Conventional empirical studies of foodborne-disease outbreaks (FDOs) in agricultural markets are linear-stochastic formulations hardwiring a world in which markets self-correct in response to external random shocks including FDOs. These formulations were unequipped to establish whether FDOs cause market reaction, or whether markets endogenously propagate outbreaks. We applied nonlinear time series analysis (NLTS) to reconstruct annual dynamics of FDOs in US cattle markets from CDC outbreak data, live cattle futures market prices, and USDA cattle inventories from 1967-2018, and used reconstructed dynamics to detect causality. Reconstructed deterministic nonlinear market dynamics are endogenously unstable-not self-correcting, and cattle inventories drive futures prices and FDOs attributed to beef in temporal patterns linked to a multi-decadal cattle cycle undetected in daily/weekly price movements investigated previously. Benchmarking real-world dynamics with NLTS offers more informative and credible empirical modeling at the convergence of natural and economic sciences.