Comparison of two mean-field based theoretical analysis methods for SIS model: Classical MF reaction equation and a modified equation

•For SIS model, exploring the difference between classical mean-field theory and simulation.•A new equation based on classical MF theory equation, which is more consistent with the simulation, is proposed.•Taylor's expansion is applied to compare the computation of critical infection rate λc.•A case study on small-world networks is proceeded to verify the results.

Epidemic spreading has been intensively studied in SIS epidemic model. Although the mean-field theory of SIS model has been widely used in the research, there is a lack of comparative results between different theoretical calculations, and the differences between them should be systematically explained. In this paper, we have compared different theoretical solutions for mean-field theory and explained the underlying reason. We first describe the differences between different equations for mean-field theory in different networks. The results show that the difference between mean-field reaction equations is due to the different probability consideration for the infection process. This finding will help us to design better theoretical solutions for epidemic models.