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.