An epidemic model with pulses for pest management

Using parasitic wasps that deliver lethal viruses to crop pests is a new way to protect crops. In this paper, we propose and analyze an epidemic model with birth pulse and pulse infection by virus, which periodic birth pulse and pulse infection occur at different fixed time. An exact cycle of the system and the threshold conditions for its stability are obtained. Some numerical simulations are given. Moreover, the sufficient conditions of global stability of semi-trivial periodic solutions are investigated. Our proposed strategy of delivering deadly viruses is effective and adequate from the environmental point of view.