题 目：Threshold dynamics of a nonlocal dispersal HIV/AIDS epidemicmodel with spatial heterogeneity and antiretroviral therapy

主讲人：吴鹏博士

时 间：2022年10月25日（周二）13：30-14：30

地 点：6号学院楼402会议室

主办单位：数据科学学院 浙江省2011“数据科学与大数据分析协同创新中心”

摘要：

Antiretroviral therapy and long-range diffusion of HIV-infected individuals in heterogeneous environments can greatly impact the transmission and distribution of HIV/AIDSin a population. In this paper, we present a nonlocal dispersal HIV/AIDS epidemicmodel incorporating spatial heterogeneity as well as antiretroviral therapy to studythe spatial and temporal dynamics of HIV/AIDS in China. To overcome the difficultyabout a lack of compactness of the semiflow and the challenge about the existenceand uniqueness of the principal eigenvalue of an eigenvalue problem without obviouscompactness, we apply the operator semigroup and dissipative system theories. Weestablish the well-posedness and the existence of the global attractor for the system.

Then we derive the basic reproduction number R0 which is defined as the spectral radiusof the next generation operator by the renewal equation. Afterwards, we obtain theglobal dynamics of the system in terms of R0. Our numerical simulations suggest that:(1) the dynamics of HIV/AIDS transmission largely depends on the nonlocal dispersalkernel function; (2) it is necessary to monitor and design/refine rules for the mobility ofHIV-infected population between remote and metropolitan areas to control the HIV/AIDStransmission; (3) antiretroviral therapy benefits not only each treated individual butalso the entire community, and increasing the therapy coverage rate is one of the mosteffective ways to prolong the longevity of HIV-infected population. Moreover, spatialdispersal is also an important factor that cannot be ignored for designing antiretroviraltherapy strategies.

主讲人简介：

吴鹏，应用数学博士，研究方向是动力系统理论研究及其应用，主要研究内容是HIV/AIDS传染病动力学建模与研究（ODE,PDE建模、数值分析、最优控制问题）。以第一作者在Journal of FranklinInstitute、Applied Mathematical Modelling、Nonlinear Analysis: Real World Applications、Discrete and Continuous Dynamical Systems Series B、Journal of Computational and Applied Mathematics、高校应用数学学报、系统科学与数学等应用数学和生物数学方面知名SCI及国内权威学术期刊发表论文20余篇。

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