Spatial transmission network construction of influenza-like illness using dynamic Bayesian network and vector-autoregressive moving average model

Abstract

Background: Although vaccination is one of the main countermeasures against influenza epidemic, it is highly essential to make informed prevention decisions to guarantee that limited vaccination resources are allocated to the places where they are most needed. Hence, one of the fundamental steps for decision making in influenza prevention is to characterize its spatio-temporal trend, especially on the key problem about how influenza transmits among adjacent places and how much impact the influenza of one place could have on its neighbors. To solve this problem while avoiding too much additional time-consuming work on data collection, this study proposed a new concept of spatio-temporal route as well as its estimation methods to construct the influenza transmission network.

Methods: The influenza-like illness (ILI) data of Sichuan province in 21 cities was collected from 2010 to 2016. A joint pattern based on the dynamic Bayesian network (DBN) model and the vector autoregressive moving average (VARMA) model was utilized to estimate the spatio-temporal routes, which were applied to the two stages of learning process respectively, namely structure learning and parameter learning. In structure learning, the first-order conditional dependencies approximation algorithm was used to generate the DBN, which could visualize the spatio-temporal routes of influenza among adjacent cities and infer which cities have impacts on others in influenza transmission. In parameter learning, the VARMA model was adopted to estimate the strength of these impacts. Finally, all the estimated spatio-temporal routes were put together to form the final influenza transmission network.

Results: The results showed that the period of influenza transmission cycle was longer in Western Sichuan and Chengdu Plain than that in Northeastern Sichuan, and there would be potential spatio-temporal routes of influenza from bordering provinces or municipalities into Sichuan province. Furthermore, this study also pointed out several estimated spatio-temporal routes with relatively high strength of associations, which could serve as clues of hot spot areas detection for influenza surveillance.

Conclusions: This study proposed a new framework for exploring the potentially stable spatio-temporal routes between different places and measuring specific the sizes of transmission effects. It could help making timely and reliable prediction of the spatio-temporal trend of infectious diseases, and further determining the possible key areas of the next epidemic by considering their neighbors' incidence and the transmission relationships.

Keywords: Dynamic Bayesian network; Influenza; Spatial transmission network; Spatio-temporal route; Vector autoregressive moving average model.

Fig. 1

The ILI% time series in Sichuan surveillance sentinels, 2010–2016. *The time series of ILI% in Sichuan was generally stable from 2010 to 2016, with maximum of 3.66% at week 237 and minimum of 1.69% at week 46

Fig. 2

The yearly ILI% time series in Sichuan surveillance sentinels, 2010–2016. *The time series of ILI% in different years were almost similar

Fig. 3

The Sequential-week lagged spatio-temporal routes of influenza among different cities. a 1-week lagged b 2-week lagged c 3-week lagged. *The No. of influenza spatio-temporal routes showed a decreasing trend in 3-week period. The maps of Sichuan were generated by R software

Fig. 4

1-week lagged influenza transmission network in different subregions of Sichuan province. (a) Western Sichuan subregion (b) Chengdu Plain subregion (c) Northeastern Sichuan subregion (d) Southern Sichuan subregion. *There were four cities with single-direction arrows pointing to other cities in the province while with no city in the province pointing to themselves, i.e., Ziyang, Guangyuan, Yibin and Panzhihua. The map of Sichuan was generated by R software