mei Li

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

Abstract 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.

Dynamics of a periodic switched predator–prey system with impulsive harvesting and hibernation of prey population ☆

Abstract Winter hibernation constitutes an effective strategy of animals in order to correspond survive cold environments and limited availability of food, it plays an important role in biological evolution. In this work, we firstly introduce hibernation behaviors of prey population into predator–prey systems with impulsive effect, then construct a periodic switched predator–prey system with winter hibernation in prey population and impulsive effect. We prove that the solutions of system (2.1) are uniformly ultimately bounded. We obtain the conditions of the globally asymptotically stable predator-extinction boundary periodic solution of system (2.1) , and also obtain the permanent conditions of system (2.1) . Finally, numerical analysis is employed to illustrate the results. Our results provide reliable tactic for the biological economics management and the protection of biodiversity.

Dynamics of a stage-structured single population system with winter hibernation and impulsive effect in polluted environment

In this work, we construct a stage-structured single population system with winter hibernation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the population-extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is inserted to illustrate the results. Our results indicate that the environmental pollution will reduce biological diversity of the natural world. Our results also provide reliable tactic basis for the practical biological resource management.