Plague is a rare but potentially fatal flea-borne zoonosis caused by Yersinia pestis. In the United States, plague occurs episodically in western states, with most cases reported from the Southwest.¹ Human plague is often associated with sporadically occurring epizootics, periods of time when Y. pestis spreads rapidly in susceptible rodent populations. Widespread rodent mortality during epizootics forces infected rodent fleas to seek new hosts, including humans.²

The timing of epizootics and increases in human plague cases have often been associated with increased rainfall and moderate summer temperatures.³ In the American Southwest, above-average precipitation was associated with higher-than-average reported cases.^4,5 Similar trends were described for plague cases among companion animals, which were significantly correlated with human cases in New Mexico.⁶ Temperature also played a significant role,^5,6 with cooler summer temperatures favoring transmission and very hot temperatures having a negative impact. The trophic cascade hypothesis provides a biological rationale for these associations. Specifically, increased precipitation is hypothesized to set the stage for epizootic transmission by building up food sources that promote increased rodent reproduction and populations in the next summer and that provide favorable conditions for the survival and reproduction of fleas. Increased contact between fleas and rodents is thought to increase the rate of Y. pestis transmission, resulting in epizootics. Extreme heat is proposed to counteract this by decreasing flea survival, Y. pestis transmission, and human–flea encounters, thereby reducing the number of human plague cases.^3,7

Understanding the relationship between weather and plague occurrence (weather–plague relationship) could be useful for forecasting periods of elevated risk. Given the generalizability of the trophic cascade hypothesis in the Southwest, we sought to 1) recreate a previous well-fitting model⁵ from northeastern Arizona (Climate Division 2; 1960–1997) and 2) assess if these relationships could predict observed case counts in the next 25 years (1998–2022). Although separate models were previously developed for Arizona and New Mexico,⁵ changes in case reporting prevented us from identifying which cases occurred in the New Mexico climate division in the recent 25 years (see Supplemental Text), so we focus only on Arizona.

To recreate this trophic cascade model,⁵ we fitted a Poisson generalized linear model (GLM; using the stats R package⁸) of human plague cases per plague year (defined previously⁵ as June 16–June 15) relative to temperature and lagged precipitation. We used lagged February to March precipitation (one- and two-plague year lags), lagged July to August precipitation (one-plague year lag), and “degree days” (90°F [32.2°C] and 95°F [35°C] thresholds) as covariates (Figure 1A, schematic). For this, we acquired monthly precipitation data for the climate division⁹ and calculated “degree days” (the annual number of days at least certain temperature thresholds) using maximum daily temperatures from Winslow Municipal Airport.¹⁰ We tabulated human plague data from case reports sent to CDC.^1,11 See Supplemental Figure 1 and Supplemental Text for case, temperature, and precipitation data details.

We were unable to recreate the model fit (Figure 1B, fit) using the presented description⁵ (Figure 1A, schematic). To produce the previous fit, degree days needed to correspond to the calendar year in which the June-to-June plague year ended (i.e., shifted forward in time) (compare Figure 1A and B). This resulted in a temporal mismatch between case and temperature data, with plague cases associated with future temperatures; each year, most days with temperatures ≥32.3°C (mean: 87.6%, range: 78.0–100%) and ≥35°C (mean: 93.3%, range: 75.8–100%) occurred after June 16 (1960–1997). Additionally, one-plague year lagged July to August precipitation was included in the original model, but we found it to be not significant here (P = 0.86) and thus, dropped the variable (Figure 1C) without degradation of fit (Supplemental Table 1). See Supplemental Text for additional details.

With the described temporal mismatch, the implemented model (Figure 1B) used future conditions that could not impact case occurrence. Therefore, we fitted a variety of models with biologically plausible relationships of temperature and plague occurrence to assess their relative fit and predictive performance (Table 1). These models included degree days for the calendar year in which the June-to-June plague year began (as intended in the original model; model 1) (Figure 1C), for the winter/spring of the plague year (January 1–June 15; model 3) (Figure 1D), for the summer of the plague year (June 16–September 30; model 4) (Figure 1E), and aligned to the plague year (June 16–June 15; model 5) (Figure 1F). The precipitation covariates as originally presented were not impacted by the mismatched timing, so we included both one- and two-plague year lagged February to March precipitation; one-plague year lagged July to August precipitation was not significant in any model and thus, was dropped (Supplemental Table 1). We also fitted a version of the model with the plague data aligned to the calendar year (January 1–December 31; model 8) (Figure 1G) for more intuitive temporal relationships and because it aligns with broad plague seasonality in the United States (Supplemental Figure 2). This model included lagged February to March precipitation (one- and two-year lags) and concurrent degree days (90°F and 95°F). Covariates for July to August precipitation were not significant at either one-year (P = 0.13) or two-year lags (P = 0.53) and were removed (Supplemental Table 1). Using both the June-to-June and calendar plague years, we fitted models without degree days (only lagged precipitation; models 6 and 9) and no weather covariates (“simple”; models 7 and 10) as comparisons for model training performance with less weather information. Model 7 was an autoregressive order-1 Poisson model to remove residual autocorrelation. Model 10 was an intercept-only Poisson GLM because we did not detect residual autocorrelation (Supplemental Text). We used each fitted model to predict human plague cases for 1998–2022, calculating training (1960–1997) and testing (1998–2022) error (Table 1). We assessed predictive accuracy of all models by determining the proportion of observations contained within 95% prediction intervals (PIs) (Supplemental Text).

Across models, the magnitude and direction of fitted coef-ficients were similar (Supplemental Figure 4; Supplemental Tables 2–11) and aligned with the trophic cascade hypothesis; increased February to March precipitation, more days ≥32.3°C, and fewer days ≥35°C were associated with increased plague cases. All models had similar fit and predictive capacity as measured by mean absolute error (MAE) (Table 1). For example, with all training MAE between 0.79 and 1.36 cases, average fitted values differed from observed values by ≤1.36 plague cases per year.

Inclusion of future temperature (our recreation of the originally presented model⁵; model 2), inclusion of temperature from the summer of the plague year (model 4), or using a calendar plague year (model 8) resulted in the lowest training error (“best” model) (Table 1) and fitted well to the spikes in plague years 1983 and 1994 (Supplemental Figure 3A and C). Other models underpredicted the 1983 spike. For models with June-to-June plague years, model 1, our correctly time-matched recreation of the originally intended model⁵ (Figure 2A), had the best predictive performance (lowest testing MAE) (Table 1). For models that used a calendar plague year, model 8 had the best prediction (Figure 2B). “Simple” models had the worst fit (poor training performance), so we did not focus on their predictive capacity.

All models accurately predicted few human cases (fewer than or equal to two) with all observations within the 95% point-wise PIs, indicating “good” prediction. There were no instances when models failed to predict or incorrectly predicted elevated cases (four or more). Weather conditions associated with elevated cases (four or more) during the training period (1960–1997), >6 inches of combined precipitation over the two previous springs, were only observed in 2021 in the testing time frame (Supplemental Figure 7). No cases were reported that plague year, as was the case in 1980. We did not identify a difference in degree days between years with low or elevated cases (Supplemental Text). Thus, although this cumulative amount of spring precipitation may represent a threshold for increased human plague risk, additional factors are needed for elevated cases to occur. Identification of such conditions would provide useful information for public health.

In the original study,⁵ models were developed to describe historical trends and were not intended for prediction. The good fit of the trophic cascade model to the historical data included plausible biological relationships (increased precipitation before years with increased case counts mediated by high temperatures during the transmission season) but relied on an inadvertent temporal shift in degree day covariates. Our model recreation using the intended, biologically plausible relationships agreed with the trophic cascade hypothesis and accurately predicted low counts. Weather conditions were similar between low (fewer than or equal to two cases) years in the training and testing periods. As elevated precipitation totals previously associated with elevated cases (four or more) did not occur in the recent quarter century, we were unable to fully test the predictive accuracy of proposed trophic cascade associations in these more extreme cases. Thus, although weather appears to impact Y. pestis transmission,^12–16 conditions in northeastern Arizona did not enable us to fully test the accuracy of the proposed weather drivers of elevated plague cases; the impact and any underlying thresholds might be more apparent if evaluated in counties across the western United States where plague is endemic. Consideration of human socioeconomic risk factors might also improve prediction.^17,18 Additional work to identify factors associated with above-average cases across a wider area could further improve the usefulness of predictions for public health.