INTRODUCTION
Yersinia pestis, the etiologic agent of plague, appears to have invaded the continental United States in 1900 through the Port of San Francisco, where it quickly emerged into an epidemic that lasted, uninterrupted, until 1904.1,2 Successive outbreaks of varying sizes occurred in urban areas along the Pacific coast, including San Francisco, Seattle, Oakland, and Los Angeles until 1925, resulting in at least 494 human cases and a case-fatality rate of more than 50% (Centers for Disease Control and Prevention, Atlanta, GA, unpublished data).1,3 Concurrently, plague became established enzootically in wild rodent populations in several western states.4–7 By the mid-1940s, epizootics were documented in woodrat (Neotoma spp.), deer mice (Peromyscus spp.), ground squirrel (Spermophilus spp.), and prairie dog (Cynomys spp.) populations as far east as Oklahoma and Kansas.8 However, although Y. pestis traversed more than 2,250 km in just more than 40 years, it has since ceased its eastward expansion; plague has not spread beyond the 103rd meridian, or the plague line, in the western Great Plains despite the passage of an additional 60 years.9
The specific path of the eastward expansion of plague after it was introduced into the United States is poorly understood. Plague outbreaks were first detected in Oregon in 1934, in Montana in 1935, and in Utah, Idaho, and Nevada in 1936.10 Unconfirmed epizootics with die-offs of ground squirrels were observed as early as 1929 in Oregon and Nevada, 1930 in Washington, 1932 in Idaho, and 1933 in Montana, and die-offs of prairie dogs suspected to be caused by plague were reported in Arizona in 1932.10 Little evidence is available to indicate the method by which the disease spread, possibly because relatively few surveys were made beyond California prior to 1935, when the U.S. Public Health Service first instituted a search for foci of wild rodent plague in other states.10,11
A retrospective analysis of the temporal and spatial dynamics of the expansion of plague over the U.S. landscape can provide significant insight into the mechanisms of disease spread.12–14 Specifically, the velocity of the traveling wavefront of plague and the geographic path that plague most likely followed can be calculated directly from historical data, and can be depicted by a method called trend-surface analysis (TSA), a global surface fitting procedure. This procedure uses a polynomial expansion of the geographic coordinates of historical cases to fit a multiple linear regression model by the method of least squares (so that the sum of the squared deviations from the trend surface is at a minimum), and aims to capture the generalized direction(s) and speed(s) of the propagating wave of an infectious disease.15 This analytic method permits the identification of linear, quadratic, and cubic spatio-temporal trends in the path of disease spread and gives a quantitative measure of the importance of these large-scale trends and relationships.15,16
The observed rates of disease spread across various spatio-temporal points along the traveling wavefront can then be analyzed from directly observed and TSA-calculated data using generalized linear models to identify key variables affecting the underlying dynamics. The simplest model of disease spread is a reaction-diffusion-based model, such as the Fisher-Kolmogorov equation, which predicts the speed at which the wavefront will diffuse across a susceptible population based on the initial conditions present upon disease introduction.14,17,18 Here, the velocity at which the disease propagates across the landscape from its origin is calculated under the assumption that it spreads homogeneously and at a constant rate from each independent introduction site according to the equation V = 2(rS0D)1/2[1 − (a/rS0)]1/2.15 This equation was built on the theoretical research originally conducted by Fisher, who used a logistic-based reaction-diffusion model to investigate the spread of an advantageous gene within a population.19 Fisher-based models predict the eventual establishment of a well-defined invasion front, dividing a spatial landscape into invaded regions and uninvaded regions, with the invasion front moving from the former to the latter regions with a constant velocity.18 Under the Fisher-Kolmogorov equation, wave velocity, V, is dependent upon S0, which represents the initial susceptible population density, r, a measure of the transmission efficiency of the disease from infective individuals to susceptible individuals, D, the diffusion coefficient, or a measure of how quickly cases will disperse, and a, the proportion of infected individuals expected to die of disease. With a given susceptible population and transmission coefficient, we get a threshold mortality rate, rS0, which, if exceeded, prevents an epidemic. Thus, a* = [a/(rS0)] < 1 represents the threshold criterion for maintaining the epidemic.
The Fisher-Kolmogorov equation focuses on diffusion as a product of host population parameters and disease dynamics. However, plague is a disease that is maintained in a network of multiple rodent host and flea vector species, each varying in the extent to which it contributes to disease maintenance and emergence. Therefore, the rate at which the traveling wave of plague diffused outward across the United States landscape would be expected to differ from the theoretical Fisher-Kolmogorov-based baseline rate (represented by the intercept of a generalized linear model) because of effects of climatic and environmental factors on both vector and host population dynamics.3,20,21 Both temperature and humidity greatly modify plague risk in fleas.3 In addition, several studies have demonstrated that increases in outbreaks of diseases such as hantavirus infection and plague were associated with above average precipitation, which, according to a trophic cascade hypothesis, led to greater available food resources and increased populations of rodent reservoirs.17,22–24 These environmental changes and resulting fluctuations in rodent populations can alter their typical home ranges,24 which can directly impact the rate of disease spread. Similarly, the vegetational features of a particular geographic location will also impact the species of rodents present, typical home ranges, population dynamics, and roles in disease spread.24
This study uses a comprehensive database of human, domestic animal, and wildlife plague cases in the United States, starting from 1900, to evaluate the spatio-temporal distribution of plague. In particular, we aim to characterize the traveling wavefront(s) of plague through the United States as it spread from its initial invasion site(s) to its currently established range using both descriptive and inferential statistics. Large-scale trends and descriptions will first be identified and summarized using a geographic information system to determine patterns associated with disease spread, the number of potentially independent plague introduction events, and the relative rates of disease spread observed. The TSA models, direct observations of cases, and maps will then be used to calculate the observed velocities at which plague propagated across the western United States. The observed and predicted velocities will then be analyzed using generalized linear regression models, with key environmental and climatic factors as explanatory variables, to identify significant determinants of the rate of disease spread.
MATERIALS AND METHODS
Compilation of historical plague data.
Data were compiled on historical human and animal plague cases representing the first report of plague in a geographic location (at the city or county level) where plague was not previously confirmed. Data for domestic animal and wildlife plague cases were obtained from state and federal public health reports and from peer-reviewed scientific publications; data on human plague cases (from 1900 through 2005) were obtained from the Centers for Disease Control and Prevention.8,10–13,25,26 The data obtained for this study are limited to reports of cases that were actually observed and confirmed by people; however, they still represent the most complete, available set of historical plague records (Gage KL, unpublished data). Information recorded for each case included its decimal-degree latitude and longitude coordinates (ranging from precise locations to county centroids), species identification, and date of infection for humans or confirmation of plague for animals (month and year). Although using county-centroid coordinates limits the amount of detail that can be observed and reported regarding plague dynamics at a finer spatial scale, the large geographic range being covered by this analysis (from the Pacific coast to the western Great Plains) will still facilitate the identification of broad trends and relationships, including the generalized direction and speed of disease spread.
Although the first introduction of plague into the continental United States was in San Francisco in 1900, preliminary inspections of the data identified other potentially independent disease introductions that may have resulted in the establishment of plague due the presence of both human and animal cases, resulting in the possibility of multiple traveling wavefronts of plague. To account for this, each case was labeled according to the introduction event(s) it was potentially related to based on its geographic location, under the assumption that definitely one and as many as three events, including the outbreaks in San Francisco, CA in 1900, Seattle, WA in 1907, and Los Angeles, CA in 1908, were potentially independent. The null hypothesis was for all cases to have originated from the San Francisco introduction. However, the velocity of disease spread for a particular case was also calculated relative to Los Angeles and Seattle as the distance of the case in kilometers from the introduction site divided by the years that elapsed since the introduction. If this velocity was within one SD of the velocity observed for that case relative to San Francisco, it was also labeled as potentially being related to a non-San Francisco event. Descriptive statistical analyses were then conducted to explore how each of these scenarios could impact the rates at which plague spread through the continental United States. Although additional introductions of plague occurred along the Gulf Coast, historical records indicate that they were limited to urban human outbreaks, and most likely did not result in the establishment of plague in these regions. Therefore, this study makes the assumption that only Pacific coast introductions resulted in the establishment of plague, and human cases from the Gulf Coast outbreaks were not considered in our models.
Trend-surface analysis.
The decimal-degree latitude and longitude coordinates of cases were uploaded into ArcGIS ArcInfo version 9.1 (Environmental Systems Research Institute, Redlands, CA), which were then converted into X- and Y-coordinates (in kilometers) using an Albers equal-area projection map of the United States, with the origin adjusted to the location of the San Francisco introduction event. The X-and Y-coordinates were then expanded to represent a polynomial equation that included linear, quadratic, and cubic terms. The TSA was conducted in R (The R-Development Core Team, http://www.r-project.org) using the polynomial expansions of the coordinates as the independent variables and the number of years since plague was introduced into the continental United States as the continuous outcome. An additional TSA was also performed to determine how the removal of the human plague cases from the database would impact the final results because these cases could introduce bias from human travel that was not indicative of the real spread of, nor led to the establishment of, enzootic plague.
The full TSA model is Years since invasion = β0 + β1X + β2Y + β3X2 + β4XY + β5Y2 + β6X3 + β7X2Y + β8XY2 + β9Y3 + ε , where βx are fitted parameters, X and Y represent the geographic coordinates, and ε represents the error term (which is assumed to have a mean of zero, be normally distributed, and have a constant variance).15 Backward stepwise selection was used for model development. Parameters with P values > 0.1 were excluded from the model; the final models were chosen to minimize Akaike’s Information Criterion. Upon selecting the final model, diagnostic procedures were performed to check for violation of model assumptions (i.e., linearity, normality, independence, homoscedasticity, and a lack of outliers).
Results of the TSA models were used to generate contour maps in ArcGIS using the ArcView Geostatistical Analyst extension to depict the linear, quadratic, and cubic trends associated with disease spread after the initial United States introduction both with and without human cases; each isochrone or contour line represents a defined time period since the initial introduction event occurred. Additionally, the predicted spatio-temporal distribution of plague under each scenario was depicted in ArcGIS using the kriging function in the ArcView Spatial Analyst extension, a Bayesian interpolation method that yields a best estimate for all unsampled locations, with a minimized error variance at each location.
Traveling wave velocities.
The velocities of the traveling waves of plague with respect to San Francisco were calculated using two separate procedures. First, the final trend-surface models were used to derive partial differential equations with respect to the X- and Y-coordinates, representing the rate of change of the X and Y position, respectively, as a function of time. Substituting the specific X- and Y-coordinates observed for a case into these equations allowed the X and Y vectors contributing to the slope of the traveling wavefront (i.e., its magnitude) to be described. These resultant vectors for each case were summed to obtain the overall magnitude and direction of its slope of disease spread; the inverse of this slope was taken to identify the velocity of disease spread associated with the spatio-temporal position of that case (in km per year).
The observed velocities for each case were also calculated directly from the data by measuring the linear distance (in kilometers) from the introduction event being considered to the geographic position of the case and then dividing it by the time in years that elapsed since that introduction event. Here, a case had anywhere from one to three observed velocities depending on the traveling wave(s) with which it was potentially associated.
A paired, two-tailed t-test was conducted to determine if the observed velocities with respect to San Francisco differed significantly (α < 0.05) from those calculated using the partial derivatives of the TSA models. If the two velocity estimates were not significantly different, then the average of the two estimates would be calculated and used for subsequent analyses.
The velocity estimates, first for all cases and then for just the animal cases relative to San Francisco, were used as the outcome variables in multiple linear regression models, where possible variables included the average annual precipitation totals, the mean snowfall rates, and the mean minimum, maximum, and overall average annual and seasonal temperatures. All historical climatic data were obtained from the Western Regional Climate Center (Reno, NV) and the National Climatic Data Center (Asheville, NC). Data from all weather stations located within the city or county from which the case was located (depending on the level of specificity available) were averaged to obtain historical estimates. Mean estimates were used when historical data were not consistently available. Levels I and III ecoregion data (based on the Environmental Protection Agency’s classification system) were used to classify the habitat type for each case location. Level I ecoregion predictor variables were marine west coast, Mediterranean California, northwestern forested mountains, North American deserts, temperate sierras, and the Great Plains. Level III ecoregion predictors were coast range, chaparral and oak woodlands, Central California valley, Sierra Nevada, Eastern Cascades, Northern basin and range, Middle Rockies, Blue Mountains, Wyoming basin and range, Snake River plain, Central basin and range, Wasatch and Uinta Mountains, Colorado plateau, Arizona and New Mexico Plateau, Southern Rockies, Southwestern Tablelands, Western High plains, and the Chihuahuan Deserts.
To avoid problems caused by collinearity, a correlation matrix of all predictor variables was analyzed. Highly correlated variables (r > 0.7 or < −0.7) were then further investigated using simple linear regression to determine which explained the greatest amount of variability in the outcome variable; only that variable was retained for model development. All final linear regression models were then developed in R using backward stepwise regression according to the methods outlined above.
RESULTS
Of 943 human plague cases and 92 animal plague epizootics in the United States from 1900 through 2005, a combined total of 95 human cases and animal epizootics were spatio-temporally unique cases representing the first evidence of the presence of plague in a geographic location (Figure 1). These 95 case events occurred between 1900 and 1966 and comprised 24 ground squirrel reports (including Spermophilus armatus, S. columbianus, S. elegans, S. grammurus, S. lateralis, S. oregonus, and S. townsendi), 5 rat and woodrat reports (including Rattus spp. and Neotoma spp.), 20 prairie dog reports (including Cynomys gunnisoni zuniensis, C. leucurus, C. parevidens, and C. ludovicianus), 5 marmot reports (all Marmota flaviventris), 3 general wild mammal reports, 32 human cases, and 6 reports simultaneously representing both human and wildlife cases.
Directly calculated and TSA-generated velocities.
The mean ± SD velocity of disease spread calculated directly for all cases relative to San Francisco was 35.02 ± 22.79 km/year and, for just the animal cases relative to San Francisco, 39.06 ± 13.37 km/year. When all cases were analyzed for their potential to have originated from Seattle and/or Los Angeles, in addition to San Francisco, 74 cases were determined to have potentially originated from Los Angeles with a mean ± SD velocity of 31.86 ± 14.39 km/year, and 66 cases were determined to have potentially originated from Seattle with a mean ± SD velocity of 37.13 ± 17.09 km/year. There were 59 cases that could have originated from San Francisco, Los Angeles, or Seattle. Only 11 cases clearly had San Francisco as the only possible site of origin (velocities averaged 8.55 km/year); these cases represent all but two of the earliest plague events reported (from 1900 through 1923), occurring in a progressively southward direction along the California coast. The only exceptions were a human outbreak in Seattle in 1907 (velocity of disease spread relative to San Francisco was 185.95 km/year) and a human and ground squirrel outbreak in Los Angeles in 1908 (velocity of disease spread relative to San Francisco was 80.38 km/year). Although plague was confirmed in Los Angeles in 1908, a separate and much larger human and ground squirrel outbreak erupted in 1924, after which 93.3% of the spatio-temporally unique California plague events recorded in our database were labeled as having potentially originated from either San Francisco or Los Angeles, with average velocities of 11.26 km/year and 20.68 km/year, respectively. By the mid-1930s and beyond, 73% of all cases were labeled as potentially originating from any of the three possible introduction sites, showing average velocities of 36.19 km/year, 34.64 km/year, and 41.25 km/year, respectively. Table 1 shows the average velocities of disease spread by decade for all cases relative to the introduction site being considered.
The final TSA models (with and without human cases) are shown in Table 2. No violations of the statistical assumptions were observed during diagnostic procedures. Contour maps developed from the TSA models are shown in Figure 2A and B. Contour maps using the kriging function were also developed to illustrate predicted spatio-temporal distributions of plague (Figure 3A and B). The partial first derivatives of the TSA models with respect to the X- and Y-coordinates, which give velocities of disease spread for each case as well as the average velocities by decade, are shown in Table 3. Equations for models 1 (M1), with human cases, and 2 (M2), without human cases are ∂YRS/∂XM1 = 0.06877 - 1.0298 × 10−4X -1.336 ×10−4Y + 1.1296 × 10−7XY + 5.397 × 10−8Y2 + 3.933 × 10−8X2 and ∂YRS/∂YM1 = 0.06363 − 1.03 × 10−4Y − 1.3349 × 10−4X + 5.648 × 10−8X2; ∂YRS/∂XM2 = 0.04828 − 6.584 × 10−5X − 6.86 × 10−5Y + 7.32 × 10−8XY + 2.263 × 10−8X2 and ∂YRS/∂YM2 = 0.02303 − 6.86 × 10−5X + 3.66 ×10−8X2. The mean ± SD TSA velocities for models 1 and 2, respectively, were 31.84 ± 33.29 km/year and 74.25 ± 40.09 km/year.
Paired, two-tailed t-tests comparing the TSA velocities for each case in models 1 and 2 to the directly calculated velocities showed no significant differences between the TSA estimates from model 1 and the directly calculated velocities (P = 0.41). However, the TSA velocities from model 2 were significantly different from the directly calculated velocities (P = 9.52 ×10−10). Therefore, the directly calculated velocity estimates were averaged with those from model 1 for the multiple linear regression analysis, and the velocity estimates calculated under model 2 were analyzed independently from the corresponding directly calculated values to compare how the resulting multiple linear regression models differed.
Multiple linear regression analyses.
A correlation matrix was constructed for all predictor variables. Among the climatic variables, the mean minimum, maximum, and average annual temperatures, mean minimum winter temperature, and all mean seasonal temperatures were highly correlated (r ranged from 0.82 to 0.96). Of these, the mean minimum winter temperature was the most significantly associated with the observed velocities in all cases (P < 0.0001), and was therefore retained for subsequent model development. Significant correlations were also observed between the ecoregion level I and III variables coast and coast range (r = 0.89), and chaparral and oak woodlands and Mediterranean California (r = 0.8). Of these, coast range and Mediterranean California were the most significant (P < 0.01 and < 0.0001, respectively) and were retained for subsequent model development.
Results from the multiple linear regression analysis for all spatio-temporally unique plague cases are shown in Table 4. This model did not violate any statistical assumptions. The most significant factors affecting the rate at which plague spread were the level III Environmental Protection Agency ecoregions, with only one level I ecoregion, Mediterranean California, left in the model. Of the climatic variables, precipitation and an interaction between the mean minimum winter temperature and precipitation were significant. By itself, the mean minimum winter temperature was not significant (P < 0.2); however, it was included because of the significant interaction.
The intercept suggests that the baseline rate of the spread of plague, without the impact of these additional factors, was 43.52 ± 11.1 km/year. The Mediterranean California, coast range, and Chihuahuan deserts ecoregions were each associated with a significant decrease in the rate at which plague spread (by 18.41 ± 5.73 km/year, 28.43 ± 8.65 km/year, and 22.25 ± 9.15 km/year, respectively). Similarly, a one degree Fahrenheit increase in the mean minimum winter temperature and a one inch increase in the annual precipitation resulted in a moderately significant velocity decrease of 0.57 ± 0.42 km/year and 1.61 ± 0.71 km/year, respectively, although their interaction resulted in a 0.05 ± 0.02 km/year increase. All remaining ecoregion variables led to a significant increase in the velocity of the spread of plague, ranging from 14.5 ± 5.48 km/year for the Colorado plateau to 25.58 ± 5.05 km/year for the Arizona and New Mexico plateau.
The second and third multiple linear regression models that were developed using the TSA-generated velocities and the directly calculated velocities for all spatio-temporally unique animal plague cases are shown in Table 5. In the model using the TSA-generated velocities, the intercept, or rate of disease spread without the influence of external factors, was 86.75 ± 9.64 km/year. Here, a one degree Fahrenheit increase in the mean minimum winter temperature was associated with a decrease in velocity of 1.41 ± 0.42 km/year. The only significantly important ecoregion variables were the Blue Mountains and the Southern Rockies, which each resulted in an increase in velocity of 32.36 ± 15.33 km/year and 43.76 ± 9.48 km/year, respectively.
Using directly calculated velocities of only animal cases as the outcome, we determine that the baseline rate of disease spread was 80.81 ± 15.28 km/year. A large number of environmental variables were significant, including all level I ecoregion variables, several level III ecoregion variables, and two climatic factors. The coast range was associated with the greatest decrease in velocity, with an estimate of −43.84 ± 6.70 km/year, while the Great Plains were associated with the largest increase in velocity (26.95 ± 2.57 km/year). Other variables associated with a decrease in velocity were Mediterranean California, the Sierra Nevada, the Eastern Cascades, the Blue Mountains, a one degree Fahrenheit increase in the mean maximum summer temperature, and a one inch increase in the annual snowfall. Additional ecoregions associated with an increase in velocity include the northwestern forested mountains, North American deserts, Central California valley, and the Southern Rockies.
DISCUSSION
The initial introduction and subsequent urban outbreaks of plague in the continental United States are well documented.1–3 However, since additional human cases and wildlife die-offs occurred in locations where plague had not previously been observed, it became clear that the bacteria had become established in enzootic cycles, aiding its eastward spread in a manner that has remained poorly understood.4–8 This study used historical human plague case data and wildlife plague reports to analyze the spread of plague across the United States landscape, which facilitated an increased understanding of the key drivers behind its spatio-temporal dynamics.
It was important to first determine if there were one or multiple independent introductions of plague into the continental United States. Multiple introduction events would present as several independent traveling waves of plague spreading at either constant or varying rates. This is observed in Figures 2A and 3A, which were developed using both human and animal plague reports, and could be the result of translocations of infected individuals or additional introductions from ships along the coast. Descriptive statistical analyses also suggested two additional independent introductions of plague into the United States based on the improbably rapid rates at which plague would have had to spread for it to have originated from San Francisco. These included six human cases that occurred in Seattle, WA in 1907 with a velocity of more than 185 km/year relative to San Francisco (more than five times the average speed observed for all cases relative to that introduction site) and a human case and squirrel epizootic in Los Angeles in 1908 with a velocity of more than 80 km/year (more than twice the average speed observed). Since only human cases were reported in Seattle, these individuals could have contracted the disease prior to traveling into the region, or perhaps from infected rodents on a ship that came from a plague-endemic area. Therefore, these cases may not be indicative of the establishment of plague in the state of Washington at that point in time. In contrast, in Los Angeles, plague-positive squirrels were reported in addition to a human case, which suggested that plague had become established enzootically. This enzootic establishment could have resulted from a greater-than-average rate of disease spread along the southern Pacific coast because velocities of 80 km/year were also predicted to be the baseline rate of disease spread according to the TSA models using only animal plague data. However, it is more likely that this is a separate, independent introduction event, as shown in Figures 2B and 3B, based only on animal plague reports.
Regardless of the number of introduction events that occurred, one possibility for the spread of plague throughout the western United States was diffusion from the initial introduction site(s), spreading homogeneously over time at a steady rate. This type of pure diffusion, with the constant rate of disease spread, was observed for the Black Death from 1347 through 1350 AD by Noble, who modeled the traveling wave of plague as it propagated across Europe by parameterizing the modified Fisher-Kolmogorov equation with human-based data.12 Using this equation, he calculated an expected velocity of approximately 480 km/year, which was in agreement with the actual rate observed during the European human plague epidemic.11 However, in none of the TSAs or direct calculations performed in this study did the United States plague velocities appear to be consistent across various spatio-temporal locations to support pure diffusion. The model of Noble used only human data, largely capturing the dynamics of pneumonic plague, which spreads from person to person. Our study incorporates animal cases, which usually precede human cases,12 and captures the complex dynamics of bubonic plague as it spreads enzootically. These dynamics are determined by interactions of flea vectors with mammalian hosts, varying tremendously by species and modified by climatic factors such as temperature and relative humidity.3,7,22–24 Our results suggest that the spread of plague in the United States, which initially included pneumonic outbreaks in humans, but shortly thereafter became established as an enzootic disease, was affected by external factors, and cannot be explained by diffusion alone.
Other studies have also found that geography and environment modulate disease spread. In a study using TSA to explain the spread of rabies in Pennsylvania, the pattern and speed of disease spread differed significantly from what one would expect if the disease diffused outward from a point source. Instead, Moore found that the velocities of rabies’ spread varied tremendously across differing geographic landscapes within the state, with the disease spreading fastest through valleys bordered by the large mountainous regions.15 Similarly, Sayers and others found significant correlations between geographic features and the distribution of cases in a study on the spread of rabies in foxes through Europe.27 The velocities calculated in this study under all models also demonstrate extreme fluctuations across various spatio-temporal points, which suggests that the environmental conditions present significantly affected how plague spread across the western United States.
To fully understand how specific environmental variables impacted the dynamics of plague, it was important to analyze the spatio-temporally unique animal reports separately and together with human cases. Although the human cases in this database represent the first recorded occurrence of plague in a particular geographic location, it is probable that such cases resulted after plague was already established endemically in wild rodents. Human dynamics are reported to not affect the natural behavior of plague; instead, human cases are considered to be a by-product of the progression of the disease in the rodent community.13 This is further reinforced by the fact that, once the United States initiated mobile searches for plague, many western states were found to have plague-positive rodents despite human cases not being reported until at least several years later, and in some instances, such as Kansas, never at all (Centers for Disease Control and Prevention, unpublished data).8,10,11
When only animal cases were considered, the TSA velocities were significantly greater than directly calculated velocities, which implied that the actual path of spread was not the most direct route. Similarly, the velocities generated by the TSA model using animal-only data were much greater by decade than those generated by the TSA model using all case data. This result supports the conclusion that human cases likely arose after plague was already established in an area, rather than signifying the arrival of the disease (Centers for Disease Control and Prevention, unpublished data).8,10,11
The intercepts of the regression models identify the baseline rates of disease spread without the impact of the other variables being analyzed, and can thus be interpreted as the rate at which plague diffused outward should the parameters of the Fisher-Kolmogorov model be the sole governing forces behind disease spread. In both animal-based regression models, the intercepts show similar baseline rates of disease spread, with estimates of 81 km/year and 87 km/year, respectively. In contrast, the model developed using all data shows a slower baseline rate of 45 km/year. This model suggests that once plague enters a new geographic area, human cases on average arise in up to as much as twice the amount of time it took for plague to initially enter into the region. This modeled lag is much larger than what is actually observed in our database (which shows lags ranging from 4 years in Idaho to up to 16 years in Colorado). However, these models also take into account instances such as Kansas, where animal plague cases were reported as early as 1945, although a human case has yet to be reported.
The baseline rates of disease spread as modeled by the Fisher-Kolmogorov equation are products of host parameters and disease dynamics, including the initial susceptible population density, a measure of the transmission efficiency of the disease from infective individuals to susceptible individuals, a measure of how quickly cases will disperse, and the proportion of infected individuals expected to die of disease. These parameters can be expected to vary according to the specific host species present, producing variations among the observed rate of disease spread. More than 200 mammalian species from 76 genera in the United States have been reported to be naturally infected with Y. pestis. Although only rodents are implicated as being important for the spread and/or maintenance of plague,13 they still represent more than half of the reported susceptible mammalian species.3 Therefore, modeling how specific rodent species, or even genera, affect the rates of disease spread is impractical. Rather, modeling the effect that different ecoregions and climatic variables have on the rates of disease spread can serve as a proxy for understanding which hosts most significantly drive the spatio-temporal dynamics of plague.
All regression models found the Southern Rockies to significantly increase the rate of disease spread, ranging from 6 to 44 km/year above the baseline rate. This ecoregion is the highest in North America, with more than 20% of the land area at an elevation higher than 3,000 meters. It is characterized by several major ecosystems, including shortgrass prairie, scrublands, woodlands and forests, grasslands and meadows, wetlands and aquatic environments, and alpine tundra.28 The Southern Rockies also includes the ranges of Cynomys ludovicianus, C. leucurus, and C. gunnisoni, which are all highly susceptible to plague, with prairie dog colony mortality rates often reaching 100% during an outbreak.28–30 Cynomys spp. are associated with a decreased natal dispersal rate relative to other rodents implicated in the spread and maintenance of plague throughout its range, such as ground squirrels.31,32 Thus, a decreased velocity of disease spread might be expected. However in the early to mid-1940s, these species were considered to be pests to ranchers, who also recognized that they were being killed off by some disease in certain locations. There are at least three confirmed cases of ranchers driving more than 400 km to catch diseased rodents and release them in prairie dog colonies on their own land.11 In addition to these accounts, there is evidence indicating that this practice was fairly common.11 These translocations likely resulted in Y. pestis spreading across the Southern Rockies at a rate that is much greater than would otherwise be expected and may explain why this ecoregion is associated with a significant increase in velocity in all of our models.
Two of the models identify the Pacific coast as being significantly associated with a decrease in velocity of 28 km/year and 44 km/year, respectively. This ecoregion includes the initial introduction site(s) of plague into the continental United States, which implies an initially slow invasion rate into the surrounding wild rodent populations compared with the faster rates observed once plague became established enzootically. Keeling theorized that invading organisms are initially highly aggregated, thus limiting the expected rate of their spatial spread.33 Additionally, the contact structure between individuals largely determines how a disease progresses,33 and in high-density urban areas, greater contact rates occurring in smaller areas will likely limit the velocity of disease spread.
Perhaps a slow invasion rate is the reason why plague did not become established endemically in other parts of the continental United States where it was previously introduced. For instance, from 1914 through 1915, there was a large human plague outbreak in Orleans Parish, Louisiana resulting in 31 cases, and again from 1919 through 1920 in Orleans Parish, Louisiana; Jefferson, Harris, and Galveston Counties in Texas; and Escambia County, Florida, resulting in 61 cases (Centers for Disease Control and Prevention, unpublished data). Similarly, incoming ships in New York in 1899 reportedly carried human plague cases.25,34 However, available historical records indicate that plague did not become established in these or the surrounding areas. These apparently failed invasions could be due to stochastically driven chance events, which can have a significant influence over the outcome of an invasion when only a small number of diseased individuals exists.35 It is also possible that slower invasion rates permit enough time for plague to be recognized, quarantined, and eradicated. When plague invaded Honolulu in 1899, it was definitively identified by authorities who then sought to eradicate the disease by burning down the houses of persons with plague, who were all Chinese immigrants.36 However, in San Francisco, local authorities largely denied the existence of plague in the city to avoid negative economic impacts. Although its presence was acknowledged in China-town, and a quarantine was imposed, non-Chinese businesses present within the controlled area were exempt from these restrictions.34 These actions likely facilitated the invasion and eventual establishment of plague into the continental United States, which provided ample time for the disease to spread through the urban rodent communities and into the surrounding wildlife populations.
Several other factors also significantly affected the velocity of the spread of plague (Tables 4 and 5), although these varied widely across models, a result that was also observed when comparing models generated by studies on the spread of rabies in the eastern United States.15,37 This is not surprising considering the extreme sensitivity of plague to the environment.22–24 The animal-only model using the TSA-generated velocities resulted in three significant factors, including the Southern Rockies, the Blue Mountains, and the mean minimum winter temperature. In contrast, the animal-only model using the directly calculated velocities found 12 predictors to be significant, several of which were also significant in the model using all plague cases. These overlapping variables include Mediterranean California and the previously mentioned Coast Range and Southern Rockies ecoregions. The similarities between these models suggest that the directly calculated velocities of the animal cases more closely resemble how plague spread when human cases were also considered. This implies that plague probably followed a more direct geographic path when transmitted between people and from infected wildlife to people, with the significant environmental factors either aiding or impeding that movement. Conversely, the spread of plague among wild rodent communities produced jagged traveling waves of plague that were sensitive to the spatial heterogeneities and climatic conditions encountered.
Overall, several important large-scale trends regarding how plague spread in the United States can be identified. First, plague entered the United States along the Pacific coast at definitely one and possibly three introduction sites, and at a much slower rate than was later observed once it became established enzootically. These introduction sites represent largely populated urban areas, and are likely the only instances where human cases occurred in an area prior to its enzootic establishment. Also, according to the conclusions of Noble on the spread of pneumonic plague in Europe,11 it is possible that the dynamics of plague in these urban sites more closely operate under a pure reaction-diffusion model. A closer historical examination of the spread of plague within San Francisco may show a pattern similar to that observed during the Black Death in Europe. Second, the baseline rates of disease spread were relatively consistent between models, which suggest that the true velocities of the traveling waves of plague likely fell within that range. This is validated by historical observations of how plague spread across Colorado. By the time plague reached Colorado, it was being carefully monitored by the United States government, and the wildlife die-offs were documented as they occurred. It appears that plague spread diagonally across Park County, CO at a rate of approximately 50–75 km/year,11 which is in agreement with the baseline rates reported in two of our regression models (and is just outside of the range reported in the third model). Third, a rapid increase in the velocity of the traveling wave of plague was observed as it spread across the large, mountainous ecoregion of the Southern Rockies, which was likely the result of anthropogenic translocations of diseased wildlife. Finally, the spread of plague across the western United States exhibits different patterns when wildlife cases are analyzed separately from all spatio-temporally unique cases observed. However, in all models, the spatio-temporal dynamics of plague appear to be highly sensitive to the existing environmental conditions and spatial heterogeneities of the landscape.
The conclusions of this study are based on the available historical records, which are limited to reports of cases that were actually observed and confirmed by people. Although there are historical reports of observed wildlife die-offs that appeared to be caused by a plague-like disease,10 it was necessary for this study to use only those reports where Y. pestis was confirmed to minimize the introduction of potential biases. Although these incidents could impact the observed path and rates at which plague may have traveled, should they in fact be due to plague, they represent only a small number of reports relative to the cases present in our database. Furthermore, all of these reports occur in areas where cases were reported to be within 1–3 years later. Thus, although their inclusion might exert a slight increase in the velocities calculated, they would not alter the large-scale trends observed using the global interpolation techniques we report here, which give tremendous insight into how plague spread across the United States landscape. It is also possible that additional invasions did result in the establishment of epizootic plague in remote areas where die-offs of wildlife went unnoticed, such as the introduction of plague into Galveston, TX and New Orleans, LA. However, by the time plague reached Idaho, Montana, and Colorado, it was being monitored by active surveillance and followed as it continued to progress eastward,11 thus limiting the likelihood that these documented invasions confounded our results.
Plague will never invade the United States as a novel disease again, although other diseases can and likely will.38 Furthermore, the possibility of the re-emergence of plague into areas where it once was, but is no longer found, such as in San Francisco and the surrounding coastal communities, remains a real risk because of more recent threats from bioterrorism and the reported existence of antibiotic-resistant strains of Y. pestis.39 Our models add support to the notion that slow invasion rates can be expected during disease introductions, and suggest that such threats could be effectively managed through the continuation of active surveillance, particularly in areas experiencing high levels of global traffic.
Average velocities of Yersinia pestis spread across the western United States by decade, calculated directly from the plague event data, with respect to San Francisco, CA (SF), Los Angeles, CA (LA),* and Seattle, WA (WA)* as potential introduction sites†
| Decade | Average velocity SF (km/year)‡ | Average velocity LA (km/year) | Average velocity WA (km/year) |
|---|---|---|---|
| * Average velocities calculated represent only those plague events labeled as potentially originating from Los Angeles or Seattle, in addition to San Franciso. | |||
| † NA = not available. | |||
| ‡ Cases representing Los Angeles and Seattle were not included in the average velocity calculations. | |||
| § Data on disease spread only extends to 1966. | |||
| 1900–1909 | 12.47 | NA | NA |
| 1910–1919 | 13.30 | NA | NA |
| 1920–1929 | 12.76 | 15.01 | NA |
| 1930–1939 | 30.73 | 37.18 | 41.91 |
| 1940–1949 | 44.96 | 45.24 | 57.85 |
| 1950–1959 | 32.38 | 31.38 | 54.35 |
| 1960–1969§ | 24.91 | 23.42 | 37.54 |
Final models selected from the trend-surface analysis (TSA) to explain the linear, quadratic, and cubic trends associated with the spread of Yersinia pestis across the western United States*
| Predictor | β | Standard error | P | |
|---|---|---|---|---|
| * Model 1 uses all spatio-temporally unique United States plague cases; Model 2 uses only animal cases. | ||||
| TSA Model 1 | Intercept | 1.689 × 10−1 | 2.856 | < 0.0001 |
| X | 6.877 × 10−2 | 1.785 × 10−2 | < 0.0005 | |
| Y | 6.363 × 10−2 | 1.305 × 10−2 | < 0.0001 | |
| X2 | −5.35 × 10−5 | 2.203 × 10−5 | < 0.02 | |
| Y2 | −5.149 × 10−5 | 1.237 × 10−5 | < 0.0001 | |
| XY | −1.336 × 10−4 | 3.372 × 10−5 | < 0.0002 | |
| (XY)2 | 5.397 × 10−8 | 1.635 × 10−8 | < 0.0002 | |
| (YX)2 | 5.648 × 10−8 | 1.836 × 10−8 | < 0.003 | |
| X3 | 1.311 × 10−8 | 7.439 × 10−9 | < 0.1 | |
| TSA Model 2 | Intercept | 1.839 × 101 | 3.075 | < 0.0001 |
| X | 4.828 × 10−2 | 1.445 × 10−2 | < 0.002 | |
| Y | 2.303 × 10−2 | 6.646 × 10−3 | < 0.002 | |
| X2 | 7.48 × 10−4 | 3.607 × 10−4 | < 0.06 | |
| XY | −6.860 × 10−5 | 1.660 × 10−5 | < 0.0005 | |
| (YX)2 | 3.660 × 10−8 | 1.110 × 10−8 | < 0.002 | |
| X3 | 7.543 × 10−9 | 5.397 × 10−9 | < 0.17 | |
Average velocities of Yersinia pestis spread across the western United States by decade according to models generated using trend-surface analysis (TSA)*
| Decade | Average velocity (km/year) TSA Model 1† | Average velocity (km/year) TSA Model 2‡ |
|---|---|---|
| * NA = not available. | ||
| † Uses all spatio-temporally unique plague cases. | ||
| ‡ Uses all spatio-temporally unique United States animal plague cases. | ||
| 1900–1909 | 8.97 | 14.11 |
| 1910–1919 | 9.19 | NA |
| 1920–1929 | 6.81 | 14.56 |
| 1930–1939 | 20.24 | 66.87 |
| 1940–1949 | 46.41 | 86.99 |
| 1950–1959 | 40.07 | NA |
| 1960–1969 | 72.48 | 126.59 |
Final model selected from a multiple linear regression analysis looking at the relationship between environmental factors and the velocity at which Yersinia pestis spread across the western United States*
| Predictor | β | Standard error | P |
|---|---|---|---|
| * CA = California; CO = Colorado; AZ = Arizona; NM = New Mexico. | |||
| Intercept | 43.51668 | 11.10018 | < 0.0002 |
| Mediterranean CA | −18.40633 | 5.73336 | < 0.002 |
| Coast Range | −28.43407 | 8.64705 | < 0.0015 |
| CO Plateau | 14.50138 | 5.47714 | < 0.01 |
| AZ/NM Plateau | 25.58397 | 5.05205 | < 0.0001 |
| Southern Rockies | 14.58454 | 4.38670 | < 0.0015 |
| Southwestern Tablelands | 15.43875 | 6.55331 | < 0.025 |
| Western High Plains | 24.03030 | 5.51095 | < 0.0001 |
| Chihuahuan Deserts | −22.24527 | 9.14647 | < 0.02 |
| Annual precipitation (in) | −1.60546 | 0.70593 | < 0.03 |
| Mean minimum winter Temperature (°F) | −0.56659 | 0.42435 | < 0.02 |
| Interaction term (Mean minimum winter temp. and precipitation) | 0.05664 | 0.02405 | < 0.025 |
Final models selected from the multiple linear regression analyses looking at the relationship between environmental factors and the velocity at which Yersinia pestis spread across the western United States*
| Predictor | β | Standard error | P | |
|---|---|---|---|---|
| * Model 1 was developed using the trend surface analysis–generated velocities; Model 2 was developed using the velocities calculated directly from the data. CA = California. | ||||
| Model 1 | Intercept | 86.7542 | 9.6441 | < 0.0001 |
| Blue Mountains | 32.3608 | 15.3318 | < 0.04 | |
| Southern Rockies | 43.7572 | 9.4804 | < 0.0001 | |
| Mean median winter temperature (°F) | −1.4083 | 0.4162 | < 0.0013 | |
| Model 2 | Intercept | 80.80537 | 15.2834 | < 0.0001 |
| Mediterranean CA | −18.43813 | 5.38906 | < 0.0013 | |
| Northwestern Forested Mountains | 6.20269 | 2.12044 | < 0.0003 | |
| North American Deserts | 6.61236 | 1.72993 | < 0.0008 | |
| Great Plains | 26.94602 | 2.57448 | < 0.0001 | |
| Coast Range | −43.84310 | 6.69676 | < 0.08 | |
| Central CA Valley | 11.38761 | 6.33473 | < 0.08 | |
| Sierra Nevada | −18.77345 | 3.51832 | < 0.0001 | |
| Eastern Cascades | −19.22669 | 5.01912 | < 0.0004 | |
| Blue Mountains | −7.14106 | 2.86675 | < 0.02 | |
| Southern Rockies | 5.73327 | 2.11386 | < 0.01 | |
| Mean maximum summer temperature (°F) | −0.59329 | 0.17356 | < 0.0013 | |
| Annual snowfall (in) | −0.06964 | 0.02572 | < 0.01 | |
Spatio-temporal distribution of spatially unique reports of plague cases in the United States, 1900–1966. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
Spatio-temporal distribution of spatially unique reports of plague cases in the United States, 1900–1966. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
Spatio-temporal distribution of spatially unique reports of plague cases in the United States, 1900–1966. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
A, Predicted traveling waves of plague through the United States as interpolated by a trend-surface analysis model using all spatio-temporally unique plague case reports, 1900–1966. Estimates cannot be accurately predicted along the edges of the spatial range. B, Predicted traveling waves of plague through the United States as interpolated by a trend-surface analysis model using all spatio-temporally unique animal plague case reports, 1900–1966. Estimates cannot be accurately predicted along the edges of the spatial range. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
A, Predicted traveling waves of plague through the United States as interpolated by a trend-surface analysis model using all spatio-temporally unique plague case reports, 1900–1966. Estimates cannot be accurately predicted along the edges of the spatial range. B, Predicted traveling waves of plague through the United States as interpolated by a trend-surface analysis model using all spatio-temporally unique animal plague case reports, 1900–1966. Estimates cannot be accurately predicted along the edges of the spatial range. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
A, Predicted traveling waves of plague through the United States as interpolated by a trend-surface analysis model using all spatio-temporally unique plague case reports, 1900–1966. Estimates cannot be accurately predicted along the edges of the spatial range. B, Predicted traveling waves of plague through the United States as interpolated by a trend-surface analysis model using all spatio-temporally unique animal plague case reports, 1900–1966. Estimates cannot be accurately predicted along the edges of the spatial range. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
A, Spatio-temporal distribution of plague in the United States as predicted using a kriging interpolation model on all spatio-temporally unique plague case reports. Estimates cannot be accurately predicted along the edges of the spatial range. Each line represents a year. B, Spatio-temporal distribution of plague in the United States as predicted using a kriging interpolation model on all spatio-temporally unique animal plague case reports. Estimates cannot be accurately predicted along the edges of the spatial range. Each line represents a year. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
A, Spatio-temporal distribution of plague in the United States as predicted using a kriging interpolation model on all spatio-temporally unique plague case reports. Estimates cannot be accurately predicted along the edges of the spatial range. Each line represents a year. B, Spatio-temporal distribution of plague in the United States as predicted using a kriging interpolation model on all spatio-temporally unique animal plague case reports. Estimates cannot be accurately predicted along the edges of the spatial range. Each line represents a year. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
A, Spatio-temporal distribution of plague in the United States as predicted using a kriging interpolation model on all spatio-temporally unique plague case reports. Estimates cannot be accurately predicted along the edges of the spatial range. Each line represents a year. B, Spatio-temporal distribution of plague in the United States as predicted using a kriging interpolation model on all spatio-temporally unique animal plague case reports. Estimates cannot be accurately predicted along the edges of the spatial range. Each line represents a year. This figure appears in color at www.ajtmh.org.
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 76, 2; 10.4269/ajtmh.2007.76.365
Address correspondence to Jennifer Zipser Adjemian, Department of Medicine and Epidemiology, School of Veterinary Medicine, University of California, Davis, CA 95616. E-mail: jczipser@ucdavis.edu
Authors’ addresses: Jennifer Zipser Adjemian and Janet E. Foley, Department of Medicine and Epidemiology, School of Veterinary Medicine, University of California, Davis, CA 95616. Patrick Foley, Department of Biological Sciences, California State University, Sacramento, CA 95819. Kenneth L. Gage, Bacterial Zoonoses Branch, Division of Vector-Borne Infectious Diseases, National Center for Infectious Diseases, Centers for Disease Control and Prevention, Fort Collins, CO 80522.
Acknowledgments: We thank the Centers of Disease Control (Fort Collins, CO) for providing historical data, and James Case and Dan Sherez for technical expertise that facilitated all ArcGIS analyses conducted. We also thank the members of the Foley Laboratory for many thoughtful discussions on the theory behind infectious disease invasions and reaction-diffusion processes, and two anonymous reviewers for their insightful comments.
Disclaimer: The findings and conclusions of this article are those of the author(s) and do not necessarily reflect the views of the Department of Health and Human Services.
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