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

研究了空间异质性、非局部相互作用和时滞对流行病学和生态学模型时空动力学的影响。 三个特殊的例子被认为是。 第一个是广义的Ross-Macdonald病媒-宿主（疟疾）模型。 本文主要研究了一类具有时滞的传染病扩散积分微分方程的行波解的存在性，以及非局部相互作用和时滞对传染病传播波和时空动力学的影响。 通过考虑多斑块模型，研究了空间异质性和时滞对病害建立和传播的影响。 第二类是具有抗生素耐药性和感染年龄的医院流行病模型。 考虑了感染人群的持久性和灭绝性。 控制措施的影响，如隔离感染耐药菌株的患者，限制使用抗生素，减少或延长住院时间，进行了讨论的模型参数。 三是生物和物理营养盐-浮游植物-浮游动物（NPZ）模型。 研究者在对流扩散NPZ模型中研究时空动力学，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的引入，包括可能导致人类疾病的病原体，进入新地区的急剧增加。 这种引进可能导致生物入侵，而生物入侵又可能威胁公共健康或影响生态系统结构。 例子包括到达、建立和传播新地区的非本地病媒，并引起人类疾病的流行，如疟疾、黄热病、斑疹伤寒、鼠疫和西尼罗河病毒。 研究人员研究了某些病媒-宿主疾病（如疟疾）的空间传播，并希望该研究有助于了解其他病媒传播疾病（如西尼罗河病毒）的建立和传播。 他还研究了具有抗生素耐药性的医院内流行病，旨在提供一些控制措施来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;这可能会导致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.