The analysis of an epidemic model on networks

The paper consider an epidemic model with birth and death on networks. We derive the epidemic threshold R0 dependent on birth rate b, death rate d (natural death) and μ from the infectious disease and natural death, and cure rate γ. And the stability of the equilibriums (the disease-free equilibrium and endemic equilibrium) are analysed. Finally, the effects of various immunization schemes are studied and compared. We show that both targeted, and acquaintance immunization strategies compare favorably to a proportional scheme in terms of effectiveness. For active immunization, the threshold is easier to apply practically. To illustrate our theoretical analysis, some numerical simulations are also included.