Predicting the human burden of vector-borne diseases from limited surveillance data remains a major challenge, particularly in the presence of nonlinear transmission dynamics and delayed effects arising from vector ecology and human behavior. We develop a data-driven framework based on an extension of Sparse Identification of Nonlinear Dynamics to systems with distributed memory, enabling discovery of transmission mechanisms directly from time series data. Using severe fever with thrombocytopenia syndrome as a case study, we show that this approach can uncover key features of tick-borne disease dynamics using only human incidence and local temperature data, without imposing predefined assumptions on human case reporting. We further ascertain the robustness of the recovered incidence-temperature model by integrating it with mechanistically derived tick-host covariates, showing that the forecasting ability does not improve. This suggests that the proposed core data-driven model already delivers strong predictions. The framework also allows for systematic sensitivity analysis of memory kernels and behavioral parameters. Although the approach prioritizes predictive accuracy over mechanistic transparency, it yields sparse, interpretable integral representations suitable for epidemiological forecasting. This methodology provides a scalable strategy for forecasting vector-borne disease risk and informing public health decision-making under data limitations.
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