Prediction of Cattle Fever Tick Outbreaks in United States Quarantine Zone

Data sources. Time series data on cattle fever tick incidence, 1959-2020, and climate variables January 1950 through December 2020, form the core information in this analysis. All variables are monthly averages or sums over the fiscal year, October 01 (of the prior calendar year, y-1) through September 30 of the current calendar year (y). Annual records on monthly new detections of Rhipicephalus microplus and R. annulatus (cattle fever tick, CFT) on premises within the Permanent Quarantine Zone (PQZ) were obtained from the Cattle Fever Tick Eradication Program (CFTEP) maintained jointly by the United States Department of Agriculture (USDA), Animal Plant Health Inspection Service and the USDA Animal Research Service in Laredo, Texas. Details of tick survey procedures, CFTEP program goals and history, and the geographic extent of the PQZ are in the main text, and in the Supporting Information (SI) of the associated paper. Data sources on oceanic indicators, on local meteorology, and their pretreatment are detailed in SI.

Data pretreatment. To address the low signal-to-noise ratio and non-independence of observations common in time series, we transformed all explanatory and response variables by using a series of six consecutive steps: (i) First differences (year y minus year y-1) were calculated, (ii) these were then converted to z scores (z = (x- μ) / σ, where x is the raw value, μ is the population mean, σ is the standard deviation of the population), (iii) linear regression was applied to remove any directional trends, (iv) moving averages (typically 11-year point-centered moving averages) were calculated for each variable, (v) a lag was applied if/when deemed necessary, and (vi) statistics calculated (r, n, df, P<, p<).

Principal component analysis (PCA). A matrix of z-score first differences of the 13 climate variables, and CFT (1960-2020), was entered into XLSTAT principal components analysis routine; we used Pearson correlation of the 14 x 60 matrix, and Varimax rotation of the first two components.

Autoregressive Integrated Moving Average (ARIMA). An ARIMA (2,0,0) model was selected among 7 test models in which the p, d, and q terms were varied, and selection made on the basis of lowest RMSE and AIC statistics, and reduction of partial autocorrelation outcomes. A best model linear regression of CFT values on ARIMA-predicted CFT was developed using XLSTAT linear regression software with the objective of examining statistical properties (r, n, df, P<, p<), including the Durbin-Watson index of order-1 autocorrelation, and Cook’s Di distance index. Cross-validation of the model was made by withholding the last 30, and then the first 30 observations in a pair of regressions.

Forecast of the next major CFT outbreak. It is generally recognized that the onset year of the first major CFT outbreak was not 1959, but may have occurred earlier in the decade. We postulated the actual underlying pattern is fully 44 years from the start to the end of a CFT cycle linked to external climatic drivers. (SI Appendix, Hypothesis on CFT cycles). The hypothetical reconstruction was projected one full CFT cycle into the future. To substantiate the projected trend, we generated a power spectrum analysis based on 1-year values of the 1959-2020 CFT dataset using SYSTAT AutoSignal software. The outcome included a forecast to 2100; this was compared to the hypothetical reconstruction and projection. Any differences were noted, and the start and end dates of the next major CFT outbreak identified.