Impulsive vaccination and dispersal on dynamics of an SIR epidemic model with restricting infected individuals boarding transports☆

To understand the effect of impulsive vaccination and restricting infected individuals boarding transports on disease spread, we establish an SIR model with impulsive vaccination, impulsive dispersal and restricting infected individuals boarding transports. This SIR epidemic model for two regions, which are connected by transportation of non-infected individuals, portrays the evolvement of diseases. We prove that all solutions of the investigated system are uniformly ultimately bounded. We also prove that there exists globally asymptotically stable infection-free boundary periodic solution. The condition for permanence is discussed. It is concluded that the approach of impulsive vaccination and restricting infected individuals boarding transports provides reliable tactic basis for preventing disease spread.
Highlights • An SIR epidemic model with restricting infected individuals boarding transports was investigated. • Impulsive vaccination and dispersal are considered, which are more reasonable. • Two thresholds are obtained for Infection-free of the system.