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The spatially heterogeneous diffusive rabies model and its shadow system
Discrete and Continuous Dynamical Systems-Series B ( IF 1.2 ) Pub Date : 2020-12-01 , DOI: 10.3934/dcdsb.2020357
Yuxin Zhang

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.

中文翻译:

空间异质性扩散狂犬病模型及其阴影系统

在本文中,我们考虑了一类空间异质反应扩散狂犬病模型,该模型用于描述在欧洲观察到的狂犬病流行病的种群动态。详细研究了原始非简并反应扩散系统及其相应阴影系统的动力学。首先,我们证明了在一定条件下,原始非简并反应扩散系统及其影子系统的及时解全局存在并保持一致有界。其次,当传染性狂犬病个体 (R) 的扩散率 $ d_R $ 足够大时,我们能够证明阴影系统是原始非简并反应扩散系统的良好近似。这意味着当$ d_R $ 足够大时,影子系统的动力学可以尽可能多地说明原始系统的动力学。最后,我们表征了阴影系统的基本再生数,并研究了无病稳态的稳定性/不稳定性。
更新日期:2020-12-01
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