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Zhang, Tongqian; Meng, Xinzhu; Zhang, Tonghua

SVEIRS: A new epidemic disease model with time delays and impulsive effects. (English) Zbl 1474.92128

Abstr. Appl. Anal. 2014, Article ID 542154, 15 p. (2014).
Summary: We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input.

Cited in 11 Documents

MSC:

92D30 Epidemiology
34K45 Functional-differential equations with impulses
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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