Propagation phenomena for man-environment epidemic model with nonlocal dispersals. (English) Zbl 1495.35069
Summary: In this paper, we focus on the propagation phenomena of a bistable man-environment epidemic model with nonlocal dispersals, where there exists a positive feedback interaction between the concentration of infectious agent and infectious human population. The monostable and bistable traveling wave solutions and three-wave entire solutions are studied. First, by applying and developing the known results for monostable case, we give a summary of the existence and asymptotic behavior of all monostable traveling wave solutions in two different monostable intervals and further find some relationship between them. The existence of bistable traveling wave solutions is obtained by introducing the results about monotone semiflows with weak compactness. Second, we give twelve types of three-wave entire solutions, which contain all possibilities of three-wave entire solutions originating from three traveling wave solutions with different nonzero wave speeds, by constructing new auxiliary functions and super- and sub-solutions for every type. We also show that these entire solutions are globally Lipschitz continuous with respect to spatial variable. In addition, the nonexistence result of entire solutions originating from more than four traveling wave solutions is obtained.
MSC:
| 35C07 | Traveling wave solutions |
| 35K57 | Reaction-diffusion equations |
| 35R09 | Integro-partial differential equations |
| 92D30 | Epidemiology |
Keywords:
nonlocal dispersal; epidemic model; monostable and bistable traveling wave solutions; three-wave entire solutionsReferences:
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