and the longer intervals between generations in infection. There are limitations to our work with regard to data as well as methods. Few cholera cases were confirmed during the epidemic, and therefore we depend on the clinical definition as well as the cases that were detected and recorded by the surveillance system. Ebola surveillance data are similarly prone to differences in reporting rates, but the use of only confirmed cases yielded similar results to those reported above using both confirmed and suspected cases. Our estimates for the effective reproductive number Fig. 6. The incubation period impacts the predictability of disease spread. depend on, and absorb the limitations of, case data, serial interval Longer incubation periods have lower overlap (predictability) in the first 50 d (A). estimates, and the chiefdom connectivity matrix. Specifically, we Over time, the predictability decreases (B), with longer incubation periods assume all cases in our dataset acquired infection from others in consistently having lower predictability.

Kahn et al. PNAS | March 3, 2020 | vol. 117 | no. 9 | 5071 Downloaded by guest on September 26, 2021 Methods Model. We simulated an agent-based model with 45,000 agents distributed × Data. Cholera cases were reported to the Sierra Leone Ministry of Health and equally in 150 locations, evenly spaced on a 15 10 lattice. Infected agents − − − Sanitation by treatment facilities throughout Sierra Leone between January 1, progressed through a traditional susceptible exposed infectious recovered compartmental transmission framework. We assumed the incubation period 2012 and May 15, 2013 (38). Following standard World Health Organization (i.e., the time from exposure to symptom onset) overlapped completely with (WHO) definitions (39), a suspected cholera case was defined as acute onset of the latent period (i.e., the time from exposure to onset of infectiousness). watery diarrhea or severe dehydration in a person aged 5 y or older in a region Similarly, the duration of illnesses (5 d) aligned with the duration of in- without a known cholera outbreak; once the government of Sierra Leone de- fectiousness. The serial interval, which comprises both the incubation period clared an outbreak of cholera on February 27, 2012, any case of acute watery and duration of infectiousness, can strongly influence epidemic dynamics. diarrhea could henceforth be included as a suspected cholera case. Data were However, to isolate the impact of presymptomatic travel on spatiotemporal compiled and anonymized by the WHO for analysis, with case reports tempo- patterns of disease spread, in our simulations, we held the duration of in- rally resolved by day and spatially resolved by chiefdom. For Ebola, we used a fectiousness constant. The attack rate also remained constant throughout the published dataset of 8,358 confirmed and 3,545 suspected Ebola cases reported epidemics, with an R of 1.5; simulations with larger R s (e.g., 3) returned similar to the Sierra Leone Ministry of Health and Sanitation from May 2014 to Sep- 0 0 results. Movement of agents between two locations was simulated through a tember 2015 (40). Our analysis included both suspected and confirmed cases of daily travel connectivity matrix A based on a gravity model, whereby connec- Ebola according to standard WHO definitions (41). Population estimates for tivity was proportional to the population sizes of each location and the inverse 2012 and 2014 were imputed by chiefdom using a linear fit between chiefdom squared distance between them (50). Different parametrizations of the gravity population estimates from the 2004 and 2015 Population and Housing Censuses model, as well as simulations with relative population size based on Sierra (42). Data and code are available on Github (43). Leone’s chiefdom census data (51), yielded similar results. Note that the Sierra Leone has four administrative regions, which are divided into 14 dis- effective dispersion kernel after x days, Kx(d), mentioned in the simulation tricts. Freetown, the capital and largest city, comprises 2 districts; the remaining results is different from the daily mobility matrix A. In our simulations, the 12 districts are subdivided into 149 chiefdoms, with a median of 11.5 chiefdoms mobility matrix is fixed independently of the disease, but the dispersion kernel per district. Chiefdom, as the finest administrative unit available for cases of both that is relevant for each disease depends on the incubation period. The ele- cholera and Ebola, was considered the unit of observation and the unit of ment Aij of the mobility matrix A describes the probability that an agent will analysis (with the exception of cases in Freetown which were solely reported at travel from location i to location j in 1 d. These elements depend on the district level), as it is the likely scale of intervention campaigns like vaccination. To populations of those locations and the distance between them as in a gravity understand what would have been observed at a coarser spatial scale that is model for mobility. The dispersion kernel Kx(d) measures the probability of more common for surveillance, we additionally aggregated cases by district. finding an agent at a distance d from the place where she was x days before. Therefore, the dispersion kernel is a direct consequence of the daily mobility Spatiotemporal Analysis. We defined the first outbreak week for each matrix. It will tell us, for infected agents, the probability of being at a distance chiefdom as the week of the first reported case in that chiefdom. We visu- d from where they became infected after x days. As travel is stopped once they alized outbreak spread using a contour map of outbreak wave front direction become infectious, the relevant dispersion kernel for each disease will be the and speed (40). Contours of spatial spread were generated using ArcMap one for which x equals the incubation period. 10.3.1 Spatial Analyst extension by applying a fourth-degree polynomial Susceptible, exposed, and recovered individuals had a daily probability of trend interpolation of chiefdom onset dates and generating contour lines of movement. To simulate the impact of a reduction in mobility during illness, this surface in 2- to 4-wk increments. With this method, more closely spaced agents in the model had their movement reduced as far as zero throughout the contour lines indicate slower propagation, similar to the slope of a topo- course of their period of infectiousness (and, equivalently, illness). Holding all graphic map of elevation. other parameters constant, we conducted 700 simulations of epidemics for To identify space−time clusters, using the SaTScan software package (44), incubation periods ranging from 1 d to 14 d. We seeded the epidemic at the we ran a retrospective discrete Poisson-based Scan Statistic over the entirety same location near the center of the lattice for all simulations. of the outbreaks for which data were available, namely, 16 mo of cholera Synchrony was assessed with the R package ncf functions mSynch and data and 17 mo of Ebola data. Disease case reports were assumed to be Correlog.Nc (47), which both estimate the correlation between the time series Poisson-distributed given chiefdom population size. The unit of time ag- in each of the 150 locations across the 500 d of the simulations, with the latter gregation for the analysis was specified as the median serial interval for each incorporating distance (47). To assess the impact of the incubation period on disease [5 d for cholera (45, 46) and 13.3 d for Ebola (1)]. the initial speed of spread, we calculated the average start time across all We calculated spline correlograms for four chiefdom outbreak metrics to locations in the first 50 d of the outbreaks as well as at increasing distances measure spatial correlation of date of first case, case count, attack rate, and from the location on the lattice where the outbreaks began. disease presence (yes/no). The maximum centroid-to-centroid distance was set To estimate the predictability of outbreak spread in space and time, we to 150 km, approximately the radius of Sierra Leone. We used the spline.correlog adapted an overlap function used to measure predictability of a severe acute π ð Þ function of the R package ncf for each disease and all chiefdom pairs (47). respiratory syndrome (SARS) outbreak (9). In each simulation, a vector j t represents the proportion of all infected individuals at time t who are at We estimated the daily effective reproductive number (R ), the average t location j. In a system with high predictability, π ðtÞ will be similar across number of onward infections generated by cases with onset on day t, using j simulations. The overlap between simulations I and II can be estimated by methods described by Wallinga and Teunis (48) and extended to meta- P qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Θð Þ = πI ð Þ πIIð Þ Θ populations by White et al. (49). This maximum likelihood method estimates t j j t * j t . (t) ranges from 0 to 1, with a higher value indi- the probability that an observed case was the infector for each subsequent cating more overlap and thus more predictability. We estimated pre- case by leveraging information on the daily case count, the serial interval dictability at each time point by calculating the average of the overlap distribution, and a weights matrix that quantifies relative contact frequency functions for each pair of simulations for each incubation period. We cal- within and between chiefdoms. The serial interval for cholera was assumed culated the average overlap across time points to provide a summary metric to follow a gamma distribution (rate = 0.1, shape = 0.5) with a median of for predictability of each incubation period. 5 d, as has been used previously after consideration of both fast, person-to- person, and slow, environmental, transmission routes (45, 46). The serial Data Availability. Code and data are available on Github (43): https://github. = interval for Ebola was assumed to follow a gamma distribution (rate 0.17, com/rek160/Sierra-Leone-Cholera-Ebola. shape = 2.59) with a median of 13.3 d derived from the estimates by the WHO Ebola Response Team (1). The contact frequency between two given ACKNOWLEDGMENTS. We thank Dr. Foday Dafae for early support of this chiefdoms was assumed to decrease with squared distance between the work. This work was supported by Award U54GM088558 from the National chiefdom centroids. Additional weights matrices with different functional Institute of General Medical Sciences. The content is solely the responsibility of forms for distance decay yielded qualitatively similar measurements of Rt. the authors and does not necessarily represent the official views of NIH.

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