Li 9626128 The investigator studies a variety of new mathematical models in epidemiology with the following three goals: (1). To build more realistic models. (2). To search new mechanisms that can generate new epidemiological phenomena. (3). To stimulate mathematical development of more effective tools for model analysis. Many of the previously studied models are special cases of the SEIRS type. On the one hand, a new analytical method developed by the investigator and his collaborators makes rigorous mathematical analysis of the SEIRS models with varying populations feasible and is a main tool in this project. On the other, problems of mathematical interest arising from the model analysis are thoroughly studied in a general mathematical setting. Computation also plays a important role, complementing analytical methods and testing the model using clinical or experimental data. The use of mathematical models to describe the spread of an infectious disease in a human or animal population has a long history. If the disease spreads through direct contact of individuals, a susceptible individual first becomes infected through contact with an infectious member; he then stays in the latent period before becoming infectious; after this he recovers from the infection with temporary immunity and later becomes susceptible again when the acquired immunity is lost. Death due to both natural causes and infection may occur during the cycle. The population is divided into four subclasses: susceptibles, exposed (those in the latent period), infectious, and recovered, according to the four stages in the above cycle. An SEIRS model for the spread of the infection is a system of ordinary differential equations that describes how the number of individuals in each class changes with time and how they interact, based on various assumptions on the way contacts between individuals are made as well as on various environmental effects. Note that every member of the p opulation is in one of these classes, so if the disease causes death then the population size varies with time too. It is expected that research on SEIRS epidemiological models with varying population size can significantly advance our understanding of the transmission dynamics for many diseases and our interpretation of complex clinical data, foster more accurate predictions on the time course of the spread of an infection, and lead to more effective disease prevention and control strategies. This is especially significant today, given the alarming global resurgence of many infectious diseases.
