The spread of disease with birth and death on networks

We introduce a modified epidemic model on regular and scale-free networks. In this model, we consider the birth rate δ, cure rate γ, infection rate λ, and death rates α and β. Through mean-field analysis, we find that on a regular network there is an epidemic threshold λ c dependent on the parameters δ, γ, α, and β, while for a power law degree distribution network the epidemic threshold is absent in the thermodynamic limit. The result is the same as that of the standard SIS model. This reminds us that the structure of the networks plays a very important role in the spreading properties of infectious disease.