具有无症状感染与多感染途径的宿主-病原体反应扩散模型研究  

Study of a Host-pathogen Reaction Diffusion Model with Asymptomatic Infection and Multiple Infection Routes

作　　者：李娇 胡振祥 聂麟飞[1] LI JIAO;HU ZHENXIANG;NIE LINFEI(School of Mathematics and System Sciences,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830017

出　　处：《应用数学学报》2025年第1期89-104,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:12361103);新疆维吾尔自治区天山英才培养计划(批准号:2022TSYCCX0015)资助项目。

摘　　要：基于空间异质性,无症状感染宿主和病原体传播途径的多样性,提出一类具有无症状感染宿主和多种感染途径的反应扩散宿主-病原体模型,并利用半群理论,讨论模型全局正解的存在性与唯一性.进一步,根据下一代算子的谱半径方法给出模型的基本再生数R_(0),并用其刻画了疾病的灭绝性和持久性.即,如果R_(0)<1,无病稳态是全局渐近稳定的;而如果R_(0)>1,疾病是一致持续的且模型至少有一个地方病平衡态.此外,通过构造合适的Lyapunov函数,证明空间匀质环境下模型无病平衡态和地方病平衡态的全局渐近稳定性.最后通过数值模拟解释主要的理论结果并探讨扩散速率对感染宿主分布的影响.Based on the spatial heterogeneity,the asymptomatic hosts and the multiplicity of pathogen transmission routes,a model of reactive diffusion host-pathogen with asymptomatic hosts and multiple infection routes is proposed,which is discussed the existence and uniqueness of the global positive solution of the model by using semigroup theory.Further,according to the spectral radius method of the next generation operator,the basic reproduction number Ro of the model is given,and the extinction and persistence of the disease are described.That is,if Ro<1,the disease-free steady state is globally asymptotically stable;while if Ro>1,the disease is uniformly persistent and the model admits at least one endemic steady state.In addition,the global asymptotic stability of the disease-free and endemic equilibrium states of the model in a spatially homogeneous environment is obtained by constructing suitable Lyapunov functions.Finally,some numerical simulations are conducted to explain the main theoretical results and to explore the infuence of diffusion rates on the distribution of infected hosts.

关 键 词：反应扩散模型 无症状感染 多感染途径 基本再生数 一致持续性 全局渐近稳定性 

分 类 号：O175.21[理学—数学]