Stability And Traveling Wave Solutions Of Reaction-diffusion Model

The thesis is concerned with the stability and the traveling wave solutions of the delayed reaction-diffusion models.In chapter 2, a diffusive vector disease model with distributed delay is studied. By using the iterative technique developed by Wang, Li and Ruan, sufficient conditions are established for the existence of traveling wave solutions connecting the zero equilibrium with the positive equilibrium. It shows that there is a moving zone of transition from the disease free state to the infective state. The analyzing of systems with spatial dependence plays important roles in understanding the dynamic processes involved in such areas as the spread and control of diseases and viruses, biological pest control and so on.In chapter 3, a stage-structured diffusive and cooperative system with delay and nonlocal spatial effect is studied. By using the upper-lower solution technique and monotone iteration, the local stability and global stability of positive equilibrium is proved. Moreover, the traveling wave solutions of stage-structured diffusive and cooperative model with nonlocal spatial effect is considered. By constructing proper upper-lower solutions of theory of Wang, Li and Ruan, the existence of the traveling wave solutions is proved.