Dynamics and profiles of a diffusive host–pathogen system with distinct dispersal rates

Wu, Yixiang; Zou, Xingfu

doi:10.1016/j.jde.2017.12.027

Cited by 99 publications

(67 citation statements)

References 24 publications

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“…Indeed, the assumption that both uninfected and infected cells in previous studies have the same diffusion rate plays a key role in theoretical analysis. To overcome this problem, Wu and Zou proposed a new method that is inspired by Alikakos . In this paper, similar to Ren et al we have solved this problem by the construction of the function

scriptH false(t false) .

This approach seems to be very technical and has been applied to show the point dissipativeness for viral models with nonlinear incidence.…”

Section: Discussionmentioning

confidence: 99%

“…Komarava studied the evolutionary competitiveness of lytic virus by a diffusive model. Soon afterwards, there are some researchers that make further investigations on diffusive viral models by incorporating (i) spatial heterogeneity; (ii) nonlinear incidences; (iii) nonlocal dispersal; (iv) time delay ; and (v) density‐dependent diffusion …”

Section: Introductionmentioning

confidence: 99%

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Global analysis of a diffusive viral model with cell‐to‐cell infection and incubation period

Wang

Guo

et al. 2020

Math Methods in App Sciences

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We propose a diffusive viral model incorporating cell-to-cell infection mode, nonlinear incidences, incubation period, and spatial heterogeneity. For the spatially heterogeneous model, we derive the extinction/persistence result by the basic reproduction number  0 . For the spatially homogeneous model, we study global stabilities of steady states by establishing Lyapunov functions. The existing method for studying global stabilities of diffusive viral models has been generalized, which weakens the required conditions. Some existing results can be covered and improved. A specific example is given to illustrate the general results. In addition, we show that  0 is underestimated if we neglect incubation period of infected cells.

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scriptH false(t false) .

This approach seems to be very technical and has been applied to show the point dissipativeness for viral models with nonlinear incidence.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global analysis of a diffusive viral model with cell‐to‐cell infection and incubation period

Wang

Guo

et al. 2020

Math Methods in App Sciences

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“…Let (ϕ 0 , φ 0 ) be a positive eigenvector associated with κ 0 of the eigenvalue problem (2.6). Motivated by [7,42], for any w 0 := (H i0 , V i0 ), we define c(t; w 0 ) := inf{c ∈ R : H i (·, t) ≤cϕ 0 and V i (·, t) ≤cφ 0 }.…”

Section: Global Stability When R 0 =mentioning

confidence: 99%

On a vector-host epidemic model with spatial structure

Magal

Webb

2018

Nonlinearity

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In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number R 0 and show that R 0 is a threshold parameter: if R 0 ≤ 1 the disease free steady state is globally stable; if R 0 > 1 the model has a unique globally stable positive steady state. Our proof combines arguments from monotone dynamical system theory, persistence theory, and the theory of asymptotically autonomous semiflows.

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“…This motivates us to consider a PDE cholera model in a general bounded spatial domain. Another motivation comes from the fact that the parameters of PDE models for infectious diseases generally are space-dependent (see [1,10,24,30,31] as examples of some recent publications). However, in the above mentioned PDE cholera models, only Wang [27] considered the case where the transmission rates are dependent on both time and positions.…”

mentioning

confidence: 99%