Abstract
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 R0, 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 mbox{R}_{0}<1 and is unstable otherwise. Moreover, we found that the dengue infection is uniformly persistent for the proposed system if mbox{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.
Highlights
It is evident that vector-borne diseases are induced by pathogenic agents such as helminths, viruses, protozoa, and bacteria
This article is ordered as follows: in Sect. 2 of the article, we introduce the dynamics of dengue fever with periodic transmission functions and impulsive vaccination strategies
As more than 50 percent of the world population are in regions with threat of dengue infection and the economic weight of dengue is increasing day by day, pulse vaccination is a beneficial strategy to lower the risk of infection and reduce the economic burden, compared with continuous vaccination strategy in endemic area of dengue fever to control the disease
Summary
It is evident that vector-borne diseases are induced by pathogenic agents such as helminths, viruses, protozoa, and bacteria. The target of this work is to initiate a dynamical model for dengue fever with periodic transmission functions and pulse vaccination. 2 of the article, we introduce the dynamics of dengue fever with periodic transmission functions and impulsive vaccination strategies. We introduce periodic transmission rates and seasonality in the vector population to represent more realistically the phenomena of dengue infection. We present that the impulsive dynamical system (6) admits a positive periodic, and globally asymptotically stable solution. Lemma 2.1 The impulsive dynamical system (6) has a positive periodic globally asymptotically stable solution b y(t) = +. We have a positive periodic globally asymptotically stable solution of the impulsive system (6), given by b y(t) = +.
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