Concentration profile of endemic equilibrium of a reaction-diffusion-advection SIS epidemic model
Concentration profile of endemic equilibrium of a reaction-diffusion-advection SIS epidemic model
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DOI：
10.1007/s00526-017-1207-8
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发表时间：
2017-08-01
影响因子：
2.1
通讯作者：
Peng, Rui
中科院分区：
文献类型：
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作者：
Kuto, Kousuke;Matsuzawa, Hiroshi;Peng, Rui
Cui和Lou （J Differ Equ, 261: 3305-3343, 2016）提出了异质环境下的反应-扩散-平流SIS流行病模型，并得出了不同条件下DFE（无病平衡）的稳定性和EE（地方性平衡）的存在性的有趣结果。在本文中，我们感兴趣的是在三种情况下EE的渐近分布（当它存在时）：(i)大平流；（ii）易感人群扩散较小；（三）受感染人群扩散小。我们证明了在情形(i)中，易感种群和感染种群的密度都只集中在下游，表现为δ函数；在第（ii）种情况下，易感者的密度只在下游集中，表现为δ函数，整个生境的受感染者密度消失；在第（iii）种情况下，易感者的密度为正值，而受感染者的密度在整个生境上消失。我们的结果表明，在情况（ii）和情况（iii）中，渐近剖面与没有平流存在的情况有本质的不同。因此，平流对人口密度空间分布的影响是显著的。
Cui and Lou (J Differ Equ 261: 3305-3343, 2016) proposed a reaction-diffusion-advection SIS epidemic model in heterogeneous environments, and derived interesting results on the stability of the DFE (disease-free equilibrium) and the existence of EE (endemic equilibrium) under various conditions. In this paper, we are interested in the asymptotic profile of the EE (when it exists) in the three cases: (i) large advection; (ii) small diffusion of the susceptible population; (iii) small diffusion of the infected population. We prove that in case (i), the density of both the susceptible and infected populations concentrates only at the downstream behaving like a delta function; in case (ii), the density of the susceptible concentrates only at the downstream behaving like a delta function and the density of the infected vanishes on the entire habitat, and in case (iii), the density of the susceptible is positive while the density of the infected vanishes on the entire habitat. Our results show that in case (ii) and case (iii), the asymptotic profile is essentially different from that in the situation where no advection is present. As a consequence, we can conclude that the impact of advection on the spatial distribution of population densities is significant.