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Background  Hand, foot, and mouth disease (HFMD) is an infectious disease caused by a group of enteroviruses, including Coxsackievirus A16 (CVA16) and Enterovirus A71 (EV-A71). In recent decades, Asian countries have experienced frequent and widespread HFMD outbreaks, with deaths predominantly among children. In several Asian countries, epidemics usually peak in the late spring/early summer, with a second small peak in late autumn/early winter. We investigated the possible underlying association between the seasonality of HFMD epidemics and meteorological variables, which could improve our ability to predict HFMD epidemics.    Methods  We used a time series analysis composed of a spectral analysis based on the maximum entropy method (MEM) in the frequency domain and the nonlinear least squares method in the time domain. The time series analysis was applied to three kinds of monthly time series data collected in Wuhan, China, where high-quality surveillance data for HFMD have been collected: (i) reported cases of HFMD, (ii) reported cases of EV-A71 and CVA16 detected in HFMD patients, and (iii) meteorological variables.    Results  In the power spectral densities for HFMD and EV-A71, the dominant spectral lines were observed at frequency positions corresponding to 1-year and 6-month cycles. The optimum least squares fitting (LSF) curves calculated for the 1-year and 6-month cycles reproduced the bimodal cycles that were clearly observed in the HFMD and EV-A71 data. The peak months on the LSF curves for the HFMD data were consistent with those for the EV-A71 data. The risk of infection was relatively high at 10 °C ≤  t  < 15 °C ( t , temperature [°C]) and 15 °C ≤  t  < 20 °C, and peaked at 20 °C ≤  t  < 25 °C.    Conclusion  In this study, the HFMD infections occurring in Wuhan showed two seasonal peaks, in summer (June) and winter (November or December). The results obtained with a time series analysis suggest that the bimodal seasonal peaks in HFMD epidemics are attributable to EV-A71 epidemics. Our results suggest that controlling the spread of EV-A71 infections when the temperature is approximately 20–25 °C should be considered to prevent HFMD infections in Wuhan, China.    Electronic supplementary material  The online version of this article (doi:10.1186/s12879-015-1233-0) contains supplementary material, which is available to authorized users.

Time series analysis of reported cases of hand, foot, and mouth disease from 2010 to 2013 in Wuhan, China