摘要
传染病的传播途径是多种多样的,如:直接传播和间接传播等.在以往的传染病模型中,大多是只考虑直接传播对疾病的影响,而忽略了环境作用对疾病的影响,即间接传播的影响.其实,间接传播在传染病的传播中同样起着重要的作用,忽略间接传播的影响会低估基本再生数,从而错估传染病爆发的规模,给人类的健康带来更大的威胁.研究了一个既有直接传播又有间接传播的SⅣ传染病模型,通过研究模型的动力学行为,给出了无病平衡点和地方病平衡点全局渐近稳定的条件,并用数值模拟证实了该结果.
The transmission of infectious diseases are various, such as direct and indirect. However, we often consider the direct impact on the spread of disease, while ignoring the influence of environmental effects, which indirectly influence the communication. Actually, the indirect spread of infectious diseases plays an important role as the same as the direct ones, and we should pay attention to it. Without considering the impact of indirect communication can underestimate the basic reproduction number, furthermore, misvalue infectious disease outbreak, and result in more threat to human health. In this paper, we consider a SIV epidemic model with direct spread and indirect spread. Through the research of the dynamic behavior of the model; we conclude the disease-free equilibrium and the endemic equilibrium are globally asymptotically stable under certain conditions. Finally, the results are confirmed by numerical simulation.
出处
《数学的实践与认识》
北大核心
2016年第4期289-296,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(11371048)
北京市教育委员会科技计划面上项目(KM201210016007)
中央支持地方的项目(21147515602)
关键词
间接传播
直接传播
全局渐近稳定
传染病
indirect communication
direct transmission
global asymptotic stability
infectious diseases
