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Characterizing the reproduction number of epidemics with early sub-exponential growth dynamics

ABSTRACT

The reproduction number is a central parameter in epidemiology used to quantify the average number of secondary cases generated by a primary infectious individual during the early epidemic growth phase. Existing methods to estimate the reproduction number generally assume early exponential epidemic growth, but do not account for the possibility of early sub-exponential (i.e., polynomial) growth. Here, we introduce a novel method for estimating the reproduction number without making explicit assumptions about the early epidemic growth profile. We demonstrate our methods using both synthetic and real epidemic datasets. Our results indicate that the effective reproduction number for epidemics characterized by early sub-exponential growth exhibits a natural downward trend over time approaching unity, even in the absence of control interventions, or depletion of susceptibles. This pattern is in stark contrast with the invariant reproduction number predicted for epidemics with an initial exponential growth phase. Our findings provide a compelling argument for understanding the early extinction of some emerging disease outbreaks during the early ascending phase of sub-exponential growth. A reliable data-driven characterization of the early epidemic phase is crucial for estimating the reproduction number, forecasting disease dynamics, and guiding public health intervention strategies.