Abstract
This paper presents practical methodologies for determining effective reproduction numbers, R(t), providing valuable insights for researchers and public health officials. It proposes multiple simplified approaches for estimating R(t) of infectious diseases and compares their effectiveness. These approaches include methods based on exponential, fixed (delta), normal, and gamma distributions for the generation time. The exponential and fixed generation time methods offer convenience as they rely solely on the mean generation time and the number of new infections. However, they are sensitive to the variance of the generation time distribution: the exponential method may underestimate R(t) when the variance is small, while the fixed generation time method may overestimate R(t) when the variance is large. The normal distribution method also risks underestimation, depending on the growth rate. In contrast, the gamma distribution method demonstrates greater robustness and accuracy across a variety of scenarios. A key contribution of this work is the consolidated presentation of these estimation methods, along with the novel derivation of an accurate R(t) formula based on the gamma distribution. This research offers practical guidance for selecting the most appropriate R(t) estimation method, emphasizing the importance of accounting for the specific characteristics of the infectious disease's generation time distribution.