Dynamical behaviors of a network-based SIR epidemic model with saturated incidence and pulse vaccination

Pulse vaccination is an effective strategy to restrain the spread of infectious diseases. This paper proposes a network-based SIR epidemic model incorporating a saturated force of infection and vertical transmission along with pulse vaccination strategy and continuous treatment plan. Dynamical behaviors of the model are analyzed in virtue of the theory for impulsive differential equations. We give the boundedness of solutions and derive the expression of basic reproduction number R0. By the Floquet theorem and comparison principle, we show that the disease-free periodic solution is globally asymptotically stable when R0<1. Moreover, a sufficient condition for the uniform permanence of the system is also obtained. Finally, numerical analyses are given to substantiate the theoretical results and a case for Rubella is studied.