摘要
利用动力系统的理论研究一类具有时滞的周期logistic反应扩散传染病模型的动力学.首先证明了周期解半流对应ω算子的全局吸引子的存在性.然后利用次代算子方法引入了模型的基本再生数.最后,利用持久性理论结合比较原理,得到了疾病持久或灭绝的阈值条件:若基本再生数小于1,无病周期解是全局渐近稳定的,疾病将逐渐消失;若基本再生数大于1,系统一致持久,疾病将继续流行并最终形成地方病.
The dynamics of periodic reaction-diffusion epidemic models with delay and logistic growth was investigated based on the theory of dynamic systems. Firstly,the existence of the global attractor of theω operator associated with the periodic semiflow was proved. Next,the basic reproduction number of the model was introduced via the next generation operator. Finally,by means of the persistence theory and the comparison principle,the sufficient conditions for the disease persistence and extinction were obtained.If the basic reproduction number is less than 1,the disease-free periodic solution will be globally asymptotically stable and the disease will go extinct. If the basic reproduction number is greater than 1,the system will be uniformly persistent and the disease will become endemic.
引文
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