Spatiotemporally-dependent models for the spread of infectious disease

This dissertation is concentrated on the boundedness and existence of classical solutions to some semilinear parabolic reaction-diffusion systems from epidemiology. In particular, our attention is focused on determining the existence of classical solutions and continuous periodic solutions to a diffusive SIR epidemic model and a diffusive criss-cross epidemic model with seasonal fluctuations in their birth rates. These two models may be applied to model infectious diseases such as influenza and malaria, respectively. Influenza and malaria are serious (sometimes fatal) diseases. Malaria alone infects well over 400 million new people each year ([14]). The intent of this dissertation is to display the existence of naturally occurring trends within the solutions to a diffusive SIR epidemic model and a criss-cross epidemic model (such as periodicity within solutions). Moreover, we efficiently simulate a one dimensional criss-cross model. The long term goal of this research, however, is to employ new tools for the analysis of semilinear parabolic reaction-diffusion systems to gain insight into methods to control and one day halt the spread of certain classes of infectious disease.