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REN Lixia,XUE Yakui.Stability analysis of Toxoplasma gondii propagation model[J].Journal of Hebei University of Science and Technology,2018,39(6):511-517
弓形虫传播模型的稳定性分析
Stability analysis of Toxoplasma gondii propagation model
Received:September 08, 2018  Revised:October 09, 2018
DOI:10.7535/hbkd.2018yx06005
中文关键词:  稳定性理论  弓形虫  最终宿主  基本再生数  全局稳定性  Lyapunov函数
英文关键词:theory of stability  Toxoplasma gondii  final host  basic reproduction number  global stability  Lyapunov function
基金项目:国家自然科学基金(11201434); 山西省自然科学基金(2015022009)
Author NameAffiliationE-mail
REN Lixia School of Science North University of China Taiyuan  
XUE Yakui School of Science North University of China Taiyuan 3024664346@qq.com 
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中文摘要:
      为了研究控制弓形虫病传播的临界值,对疾病进行有效预防,并进行相关的理论分析与研究,针对弓形虫的生活史以及传播途径建立数学模型,分析得到了决定疾病是否继续存在以及传播的基本再生数,当基本再生数小于1时,疾病将逐渐消亡,最终灭绝,当基本再生数大于1时,模型存在唯一的地方病平衡点,此时疾病将一直持续下去,形成地方病。通过建立合适的Lyapunov函数等方法,给出了无病平衡点和地方病平衡点全局渐近稳定的充分条件,同时对建立的数学模型进行了系统、完整的定性和稳定性研究。研究结果对后续弓形虫病的研究及其数学模型的建立有一定的借鉴意义。
英文摘要:
      Toxoplasma gondii as a typical zoonotic disease, because there is no suitable vaccine, its control is important in prevention, so it has been the subject of research by all scholars. in order to study the critical value of controlling its transmission and carry out relevant theoretical analysis, This paper establishes a mathematical model based on the life history and transmission route of Toxoplasma gondii, and analyzes the basic regeneration number that determines whether the disease continues to exist. When the basic reproduction number is less than 1, the disease died out finally. When the basic reproduction number is greater than 1, the model had a unique endemic equilibrium point, and the disease uniformly persisted. In addition, the sufficient conditions for the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium are given by establishing a suitable Lyapunov function. In this paper, a systematic and complete stability study of the established mathematical model can be provided to provide advice for controlling the spread of disease.
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