Integration of a Kalman filter in the geographically weighted regression for modeling the transmission of hand, foot and mouth disease

Background: Hand, foot and mouth disease (HFMD) is a common infectious disease whose mechanism of transmission continues to remain a puzzle for researchers. The measurement and prediction of the HFMD incidence can be combined to improve the estimation accuracy, and provide a novel perspective to explore the spatiotemporal patterns and determinant factors of an HFMD epidemic.

Methods: In this study, we collected weekly HFMD incidence reports for a total of 138 districts in Shandong province, China, from May 2008 to March 2009. A Kalman filter was integrated with geographically weighted regression (GWR) to estimate the HFMD incidence. Spatiotemporal variation characteristics were explored and potential risk regions were identified, along with quantitatively evaluating the influence of meteorological and socioeconomic factors on the HFMD incidence.

Results: The results showed that the average error covariance of the estimated HFMD incidence by district was reduced from 0.3841 to 0.1846 compared to the measured incidence, indicating an overall improvement of over 50% in error reduction. Furthermore, three specific categories of potential risk regions of HFMD epidemics in Shandong were identified by the filter processing, with manifest filtering oscillations in the initial, local and long-term periods, respectively. Amongst meteorological and socioeconomic factors, the temperature and number of hospital beds per capita, respectively, were recognized as the dominant determinants that influence HFMD incidence variation.

Conclusions: The estimation accuracy of the HFMD incidence can be significantly improved by integrating a Kalman filter with GWR and the integration is effective for exploring spatiotemporal patterns and determinants of an HFMD epidemic. Our findings could help establish more accurate HFMD prevention and control strategies in Shandong. The present study demonstrates a novel approach to exploring spatiotemporal patterns and determinant factors of HFMD epidemics, and it can be easily extended to other regions and other infectious diseases similar to HFMD.