Data-driven sparse identification of vector-borne disease dynamics with memory effects

TL;DR

The paper tackles forecasting human incidence of vector-borne diseases under data scarcity and memory effects by extending Sparse Identification of Nonlinear Dynamics (SINDy) to distributed-delay renewal equations. It learns memory kernels directly from time-series data (incidence and temperature) and couples these data-driven kernels with a mechanistic tick-host transmission model to improve predictions of Severe Fever with Thrombocytopenia Syndrome (SFTS) in Dalian. The authors demonstrate that sparse, interpretable integral representations can be recovered for memory kernels, and that predictive accuracy improves when the data-driven kernel is informed by established transmission pathways (systemic, co-feeding, transovarial) and tick life-stage dynamics. The study highlights a scalable, hybrid forecasting framework for vector-borne disease risk under data limitations, with potential applicability to other systems and scenarios requiring memory-aware dynamics.$ $The core predictive expression takes the form $\,\hat{y}(t)=\int_{0}^{\sigma} f(\cdot) \,\mathrm{d}a$, where past states contribute through a learned kernel, and shows robust performance when combined with mechanistic components that capture tick-host interactions and environmental drivers.

Abstract

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 (SINDy) to systems with distributed memory, enabling discovery of transmission mechanisms directly from time series data. Using severe fever with thrombocytopenia syndrome (SFTS) 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 demonstrate that predictive performance is substantially enhanced when the data-driven model is coupled with mechanistic representations of tick-host transmission pathways informed by empirical studies. The framework supports systematic sensitivity analysis of memory kernels and behavioral parameters, identifying those most influential for prediction accuracy. Although the approach prioritizes predictive accuracy over mechanistic transparency, it yields sparse, interpretable integral representations suitable for epidemiological forecasting. This hybrid methodology provides a scalable strategy for forecasting vector-borne disease risk and informing public health decision-making under data limitations.

Figures (7)

• Figure 1: Temporal connection between environmental and epidemiological factors in Dalian from 2011 to 2022 is illustrated. The blue solid line depicts the monthly average ambient temperature, whereas the red dashed line shows the monthly count of confirmed SFTS cases reported.
• Figure 2: Predictive performance of SINDy distributed delay model in forecasting SFTS cases involved utilizing two distinct polynomial order libraries within the candidate function set \ref{['eq:sindy_dd']}. The comparison of actual human case numbers (solid grey line) against SINDy predictions for polynomial degree one (blue line) and polynomial degree two (red line).
• Figure 3: Comparison of actual human cases of SFTS (grey line) with SINDy distributed delay model predictions using polynomial degrees one (blue) and two (red). The candidate library includes an exponential term $e^{\omega T}$\ref{['eq:sindy_dd_exp']} to represent temperature-dependent human outdoor activity effects. Polynomial degree one yields improved predictive accuracy.
• Figure 4: Validation of the enhanced SINDy model that integrates data of infected tick populations. The candidate library includes infected nymph and adult populations, as well as environmental and human epidemiological factors \ref{['eq:sindy_dd_exp_tina']}. Solid grey line: recorded SFTS cases; blue line: SINDy forecasts.
• Figure 5: Comparison of monthly reported cases (grey) with model predictions (blue) CSIAM-LS-1-2 and SINDy-based predictions (red) \ref{['eq:sindy_dd_exp_tina']}.