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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
Stability analysis of Toxoplasma gondii propagation model
Received:September 08, 2018  Revised:October 09, 2018
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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      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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