scholarly journals Spreading speed of a degenerate and cooperative epidemic model with free boundaries

2020 ◽  
Vol 25 (3) ◽  
pp. 981-999
Author(s):  
Meng Zhao ◽  
◽  
Wan-Tong Li ◽  
Wenjie Ni ◽  
Keyword(s):  
Epidemic Model ◽  
Spreading Speed ◽  
Free Boundaries

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>

scholarly journals Dynamics of an epidemic model with advection and free boundaries

2019 ◽  
Vol 16 (5) ◽  
pp. 5991-6014 ◽  
Author(s):  
Meng Zhao ◽  
◽  
Wan-Tong Li ◽  
Yang Zhang ◽  
Keyword(s):  
Epidemic Model ◽  
Free Boundaries

The spreading speed of an SIR epidemic model with nonlocal dispersal

2020 ◽  
Vol 120 (1-2) ◽  
pp. 163-174 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Amy Ai Ling Poh ◽  
Masahiko Shimojo
Keyword(s):  
Comparison Principle ◽  
Epidemic Model ◽  
Sir Model ◽  
Spreading Speed ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
Sir Epidemic ◽  
Scalar Equations ◽  
Asymptotic Spreading

In this paper, we study an SIR epidemic model with nonlocal dispersal. We study the case with vital dynamics so that a renewal of the susceptible individuals is taken into account. We characterize the asymptotic spreading speed to estimate how fast the disease under consideration spreads. Due to the lack of comparison principle for the SIR model, our proof is based on a delicate analysis of related problems with nonlocal scalar equations.

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