Research Article A Spatial-Temporal ARMA Model of the Incidence of Hand, Foot, and Mouth Disease in Wenzhou, China Jie Li, 1 Yanjun Fu, 1 Ancha Xu, 1 Zumu Zhou, 2 and Weiming Wang 1 1 College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China 2 Wenzhou Center for Disease Control and Prevention, Wenzhou 325000, China Correspondence should be addressed to Ancha Xu; xuancha@wzu.edu.cn and Weiming Wang; weimingwang2003@163.com Received 21 January 2014; Accepted 27 January 2014; Published 3 March 2014 Academic Editor: Kaifa Wang Copyright © 2014 Jie Li et al. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. To investigate the variability of HFMD in each county of Wenzhou, a spatial-temporal ARMA model is presented, and a general Bayesian framework is given for parameter estimation. he proposed model has two advantages: (i) allowing time series to be correlated, thus it can describe the series both spatially and temporally; (ii) implementing forecast easily. Based on the HFMD data in Wenzhou, we ind that HFMD had positive spatial autocorrelation and the incidence seasonal peak was between May and July. In the county-level analysis, we ind that ater irst-order diference the spatial-temporal ARMA (0,0)×(1,0) 12 model provides an adequate it to the data. 1. Introduction Hand, foot, and mouth disease (HFMD) is a common infectious disease which usually afects children, particularly those less than 5 years old and younger. It is characterized by a distinct clinical presentation of fever or vesicular exanthema on their hands, feet, mouths, or buttocks [1–5]. he transmission of HFMD occurs from person to person through direct contact with saliva, faeces, vesicular luid, or respiratory droplets of an infected person and indirectly by contaminated articles [1]. Ater a susceptible individual is infected he irstly enters the incubation period of HFMD, which is about 3 to 7 days. Ater the incubation period, the infected will show some clinical symptoms, such as having a fever, poor appetite, malaise, and sore throat, and few people may develop dehydration, febrile seizures, encephalitis, meningitis, cardiomyopathy, and so forth. And the infected people will fully recover ater 7 to 10 days [1]. At present, there are still no available efective vaccines or drugs against HFMD human use, but such vaccines are being developed [6]. In 2012, for instance, an epidemic in mainland China involved 2,168,737 cases and 567 deaths [2]. Particularly, in 2012, there were 147,941 HFMD cases and 17 deaths in Zhejiang province, and it ranks the irst in the ”Ten legal infectious disease” [7]. HFMD has become an emerging public health concern in the afected countries and a focus of increasing amounts of research [4]. herefore, it is important to use mathematical models to improve our understanding of infectious disease dynamics of HFMD and to help us develop preventive measures to control infection spread qualitatively and quantitatively. here are several types of analytical models that are valuable to understand and predict the transmission of HFMD. One is compartmental diferential equation model [8–15], which is important to understand the spread dynam- ics of HFMD among the susceptible populations and to enable policy makers to take efective measures to curb the disease spread and reduce the adverse impact of the disease [9, 10]. he other is statistical models which can help us ind novel information concerning pathogen detection and some probable coinfection factors in HFMD and have been applied to understand HFMD’s spatiotemporal transmission and discover the relationship between HFMD occurrence and climate [3, 16–29]. Of them, Hu et al. [4] explored the spatial association of HFMD incidence with several potential determinants and found that child population density and climate factors are potential determinants of the HFMD incidence in most areas in China. Liu et al. [5] conducted Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014, Article ID 238724, 9 pages http://dx.doi.org/10.1155/2014/238724