Spatial Heterogeneity, Nonlocal Interactions and Time Delay in Epidemiological and Biological Spread

阮氏研究了空间异质性、非局部相互作用和时滞对流行病和生态模型的时空动力学的影响。文中考虑了三个具体的例子。第一种是推广的Ross-Macdonald媒介宿主(疟疾)模型。本文主要讨论由时滞扩散积分微分方程描述的病媒模型中行波的存在性，以及非局部相互作用和时滞对传染病波和时空动力学的影响。考虑多斑块模型，研究了空间异质性和时滞对疾病建立和传播的影响。第二类是具有抗生素耐药性和感染年龄的医院传染病模型。考虑了感染人群的持久性和消失性。根据模型参数，讨论了隔离耐药菌株感染者、限制抗生素使用、减少延长住院时间等控制措施的影响。第三种是生物和物理营养-浮游植物-浮游动物(NPZ)模型。研究人员研究了平流扩散NPZ模型中的时空动力学，如行波和混沌混合。全球化最重要的环境影响之一是外来物种引入新地区的急剧增加，包括可能导致人类疾病的病原体。这种引入可能导致生物入侵，进而威胁公共健康或影响生态系统结构。例子包括在新地区到达、建立和传播的非本土媒介，并煽动人类疾病的流行，如疟疾、黄热病、斑疹伤寒、鼠疫和西尼罗河病毒。研究人员研究了疟疾等某些媒介宿主疾病的空间传播，并希望这项研究能够帮助理解其他媒介传播疾病的建立和传播，如西尼罗河。他还研究了具有抗生素耐药性的医院流行病，旨在提供一些控制措施，以对抗医院内的此类流行病。最后，他研究了浮游生物种群的时空动态；这可能有助于更好地理解全球问题，如海洋鱼类市场的枯竭和温室效应。

RuanThe investigator studies the effect of spatial heterogeneity,nonlocal interactions and time delay on the spatiotemporaldynamics of epidemiological and ecological models. Threeparticular examples are considered. The first is the generalizedRoss-Macdonald vector-host (malaria) models. The focus here ison the existence of traveling waves in a vector disease modeldescribed by diffusive integrodifferential equations with delayand the effects of nonlocal interaction and time delay on theepidemic waves and spatiotemporal dynamics. The effects ofspatial heterogeneity and time delay on the establishment andtransmission of the disease are studied by considering amulti-patch model. The second is nosocomial epidemic models withantibiotic resistance and infection age. Persistence andextinction of the infected population are considered. The impactof control measures such as isolation of patients infected withresistant strains, restricted use of antibiotics, and reduced orextended hospital stays, are discussed in terms of the modelparameters. The third is the biological and physicalnutrient-phytoplankton-zooplankton (NPZ) models. Theinvestigator studies spatiotemporal dynamics such as travelingwaves and chaotic mixing in the advective-diffusive NPZ models.One of the most important environmental effects of globalizationis the dramatic increase in the introduction of exotic species,including pathogens that may cause disease in humans, into newregions. Such introductions can lead to biological invasions,which in turn can threaten public health or affect ecosystemstructure. Examples include nonindigenous vectors that arrive,establish, and spread in new areas and foment epidemics of humandiseases such as malaria, yellow fever, typhus, plague, and WestNile virus. The investigator studies the spatial transmission ofcertain vector-host diseases such as malaria and hopes that thestudy can help to understand the establishment and spread ofother vector-borne diseases such as West Nile. He also studiesnosocomial epidemics with antibiotic resistance, aiming toprovide some control measures to combat such epidemics insidehospitals. Finally, he examines the spatiotemporal dynamics ofplankton populations; this may lead to a better understanding ofglobal issues such as the depletion of ocean fish markets and thegreenhouse effect.