Spatial Epidemic Models on Transmissions of Infectious Diseases
Dr. Yixiang Wu
Department of Mathematics
Vanderbilt University
ABSTRACT: Mathematical models can describe the progress and predict the outcome of the spatial spread of infectious diseases. Many mathematical tools, such as ordinary and partial differential equation theory, dynamical system theory, matrix theory, network theory, numerical and computational techniques, have been adopted to investigate the spatial transmissions of diseases. These investigations in turn have enriched the development of mathematics.
In the first part of this talk, I will present some recent development on using reaction-diffusion models to study the impact of environmental heterogeneity and the mobility of individuals on the spatial spread of infectious diseases. Specifically, the analysis of the endemic equilibria, the basic reproduction number and the global dynamics of these epidemic models will be discussed. In the second part, I will talk about our recent efforts to use geographical and population data to simulate the spatial transmission of influenza. The simulations demonstrate the effectiveness of epidemic models in understanding the spatial spread patterns of infectious diseases.
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