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

点击翻译按钮获取中文摘要

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.