Grant: Discovery Grants Program - Individual

The general objectives of the proposed program are to further the study of various mathematical models in physical and biological sciences via mathematical methods. The expected outcome will not only solve some open and long-standing problems in various applied dynamical systems, but also help to establish a fundamental theory about asymptotic analysis of delay differential equations. Specifically, we aim to to advance the field in the following ways: (a) develop a completely new method to construct traveling wave fronts; (b) theoretically establish the stability of traveling wavefronts in periodic media; (c) solve or partially solve some open problems in this field; (d) theoretically give sufficient conditions under which pattern formations are certain to happen. These mathematical analyses will have practical applications: (a) help us better understand transmission patterns in infectious diseases (e.g. rabies); (b) better identify the impact of the period of incubation in the spreading of diseases; (c) this result can be used to assess the effectiveness of different methods used during past years for controlling the infectious disease.