Dynamics of an SIR epidemic model with stage structure and pulse vaccination

Abstract

Pulse vaccination is an important strategy to eradicate an infectious disease. In this paper, we investigate an SIR epidemic model with stage structure and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, we obtain the conditions for the global asymptotical stability of the infection-free periodic solution of the studied system. The permanent conditions of the investigated system are also given. The results indicate that a large pulse vaccination rate is a sufficient condition to eradicate the disease. It provides a reliable tactic basis for preventing the epidemic outbreak.

Stability and Hopf Bifurcation Analysis of an Epidemic Model with Time Delay

“…And then, many infectious diseases with sage structure have been built and investigated [9][10][11][12][13][14]. Xiao and Chen [15] improved (1) by separating the population into mature and immature and supposing that only the immature were susceptible to the infection.…”

An extended epidemic model with vaccination: Weak-immune SIRVI

“…The finale size of an epidemic was computed for a two-group SIR epidemic model in [8] . In order to completely eradicate an infectious disease, pulse vaccination was suggested in [9] , which was also pointed out in [7] . In [10] , the SIR model was extended to vaccinated and reinfected after vaccinated in order to simulate the direct and indirect effects of influenza vaccination within a population exposed to seasonal transmission of four influenza strains, and it was concluded that when the reproduction number is close to the endemic value, indirect vaccination effects are stronger.…”

Computational modeling of human papillomavirus with impulsive vaccination

“…Some scholars, for instance, the authors [8,[15][16][17], have studied the basic SIR and SIS models as impulsive differential equations by applying pulse vaccination. Currently, there are also published reports of the dynamic study of the infectious disease models with pulse vaccination [12,[18][19][20][21][22][23]. For example, the authors [19] investigated the global stability of a SIR epidemic model with impulsive vaccination, and the authors [18] investigated an optimal control impulsive SQEIAR epidemic of COVID-19; the authors [12] also analyzed a SIR optimal impulse vaccination model for a short period of time.…”