Global dynamics of a spatial heterogeneous viral infection model with intracellular delay and nonlocal diffusion

Liu, Huan; Xu, Rui; Jin, Zhen

doi:10.1016/j.apm.2020.01.035

Cited by 20 publications

(20 citation statements)

References 36 publications

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“…In our model, there are some restrictions. In the parabolic equation, we assume that free virus move in the same location (local place ) which represents by the Laplace diffusion (Fickian diffusion); this fact can be corrected by taking the nonlocal diffusion (see, e.g., earlier studies [15,23,[43][44][45][46][47]). We leave this in the future work.…”

Section: Discussionmentioning

confidence: 99%

“…One the more important functions in the modeling of vivo is that the interaction between a free virus and host cells takes a linear form; see, for example, earlier studies [4, 11, 15, 17, 20–24], but in the reality, it is more realistic to assume that the function takes a nonlinear form to consider into account the inhomogeneous distribution of the population in spatial location within a fixed bounded domain

\Omega

at any given time.…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

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Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment with general nonlinear function

Mahroug,

Bentout

2023

Math Methods in App Sciences

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We propose a generalization of a model with age of infection in a heterogeneous environment. Firstly, we give the well‐posedness of the model and prove that the solutions are bounded and positive. The difficult mathematical issue in this research is that the model is partially degenerate, and the solution map is not compact. In addition, we construct a global attractor of a bounded set to establish the existence of total trajectory. Moreover, we define the principal eigenvalue associated with a principal eigenvalue problem to give a relation with the basic reproduction number and this value. By assuming that , then the infection‐free steady‐states is globally asymptotically stable. Furthermore, for and by using the persistence results, we prove the existence of endemic steady‐states , and by constructing an appropriate Lyapunov function, we show that is globally asymptotically stable. Lastly, we validate our theoretical analysis by giving some numerical graphics.

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Section: Discussionmentioning

confidence: 99%

\Omega

at any given time.…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment with general nonlinear function

Mahroug,

Bentout

2023

Math Methods in App Sciences

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“…However, the Laplace operator can be regarded as a local approximation of a nonlocal diffusion operator. In fact, when J(•) is symmetric and has compact supports, such as J(x) = (1/ǫ)K(x/ǫ) with 0 < ǫ ≪ 1 and K(x) is a general mollification function with support x ∈ [−1, 1], we can transform nonlocal operators into local operators by using the Taylor formula [29].…”

Section: The Free Boundary Conditions Hmentioning

confidence: 99%

Threshold dynamics of a nonlocal dispersal SIS epidemic model with free boundaries

Tong¹,

Ahn²,

Zhang³

2023

Preprint

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To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal SIS (susceptible-infected-susceptible) reaction-diffusion model with media coverage, hospital bed numbers and free boundaries. The principal eigenvalue of the integral operator is defined, and the impacts of the diffusion rate of infected individuals and interval length on the principal eigenvalue are analyzed. Furthermore, sufficient conditions for spreading and vanishing of the disease are derived. Our results show that large media coverage and hospital bed numbers are beneficial to the prevention and control of disease. The difference between the model with nonlocal diffusion and that with local diffusion is also discussed and nonlocal diffusion leads to more possibilities.

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“…One classic target (T)‐infection cell (

{T}&amp;amp;amp;#x0005E;{\ast }

)‐virus (

V

) model was proposed by Perelson [1, 2]. Afterwards, various models have been used to analyze the dynamics of HIV infection, including ODEs models [3, 4], age‐structured models [5, 6], functional differential equations models (such as discrete delay and distributed delay models [7, 8]), and PDEs models (such as reaction‐diffusion models [9, 10] and non‐local diffusion models [11, 12]). Many profound results have been achieved based on the assumption that the probability of infected cells staying in different stages follows an exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

HIV models with non‐exponential probability distributed infection progression

2023

Math Methods in App Sciences

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Existing HIV infection dynamics models are based on the classical target cell‐infected cell‐free virus compartment model. In fact, in order to facilitate modeling and dynamical analysis, these models assume that the probability of infected cells staying in different infection stages obeys an exponential distribution. However, this does not accurately describe the process of HIV infection from target cells to budding of virus, that is, fusion‐reverse transcription‐reproductivity formation‐budding process. Therefore, to expand the idea of HIV modeling, in this paper, we first establish the HIV integral‐differential equation model that obeys the general distribution, and then degenerate the model into a subclass ODEs model under the assumption of gamma distribution. Finally, an equivalent age structure model is given, and numerical simulations are conducted to describe the integral‐differential equations model. It is worth mentioning that ODEs models with subclasses can provide good numerical implementations for age structure as well as other PDEs HIV models. This is another important purpose of our work.

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Global dynamics of a spatial heterogeneous viral infection model with intracellular delay and nonlocal diffusion

Cited by 20 publications

References 36 publications

Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment with general nonlinear function

Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment with general nonlinear function

Threshold dynamics of a nonlocal dispersal SIS epidemic model with free boundaries

HIV models with non‐exponential probability distributed infection progression

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