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

University Of Miami, Coral Gables FL

Investigators

Abstract

Ruan The investigator studies the effect of spatial heterogeneity, nonlocal interactions and time delay on the spatiotemporal dynamics of epidemiological and ecological models. Three particular examples are considered. The first is the generalized Ross-Macdonald vector-host (malaria) models. The focus here is on the existence of traveling waves in a vector disease model described by diffusive integrodifferential equations with delay and the effects of nonlocal interaction and time delay on the epidemic waves and spatiotemporal dynamics. The effects of spatial heterogeneity and time delay on the establishment and transmission of the disease are studied by considering a multi-patch model. The second is nosocomial epidemic models with antibiotic resistance and infection age. Persistence and extinction of the infected population are considered. The impact of control measures such as isolation of patients infected with resistant strains, restricted use of antibiotics, and reduced or extended hospital stays, are discussed in terms of the model parameters. The third is the biological and physical nutrient-phytoplankton-zooplankton (NPZ) models. The investigator studies spatiotemporal dynamics such as traveling waves and chaotic mixing in the advective-diffusive NPZ models. One of the most important environmental effects of globalization is the dramatic increase in the introduction of exotic species, including pathogens that may cause disease in humans, into new regions. Such introductions can lead to biological invasions, which in turn can threaten public health or affect ecosystem structure. Examples include nonindigenous vectors that arrive, establish, and spread in new areas and foment epidemics of human diseases such as malaria, yellow fever, typhus, plague, and West Nile virus. The investigator studies the spatial transmission of certain vector-host diseases such as malaria and hopes that the study can help to understand the establishment and spread of other vector-borne diseases such as West Nile. He also studies nosocomial epidemics with antibiotic resistance, aiming to provide some control measures to combat such epidemics inside hospitals. Finally, he examines the spatiotemporal dynamics of plankton populations; this may lead to a better understanding of global issues such as the depletion of ocean fish markets and the greenhouse effect.