一类具有空间异质性SIS传染病模型的阈值动力学分析  

THRESHOLD DYNAMICS ANALYSIS OF A CLASS OF SIS INFECTIOUS DISEASE MODEL WITH SPATIAL HETEROGENEITY

作　　者：胡萌 张雅荣 HU Meng;ZHANG Ya-rong(School of Science,Xi'an University of Architecture and Technology,Shaanxi 710055,China)

机构地区：[1]西安建筑科技大学理学院,西安710055

出　　处：《数学杂志》2024年第4期331-342,共12页Journal of Mathematics

基　　金：省重点研发项目资助(2023-YBSF-372);中国博士后面上项目资助(2022M722604)。

摘　　要：本文研究了空间异质性下水平传播和垂直传播的SIS传染病模型的问题.利用半群理论、下一代再生算子谱半径的定义、Lyapunov函数、渐近自治半流理论以及数值模拟的方法,获得了空间异质性下水平传播和垂直传播的SIS传染病模型的动力学行为和传播规律的结果.这些结果推广了之前的相关研究结果,为理解此类传染病模型提供了更深入的理论依据.This article studies the dynamics and transmission laws of the SIS infectious disease model with the horizontal and vertical transmission under the spatial heterogeneity.Using the semigroup theory,the de nition of the spectral radius of the next-generation generator,Lyapunov functions,asymptotic autonomous semigroup theory,and numerical simulation methods,we obtain the dynamical behavior and transmission laws of the SIS infectious disease model with the horizontal and vertical transmission under the spatial heterogeneity.These results extend previous related research results and provide a deeper theoretical basis for understanding such infectious disease models.

关 键 词：空间异质性 SIS传染病模型 LYAPUNOV函数 全局稳定性 

分 类 号：O242.1[理学—计算数学]