Spatially Adjusted Time-varying Reproductive Numbers: Understanding the Geographical Expansion of Urban Dengue Outbreaks

The basic reproductive number (R(0)) is a fundamental measure used to quantify the transmission potential of an epidemic in public health practice. However, R(0) cannot reflect the time-varying nature of an epidemic. A time-varying effective reproductive number R(t) can provide more information because it tracks the subsequent evolution of transmission. However, since it neglects individual-level geographical variations in exposure risk, R(t) may smooth out interpersonal heterogeneous transmission potential, obscure high-risk spreaders, and hence hamper the effectiveness of control measures in spatial dimension. Therefore, this study proposes a new method for quantifying spatially adjusted (time-varying) reproductive numbers that reflects spatial heterogeneity in transmission potential among individuals. This new method estimates individual-level effective reproductive numbers (R(j)) and a summarized indicator for population-level time-varying reproductive number (R(t)). Data from the five most severe dengue outbreaks in southern Taiwan from 1998–2015 were used to demonstrate the ability of the method to highlight early spreaders contributing to the geographic expansion of dengue transmission. Our results show spatial heterogeneity in the transmission potential of dengue among individuals and identify the spreaders with the highest R(j) during the epidemic period. The results also reveal that super-spreaders are usually early spreaders that locate at the edges of the epidemic foci, which means that these cases could be the drivers of the expansion of the outbreak. Therefore, our proposed method depicts a more detailed spatial-temporal dengue transmission process and identifies the significant role of the edges of the epidemic foci, which could be weak spots in disease control and prevention.