A nonlocal SIS epidemic problem with double free boundaries

Huang, Haomin; Wang, Mingxin

doi:10.1007/s00033-019-1156-5

Cited by 14 publications

(6 citation statements)

References 25 publications

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“…Proof We can refer to Cao et al [7, Proposition 3.4] and Huang and Wang [6, Proposition B.1] to prove it. Thus, we omit the details here.…”

Section: Eigenvalue Problem and Comparison Principlementioning

confidence: 95%

“…At last, some sufficient conditions for the disease vanishing were established. Then Huang and Wang [6] considered the following nonlocal case with double free boundaries

$$ \left\{\begin{array}{ll}{S}_t-{S}_{xx}&#x0003D;\gamma I-S\left(K\ast I\right),&amp; t&gt;0,x\in \mathrm{\mathbb{R}},\\ {}{I}_t-{I}_{xx}&#x0003D;S\left(K\ast I\right)- bI,&amp; t&gt;0,x\in \left(g(t),h(t)\right),\\ {}I\left(t,x\right)&#x0003D;0,&amp; t\ge 0,x\in \mathrm{\mathbb{R}}\setminus \left(g(t)...

…”

Section: Introductionmentioning

confidence: 99%

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A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and free boundaries

Zhou

Chen

2023

Math Methods in App Sciences

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This paper is concerned with the spreading or vanishing of an epidemic disease which is characterized by a nonlocal diffusion SIR model with nonlocal incidence rate and double free boundaries. We prove that the disease will vanish if the basic reproduction number , or the initial area , the initial datum , and the expanding ability are sufficiently small when . Otherwise, the disease will spread to the whole area if , when is suitably large or is small but is large enough. Moreover, we also show the long‐time asymptotic limit of the solution when vanishing happens.

show abstract

“…Proof We can refer to Cao et al [7, Proposition 3.4] and Huang and Wang [6, Proposition B.1] to prove it. Thus, we omit the details here.…”

Section: Eigenvalue Problem and Comparison Principlementioning

confidence: 95%

“…At last, some sufficient conditions for the disease vanishing were established. Then Huang and Wang [6] considered the following nonlocal case with double free boundaries

$$ \left\{\begin{array}{ll}{S}_t-{S}_{xx}&#x0003D;\gamma I-S\left(K\ast I\right),&amp; t&gt;0,x\in \mathrm{\mathbb{R}},\\ {}{I}_t-{I}_{xx}&#x0003D;S\left(K\ast I\right)- bI,&amp; t&gt;0,x\in \left(g(t),h(t)\right),\\ {}I\left(t,x\right)&#x0003D;0,&amp; t\ge 0,x\in \mathrm{\mathbb{R}}\setminus \left(g(t)...

…”

Section: Introductionmentioning

confidence: 99%

A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and free boundaries

Zhou

Chen

2023

Math Methods in App Sciences

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show abstract

“…Proof. We can refer to [2, Proposition 3.4] and [8,Proposition B.1] to prove it. We omit the details here.…”

Section: Eigenvalue Problem and Comparison Principlementioning

confidence: 99%

“…At last, some sufficient conditions for the disease vanishing were established. Then in [8], Huang and Wang considered the following nonlocal case with double free boundaries…”

Section: Introductionmentioning

confidence: 99%

A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and free boundaries

Chen

Zhou

2022

Preprint

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This paper is concerned with the spreading or vanishing of an epidemic disease which is characterized by a nonlocal diffusion SIR model with nonlocal incidence rate and double free boundaries. We prove that the disease will vanish if the basic reproduction number R 0 < 1 , or the initial area h 0 , the initial datum S 0 , and the expanding ability µ are sufficiently small even that R 0 > 1 , and the disease will spread to the whole area if R 0 > 1 , when h 0 is suitably large or h 0 is small but µ is large enough. Moreover, we also show that the long-time asymptotic limit of the solution when vanishing happens.

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“…Ge et al. in ( Ge, Kim, Lin, & Zhu, 2015 ) studied a simplified SIS model with advection and free boundary and gave the spreading speeds when spreading happens; a diffusion-advection simplified SIS epidemic model in a heterogeneous time-periodic environment was studied in ( Ge, Lei, & Lin, 2017 ); a SIS reaction-diffusion model with free boundary and mass action mechanism was discussed in ( Wang & Guo, 2019 ); recently an SIS epidemic reaction-diffusion model with mass-action incidence incorporating spontaneous infection in a spatially heterogeneous environment was examined ( Tong, Ahn, & Lin, 2021 ); a SIS model risk-induced dispersal of infected individuals has been studied ( Choi, Lin, & Ahn, 2022 ); the spreading or vanishing of an SIS epidemic model with free boundary and nonlocal incidence rate was analyzed in ( Cao et al., 2017b ; Huang & Wang, 2019 ).…”

Section: Introductionmentioning

confidence: 99%

The impact factors of the risk index and diffusive dynamics of a SIS free boundary model

Tong¹,

Ahn²,

Lin³

2022

Infectious Disease Modelling

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A nonlocal SIS epidemic problem with double free boundaries

Cited by 14 publications

References 25 publications

A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and free boundaries

A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and free boundaries

A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and free boundaries

The impact factors of the risk index and diffusive dynamics of a SIS free boundary model

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