Modeling and statistical analysis of the spatio-temporal patterns of seasonal influenza in Israel.

Background: Seasonal influenza outbreaks are a serious burden for public health worldwide and cause morbidity to millions of people each year. In the temperate zone influenza is predominantly seasonal, with epidemics occurring every winter, but the severity of the outbreaks vary substantially between years. In this study we used a highly detailed database, which gave us both temporal and spatial information of influenza dynamics in Israel in the years 1998-2009. We use a discrete-time stochastic epidemic SIR model to find estimates and credible confidence intervals of key epidemiological parameters.

Findings: Despite the biological complexity of the disease we found that a simple SIR-type model can be fitted successfully to the seasonal influenza data. This was true at both the national levels and at the scale of single cities.The effective reproductive number R(e) varies between the different years both nationally and among Israeli cities. However, we did not find differences in R(e) between different Israeli cities within a year. R(e) was positively correlated to the strength of the spatial synchronization in Israel. For those years in which the disease was more "infectious", then outbreaks in different cities tended to occur with smaller time lags. Our spatial analysis demonstrates that both the timing and the strength of the outbreak within a year are highly synchronized between the Israeli cities. We extend the spatial analysis to demonstrate the existence of high synchrony between Israeli and French influenza outbreaks.

Conclusions: The data analysis combined with mathematical modeling provided a better understanding of the spatio-temporal and synchronization dynamics of influenza in Israel and between Israel and France. Altogether, we show that despite major differences in demography and weather conditions intra-annual influenza epidemics are tightly synchronized in both their timing and magnitude, while they may vary greatly between years. The predominance of a similar main strain of influenza, combined with population mixing serve to enhance local and global influenza synchronization within an influenza season.