| Abstract: |
| In this talk, we investigates the spreading speeds and generalized traveling wave solutions for a nonautonomous epidemic system with nonlocal dispersal. The main challenge arises from the lack of a comparison principle for such nonmonotone systems. To characterize the spreading speed of the system, we first establish the spreading speed of a scalar nonautonomous KPP equation. Then, using a derived key pointwise estimate, we compare the solution of the system with that of the scalar KPP equation and thus obtain the spreading speed of the system. Combining with the spreading speed results, we demonstrate the nonexistence of generalized traveling wave solutions with small wave speeds in average sense. By constructing proper super and sub solutions, we establish the existence of generalized traveling wave solutions and study the limiting behavior of the wave profile using the uniform persistence theory. This talk is based on a joint work with Prof. Xiongxiong Bao. |
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