A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems
Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions
The spatially heterogeneous diffusive rabies model and its shadow system
Yuxin Zhang
College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang 150001, China
Received August 2020 Revised October 2020 Published December 2020
Fund Project: The author was partially supported by the Fundamental Research Funds for the Central Universities (GK2240260048), and the National Natural Science Foundation of China (11971088)
In this paper, we consider a class of spatially heterogeneous reaction diffusion rabies model which was used to describe population dynamics of the rabies epidemic disease observed in Europe. The dynamics of both the original non-degenerate reaction-diffusion system and its corresponding shadow system are investigated in great details. Firstly, we prove that under certain conditions, the in-time solutions of both the original non-degenerate reaction-diffusion system and its shadow system exist globally and remain uniformly bounded. Secondly, we are capable of showing that the shadow system is the nice approximations for the original non-degenerate reaction-diffusion system when the diffusion rate $ d_R $ of the infectious rabid individuals (R) is sufficiently large. This implies that the dynamics of the shadow system can say as much as possible about the dynamics of the original system when $ d_R $ is sufficiently large. Finally, we characterize the basic reproduction number for the shadow system, and study the stability/instability of the disease-free steady state.
Keywords: Spatially heterogeneous diffusive rabies model, shadow system, approximations, the basic reproduction number, global existence.
Mathematics Subject Classification: Primary: 35K57, 92D30; Secondary: 35B45.
Citation: Yuxin Zhang. The spatially heterogeneous diffusive rabies model and its shadow system. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020357
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