一类具有脉冲接种疾病模型的性态分析

Analysis of the Behavior of a Disease Model with Impulsive Vaccination

传染病是危机人类身体健康的重要因素之一,人类要进步、健康发展就必须采取有效措施来预防、控制和消灭传染病。研究了一类在固定时刻对易感人群以一定比例进行接种即脉冲接种来控制的含有潜伏期的SEIR疾病模型的动力学性态。通过频闪映射求解了该模型无病周期解的存在性,应用Floquet定理研究了该种疾病模型无病周期解的局部稳定性,确保疾病的可控性,最后利用脉冲微分不等式最终证明了无病周期解也具有全局渐近稳定性。从而表明该种疾病在脉冲接种后疾病可以控制,最终可趋于平稳状态。

Infectious diseases are one of the important factors threatening human health.If human beings want to make progress and develop healthily,they must take effective measures to prevent,control and eliminate infectious diseases.The dynamic behavior of a kind of SEIR disease model with incubation period,which is controlled by a certain proportion of susceptible population at a fixed time,namely pulse vaccination,is studied.The existence of disease-free periodic solution of this model is solved by stroboscopic mapping.The local stability of disease-free periodic solution of this disease model is studied by using Floquet theorem to ensure the controllability of the disease.Finally,it is proved that the disease-free periodic solution also has global asymptotic stability by using impulsive differential inequality.This shows that the disease can be controlled after pulse vaccination,and finally tends to a stable state.