The Computational Approach for the Basic Reproduction Number of Epidemic Models on Complex Networks

The basic reproduction number plays an important role in exploring the dynamics of the epidemic models. Such value has been extensively used in the estimation of how severe an epidemic outbreak. Although several methods for calculating the basic reproduction number has been proposed, there isn't an effectively universal method to estimate such value. In this paper, we propose a general approach to calculate the explicit formulation of the basic reproduction number by the renewal equation. We apply such a method to estimate the basic reproduction number of many epidemic models on complex networks consisting of mean-field models, pairwise models, and edge-based compartmental models.