Epidemic spreading of an SEIRS model in scale-free networks

An SEIRS epidemic model on the scale-free networks is presented, where the active contact number of each vertex is assumed to be either constant or proportional to its degree for this model. Using the analytical method, we obtain the two threshold values for above two cases and find that the threshold value for constant contact is independent of the topology of the underlying networks. The existence of positive equilibrium is determined by threshold value. For a finite size of scale-free network, we prove the local stability of disease-free equilibrium and the permanence of the disease on the network. Furthermore, we investigate two major immunization strategies, random immunization and targeted immunization, some similar results are obtained. The simulation shows the positive equilibrium is stable.

Research highlights
► In this study we model an SEIRS epidemic model on the scale-free networks.
► Using the analytical method, we obtain the two threshold values for two cases and find that the threshold value for constant contact is independent of the topology of the underlying networks.
► The local stability of disease-free equilibrium and the permanence of the disease are studied on the finite size network.
► We investigate two major immunization strategies, random immunization and targeted immunization, some similar results are obtained. The results are benefical to the control of the epidemic.