Dynamics of a PDE viral infection model incorporating cell-to-cell transmission

Wang, Jinliang; Yang, Jie; Kuniya, Toshikazu

doi:10.1016/j.jmaa.2016.07.027

Cited by 73 publications

(34 citation statements)

References 25 publications

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“…There is a number of works studying the case d 1 = d 2 = 0, d 3 > 0 (see e.g. [38,37,39] for models without delay and [17,10] with constant delay; see also references therein). In the mentioned works authors assume that the host cells (healthy and infected) do not move or are well mixed, while viral particles diffuse freely.…”

Section: ∂T (Tx)mentioning

confidence: 99%

Viral infection model with diffusion and state-dependent delay: Stability of classical solutions

Rezounenko¹

2018

Discrete &Amp; Continuous Dynamical Systems - B

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A class of reaction-diffusion virus dynamics models with intracellular state-dependent delay and a general non-linear infection rate functional response is investigated. We are interested in classical solutions with Lipschitz in-time initial functions which are adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions technique is used to analyse stability of interior infection equilibria which describe the cases of a chronic disease.2010 Mathematics Subject Classification: 93C23, 34K20,35K57, 97M60.

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Section: ∂T (Tx)mentioning

confidence: 99%

Viral infection model with diffusion and state-dependent delay: Stability of classical solutions

Rezounenko¹

2018

Discrete &Amp; Continuous Dynamical Systems - B

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“…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%

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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“…For instance, the susceptibility of a susceptible can depend on the physical age. Epidemic models with continuous age structures (generally described by partial differential equations in theoretical models) have been extensively studied in recent years (see, for example, previous studies [13][14][15][16][17][18][19][20][21][22][23][24] ). Among those on vector-borne diseases with age structures, 14,17,[20][21][22] Vargas-De-León et al 22 proposed 2 age-structured models for the transmission of a vector-borne infectious disease.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an age‐structured host‐vector model for malaria transmission

Wang

Chen

Liu

2018

Math Methods in App Sciences

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In this paper, we propose a host‐vector model for malaria transmission by incorporating infection age in the infected host population and nonlinear incidence for transmission from infectious vectors to susceptible hosts. One novelty of the model is that the recovered hosts only have temporary immunity and another is that successfully recovered infected hosts may become susceptible immediately. Firstly, the existence and local stability of equilibria is studied. Secondly, rigorous mathematical analyses on technical materials and necessary arguments, including asymptotic smoothness and uniform persistence of the system, are given. Thirdly, by applying the fluctuation lemma and the approach of Lyapunov functionals, the threshold dynamics of the model for a special case were established. Roughly speaking, the disease‐free equilibrium is globally asymptotically stable when the basic reproduction number is less than one and otherwise the endemic equilibrium is globally asymptotically stable when no reinfection occurs. It is shown that the infection age and nonlinear incidence not only impact on the basic reproduction number but also could affect the values of the endemic steady state. Numerical simulations were performed to support the theoretical results.

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Dynamics of a PDE viral infection model incorporating cell-to-cell transmission

Cited by 73 publications

References 25 publications

Viral infection model with diffusion and state-dependent delay: Stability of classical solutions

Viral infection model with diffusion and state-dependent delay: Stability of classical solutions

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

Dynamics of an age‐structured host‐vector model for malaria transmission

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