Probabilistic logic analysis of the highly heterogeneous spatiotemporal HFRS incidence distribution in Heilongjiang province (China) during 2005-2013

Background: Hemorrhagic fever with renal syndrome (HFRS) is a zoonosis caused by hantavirus (belongs to Hantaviridae family). A large amount of HFRS cases occur in China, especially in the Heilongjiang Province, raising great concerns regarding public health. The distribution of these cases across space-time often exhibits highly heterogeneous characteristics. Hence, it is widely recognized that the improved mapping of heterogeneous HFRS distributions and the quantitative assessment of the space-time disease transition patterns can advance considerably the detection, prevention and control of epidemic outbreaks. Methods: A synthesis of space-time mapping and probabilistic logic is proposed to study the distribution of monthly HFRS population-standardized incidences in Heilongjiang province during the period 2005–2013. We introduce a class-dependent Bayesian maximum entropy (cd-BME) mapping method dividing the original dataset into discrete incidence classes that overcome data heterogeneity and skewness effects and can produce space-time HFRS incidence estimates together with their estimation accuracy. A ten-fold cross validation analysis is conducted to evaluate the performance of the proposed cd-BME implementation compared to the standard class-independent BME implementation. Incidence maps generated by cd-BME are used to study the spatiotemporal HFRS spread patterns. Further, the spatiotemporal dependence of HFRS incidences are measured in terms of probability logic indicators that link class-dependent HFRS incidences at different space-time points. These indicators convey useful complementary information regarding intraclass and interclass relationships, such as the change in HFRS transition probabilities between different incidence classes with increasing geographical distance and time separation. Results: Each HFRS class exhibited a distinct space-time variation structure in terms of its varying covariance parameters (shape, sill and correlation ranges). Given the heterogeneous features of the HFRS dataset, the cd-BME implementation demonstrated an improved ability to capture these features compared to the standard implementation (e.g., mean absolute error: 0.19 vs. 0.43 cases/105 capita) demonstrating a point outbreak character at high incidence levels and a non-point spread character at low levels. Intraclass HFRS variations were found to be considerably different than interclass HFRS variations. Certain incidence classes occurred frequently near one class but were rarely found adjacent to other classes. Different classes may share common boundaries or they may be surrounded completely by another class. The HFRS class 0–68.5% was the most dominant in the Heilongjiang province (covering more than 2/3 of the total area). The probabilities that certain incidence classes occur next to other classes were used to estimate the transitions between HFRS classes. Moreover, such probabilities described the dependency pattern of the space-time arrangement of HFRS patches occupied by the incidence classes. The HFRS transition probabilities also suggested the presence of both positive and negative relations among the main classes. The HFRS indicator plots offer complementary visualizations of the varying probabilities of transition between incidence classes, and so they describe the dependency pattern of the space-time arrangement of the HFRS patches occupied by the different classes. Conclusions: The cd-BME method combined with probabilistic logic indicators offer an accurate and informative quantitative representation of the heterogeneous HFRS incidences in the space-time domain, and the results thus obtained can be interpreted readily. The same methodological combination could also be used in the spatiotemporal modeling and prediction of other epidemics under similar circumstances. Author summary: Heilongjiang Province reported the largest number of HFRS cases in China. Previous studies focused on identifying the severe HFRS outbreak regions, exploring the relative impact of environmental factors, forecasting HFRS cases etc. However, the study of the spatiotemporal spread dynamics and patterns of HFRS is still lacking, which is the focus of the present study. This study proposed a novel mapping technique (i.e., class-dependent Bayesian Maximum Entropy, cd-BME) for studying the distribution of HFRS, overcoming the highly heterogeneous features of HFRS data; and, probabilistic logic notions (stochastic indicators) were employed to study the spatiotemporal dependency of HFRS incidence and draw conclusions regarding the HFRS spread under conditions of uncertainty. By dividing the original HFRS data into four classes in terms of percentiles, the cd-BME exhibited better performance in mapping HFRS distribution than the standard (class-independent) BME technique and the mainstream inverse distance technique. Regarding the maps of HFRS distribution, the point outbreak character dominated the HFRS spread at high incidence levels, whereas the lowest incidence level covered more than 2/3 of Heilongjiang Province. Certain HFRS incidence generally occurred between intraclass or neighbor classes. The probabilities of HFRS transition between incidence classes with various spatial distances and temporal instants can be found in the HFRS indicator plots. The above comprehensive information can allow a better understanding of the spatiotemporal HFRS spread mechanisms and further improve HFRS decision-making, management and control.