摘要
引入随机干扰和二次感染率,推广了一类COVID-19传染病模型,使用随机微分方程理论研究其动力学特征.首先,通过证明该模型全局正解的存在唯一性,说明该系统是适定的;其次,推导了模型中疾病灭绝和遍历平稳分布存在的充分条件,并分别给出了阈值表达式;最后,给定不同的随机干扰项和参数条件,借助数值模拟验证了理论分析的正确性.研究结果表明,随机干扰对COVID-19的传播有重要影响,二次感染加大了对疾病控制的需求.
An infectious disease model of COVID-19 is generalized via introducing random interference and reinfection,and the dynamic characteristics of the proposed model are analyzed by the theory of stochastic differential equation.Firstly,the existence and uniqueness of the global positive solution of the novel model are proved to indicate that it is well-posed.Secondly,the sufficient conditions of the extinction of disease and the existence of an ergodic stationary distribution of the model are established,and the threshold expressions are obtained respectively.Finally,the numerical simulations are carried out with different random interferences and parameter conditions to validate the theoretical results.The results indicate that random interference has an important impact on the spread of COVID-19,and the reinfection has increased the demand for disease control.
作者
李文凯
石剑平
李昌照
LI Wenkai;SHI Jianping;LI Changzhao(Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China)
出处
《昆明理工大学学报(自然科学版)》
北大核心
2025年第6期219-230,共12页
Journal of Kunming University of Science and Technology(Natural Science)
基金
国家自然科学基金项目(11561034)
云南省自然科学基金项目(202401AT070395)。
