scholarly journals An epidemic model with nonlocal diffusion on networks

2016 ◽  
Vol 11 (4) ◽  
pp. 693-719
Author(s):  
Elisabeth Logak ◽  
Isabelle Passat
Keyword(s):  
Epidemic Model ◽  
Nonlocal Diffusion

scholarly journals The dynamics of a degenerate epidemic model with nonlocal diffusion and free boundaries

2020 ◽  
Vol 269 (4) ◽  
pp. 3347-3386 ◽  
Author(s):  
Meng Zhao ◽  
Yang Zhang ◽  
Wan-Tong Li ◽  
Yihong Du
Keyword(s):  
Epidemic Model ◽  
Nonlocal Diffusion ◽  
Free Boundaries

scholarly journals Long-time dynamics of an epidemic model with nonlocal diffusion and free boundaries

2022 ◽  
Vol 30 (1) ◽  
pp. 289-313
Author(s):  
Ting-Ying Chang ◽  
◽  
Yihong Du
Keyword(s):  
Epidemic Model ◽  
Reaction Diffusion ◽  
Host Population ◽  
Kernel Functions ◽  
Nonlocal Diffusion ◽  
Threshold Condition ◽  
Free Boundaries ◽  
Time Dynamics ◽  
Long Time ◽  
Long Time Dynamics

<abstract><p>In this paper, we consider a reaction-diffusion epidemic model with nonlocal diffusion and free boundaries, which generalises the free-boundary epidemic model by Zhao et al. <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup> by including spatial mobility of the infective host population. We obtain a rather complete description of the long-time dynamics of the model. For the reproduction number $ R_0 $ arising from the corresponding ODE model, we establish its relationship to the spreading-vanishing dichotomy via an associated eigenvalue problem. If $ R_0 \le 1 $, we prove that the epidemic vanishes eventually. On the other hand, if $ R_0 &gt; 1 $, we show that either spreading or vanishing may occur depending on its initial size. In the case of spreading, we make use of recent general results by Du and Ni <sup>[<xref ref-type="bibr" rid="b2">2</xref>]</sup> to show that finite speed or accelerated spreading occurs depending on whether a threshold condition is satisfied by the kernel functions in the nonlocal diffusion operators. In particular, the rate of accelerated spreading is determined for a general class of kernel functions. Our results indicate that, with all other factors fixed, the chance of successful spreading of the disease is increased when the mobility of the infective host is decreased, reaching a maximum when such mobility is 0 (which is the situation considered by Zhao et al. <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>).</p></abstract>

Wave propagation in a nonlocal diffusion epidemic model with nonlocal delayed effects

2018 ◽  
Vol 339 ◽  
pp. 15-37 ◽  
Author(s):  
Zaili Zhen ◽  
Jingdong Wei ◽  
Jiangbo Zhou ◽  
Lixin Tian
Keyword(s):  
Wave Propagation ◽  
Epidemic Model ◽  
Nonlocal Diffusion ◽  
Delayed Effects
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