Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

Lam, King‐Yeung; Liu, Shuang; Lou, Yuan

doi:10.5206/mase/10644

Cited by 25 publications

(14 citation statements)

References 128 publications

(177 reference statements)

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“…Set u(x, t) = M e −λ1t e qx d I η 1 (x), where (λ 1 , η 1 (x)) is the principal eigen-pair of (17). It is known that λ 1 > 0 and η 1 (x) > 0 on [0, L] by Lemma 2.2.…”

Section: 3mentioning

confidence: 99%

“…The biased or passive movement behavior can be characterized by adding an advection term to the models. A survey on this subject can be found in [17]. Xiang et al [21] also considered the impact of a cross-diffusion term modelling the effect that susceptible individuals tend to move away from higher concentration of infected individuals, on the elimination of the infectious disease.…”

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confidence: 99%

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A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments

Rao

Zhang

Wang

2022

DCDS-B

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<p style='text-indent:20px;'>In this paper, we propose a reaction-diffusion-advection SIS epidemic model with linear external source to study the effects of open advective environments on the persistence and extinction of infectious diseases. Threshold-type results on the global dynamics in terms of the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_{0} $\end{document}</tex-math></inline-formula> are established. It is found that the introduction of open advective environments leads to different monotonicity and asymptotic properties of the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> with respect to the diffusion rate <inline-formula><tex-math id="M3">\begin{document}$ d_I $\end{document}</tex-math></inline-formula> and advection speed <inline-formula><tex-math id="M4">\begin{document}$ q $\end{document}</tex-math></inline-formula>. Our analytical results suggest that increasing the advection speed or decreasing the diffusion rate of infected individuals helps to eradicate the diseases in open advective environments.</p>

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“…Set u(x, t) = M e −λ1t e qx d I η 1 (x), where (λ 1 , η 1 (x)) is the principal eigen-pair of (17). It is known that λ 1 > 0 and η 1 (x) > 0 on [0, L] by Lemma 2.2.…”

Section: 3mentioning

confidence: 99%

mentioning

confidence: 99%

A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments

Rao

Zhang

Wang

2022

DCDS-B

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“…That is to say, a heterogeneity of m(x) can make the total population of the species grow. It follows that S n > 1 for any dimension number n. In the research field of diffusive logistic equations, there was a conjecture that S n is finite for any n, and, especially, S 1 = 3 (see [23,24]). Bai, He, and Li shows the validity of S 1 = 3 [25].…”

Section: Diffusive Logistic Equationmentioning

confidence: 99%

Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

Inoue

Kuto

2021

Mathematics

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This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one.

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“…The RDA approach had also been used to model the dynamics of sinking phytoplankton and populations experiencing a shift in habitat boundaries due to climate change [7,17,1]. A recent survey on a variety of RDA models is given in [9]. The development of RDA models progressed from the linear reaction term case in [20], to monostable logistic term (e.g.…”

Section: Introductionmentioning

confidence: 99%

Prevailing winds and spruce budworm outbreaks: a reaction-diffusion-advection model

Anderson

Vasilyeva

2021

Math Appl Sci Eng

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We extend the classical reaction-diffusion model for spatial population dynamics of spruce budworm on a finite domain with hostile boundary conditions by including an advection term representing biased unidirectional movement of individuals due to a prevailing wind. We use phase-plane techniques to establish existence of a critical value of advection speed that prevents outbreak solutions on any finite domain while possibly allowing an endemic solution. We obtain lower and upper bounds for this critical advection value in terms of biological parameters involved in the reaction term. We also perform numerical simulations to illustrate the effect of advection on the dependence of the domain size on the maximal population density of a steady state solution and on critical domain sizes for endemic and outbreak solutions. The results are also applicable to other ecological settings (rivers, climate change) where a logistically growing population is subject to predation by a generalist, diffusion and biased movement.

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Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

Cited by 25 publications

References 128 publications

A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments

A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments

Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

Prevailing winds and spruce budworm outbreaks: a reaction-diffusion-advection model

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