Effect of pulse vaccination on dynamics of dengue with periodic transmission functions

Pulse vaccination is a repeated vaccination policy, which plays a tremendous role in the global fight against communicable diseases in terms of saving medical resources and decreasing the economic burden. In this article, we propose a dynamic model of dengue infection with periodic transmission functions and seasonality in vector population. Furthermore, we introduce a pulse vaccination strategy in the susceptible host population to examine how frequency and intensity of implementation of this strategy affect the dynamics of dengue infection. We successfully obtained the threshold dynamics by defining the basic reproduction number R-0, which is the spectral radius of the next generation operator and governs whether the disease dies out or not. It has been established that the infection-free periodic solution of the proposed impulsive system is globally asymptotically stable if R-0 < 1 and is unstable otherwise. Moreover, we found that the dengue infection is uniformly persistent for the proposed system if R-0 > 1. Finally, we execute the system numerically to illustrate the piecewise solutions of the proposed system with impulsive vaccination measure and to investigate the influence of different control parameters on the basic reproduction. The finding indicates that a frequent implementation of the vaccination strategy with great intensity and the use of mosquito nets can essentially lead to a decline of new infections.