具有非线性发生率的诺如病毒传播动力学模型分析  

Dynamic model analysis of Norovirus transmission with nonlinear incidence

作　　者：秦海燕 侯强[1] QIN Haiyan;HOU Qiang(School of Science,North University of China,Taiyuan,Shanxi 030051,China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《河北科技大学学报》2021年第2期127-134,共8页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(11501528)。

摘　　要：为了减少因诺如病毒感染引起的感染性腹泻对人们身体健康造成的危害,在明确诺如病毒传播特征的基础上,研究了诺如病毒的传播动力学行为,考虑感染诺如病毒的潜伏者也传染疾病的特性,建立具有非线性发生率的诺如病毒传播动力学模型,在计算模型的基本再生数R_(0)的基础上,利用Lyapunov函数和几何方法证明了无病平衡点和地方病平衡点的稳定性,并进行了数值模拟。结果表明,当R_(0)≤1时,无病平衡点全局渐近稳定,疾病消失;当R_(0)>1时,在一定条件下,地方病平衡点全局渐近稳定。数值模拟验证了理论结果的正确性。研究结果丰富了感染性病毒传播理论,对进一步研究病毒的传播机理具有借鉴意义。In order to reduce the great harm of infectious diarrhoeal disease caused by Norovirus infection to human health,based on the transmission characteristics of Norovirus,the transmission dynamics behavior of Norovirus was studied.Taking into account the characteristics that the latent infected with Norovirus can also transmit the disease,a dynamic model of Norovirus transmission with nonlinear incidence was established.The basic reproduction number R_(0)of the model was calculated and then the stability of the disease-free equilibrium point and the endemic equilibrium point were proved by using the Lyapunov function and the geometric method.The results show that when R_(0)≤1,the disease-free equilibrium point is globally asymptotically stable and the disease disappears;when R_(0)>1,under certain conditions,the endemic equilibrium point is global asymptotically stable.The theoretical results are verified by numerical simulation.The research results have enriched the theory of infectious virus transmission and provide a reference for the study of virus transmission mechanism.

关 键 词：稳定性理论 诺如病毒 传染病模型 非线性发生率 基本再生数 

分 类 号：O175.1[理学—数学]