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This dissertation is a report on an interdisciplinary investigation consisting of an application of random walk techniques to problems in ecology, particularly to the spread of Hantavirus epidemic among rodents that live on an open terrain. The population of mice that we consider is made up of infectious disease-carrying mice and susceptible mice that are disease-free, and each mouse has its own home range around which it executes a random walk. We describe an event of infection transmission in such a population via reaction-diffusion theory. Our simple model consists of two mice, one infected and the other susceptible, the disease being passed upon encounter as the two mice move on the terrain. The existence of home ranges of the mice is included in the model by representing each mouse to be a Smoluchowski random walker. Such a simple model is appropriate for a dilute population where only one …