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This paper is concerned with the dynamics of a waterborne pathogen model with spatial heterogeneity and general incidence rate. We first establish the well-posedness of this model. Then we clarify the relationship between the local basic reproduction number R̃ and the basic reproduction number R0. It could be seen that R0 plays an important role in determining the global dynamics of this model. In fact, we show that the disease-free equilibrium is globally asymptotically stable when R0<1. If R0=1, then the disease-free equilibrium is globally asymptotically stable under some assumptions. In addition, the phenomena of uniform persistence occurs when R0>1. We also consider the local and global stability of endemic equilibrium when all the parameters of this model are constant. In the case R0>1, we further establish the existence of traveling wave solutions of this model. Moreover, we provide an example and numerical simulations to support our theoretical results. Our model extended some known results.
|Journal||Nonlinear Analysis: Real World Applications|
|State||Published - Jun 2020|
- Global stability
- Lyapunov function
- Traveling wave solution
- Waterborne pathogen model
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- 1 Finished
Interaction and Stability of Traveling Waves for Lattice Dynamical System and Reaction-Diffusion Equations(2/3)
1/08/19 → 31/07/20