Propagation thresholds in a diffusive epidemic model with latency and vaccination. (English) Zbl 1510.35350
Summary: This paper studies the propagation thresholds in a diffusive epidemic model with latency and vaccination. When the initial condition satisfies proper exponential decaying behavior, we present the spatial expansion feature of the infected. Different leftward and rightward spreading speeds are obtained with respect to different decaying initial values. Moreover, the convergence in the sense of compact open topology is also studied when the spreading speeds are finite. Finally, we show that the minimal spreading speed is the minimal wave speed of traveling wave solutions, which also presents the precisely asymptotic behavior of traveling wave solutions for the infected branch at the disease-free side. Here, the asymptotic behavior plays an important role that distinguishes the minimal spreading speed from all possible spreading speeds. From the definition of possible spreading speeds, we may find some factors affecting the spatial expansion ability, which includes that the vaccination could decrease the spatial expansion ability of the disease.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D30 | Epidemiology |
| 35K57 | Reaction-diffusion equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35C07 | Traveling wave solutions |
| 35R07 | PDEs on time scales |
Keywords:
generalized upper-lower solutions; asymptotic spreading; nonmonotone delayed system; minimal wave speed; fast propagationReferences:
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