Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Zhuang, Kejun

doi:10.3390/mca22010007

Cited by 4 publications

(5 citation statements)

References 41 publications

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“…These figures are illustrations that when there is an increase in the delay strictures τ, the values that are critical in Hopf bifurcations for the uninfected cell growth rate r and the rate of death a are augmented. However, the curve for the production rate of free virus k is decreased as the delay parameter τ increased; this outcome is the same as that previously reported in [27]. It is clear that the two predictions pertaining to two-term semi-analytical solutions correspond with the numerical calculations with an error rate that does not exceed 2% for all choices.…”

Section: Hopf Bifurcation Regionssupporting

confidence: 85%

“…In our everyday life, delayed reaction-diffusion models have revealed a number of oscillatory phenomena with the use of continuous well-stirred tank reactor (CSTR). CSTRs have obtained good results with experimental oscillatory systems in the theoretical research, for instance in logistical equations [4], the viral infection model [14,20,27], Nicholson's blowflies equation [5], and the limited food model [1].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Zhuang [27] considered a delay-diffusion model to investigate the spatiotemporal interactions between target cells, free virus molecules, and infected cells. He created a periodic phenomenon through diffusion stricture and spatial time delay and found that for any positive value of time delay, the healthy equilibrium is asymptotically stable when the rate of production stricture is small.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth

Alfifi¹

2019

J. Nonlinear Sci. Appl.

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In the one-dimensional reaction-diffusion domain of this study, semi-analytical solutions are used for a delayed viral infection system with logistic growth. Through an ordinary differential equations system, the Galerkin technique is believed to estimate the prevailing partial differential equations. In addition, Hopf bifurcation maps are constructed. The effect of diffusion coefficient stricture and delay on the model is comprehensively investigated, and the outcomes demonstrate that diffusion and delay can stabilize or destabilize the system. We found that, as the delay parameter values rise, the values of the Hopf bifurcations for growth and the rates of viral death are augmented, whereas the rate of production is decreased. For the growth, production, and death rates strictures, there is determination of an asymptotically unstable region and a stable region. Illustrations of the unstable and stable limit cycles, as well as the Hopf bifurcation points, are found to prove the formerly revealed outcomes in the Hopf bifurcation map. The results of the semi-analytical solutions and numerical assessments revealed that the semi-analytical solutions are highly effective.

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Section: Hopf Bifurcation Regionssupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth

Alfifi¹

2019

J. Nonlinear Sci. Appl.

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“…For the purpose of illustration of both the scenarios, we choose the equal diffusion coefficients as D 1 = D 2 = 1 mm 2 d −1 and D 3 = 1 mm 2 d −1 [38]. The one-dimensional spatial domain is taken as Ω = [0, 50] and the simulation carried out for a time window of 100 days.…”

Section: Numerical Resultsmentioning

confidence: 99%

Dynamics of an Intra-host Diffusive Pathogen Infection Model

Ahmed¹,

Nahian²

2020

Preprint

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In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number (R0), which is defined by the spectral radius of the next generation operator. Then, we derive a discrete counterpart of the continuous model by nonstandard finite difference scheme. The results show that the discrete model preserves the positivity and boundedness of solutions in order to ensure the well-posedness of the problem. Moreover, this method preserves all equilibria of the original continuous model. By constructing appropriate Lyapunov functionals for both models, we show that the global threshold dynamics is completely determined by the basic reproduction number. Further, with the help of sensitivity analysis we also have identified the most sensitive parameters which effectively contribute to change the disease dynamics. Finally, we conclude the paper by an example and numerical simulations to improve and generalize some known results.

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“…The units of cells were normalized in order for the carrying capacity of normal cells to be kept above threshold of 0 ≤ t ≤ t f [34][35][36]. On the other hand, the aim is to reduce the tumor-size which indicates the degree of the disease in the body and it requires the application of as much anti-cancer drugs as much as possible.…”

Section: Analysis Of Optimal Controlmentioning

confidence: 99%

Optimal Control Analysis of a Mathematical Model for Breast Cancer

Oke

Matadi

Xulu

2018

MCA

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Abstract:In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analyses were carried out using a variety of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs, ketogenic diet, and cancer emission when anti-cancer drugs, immune-booster, and ketogenic diet are included were established. Furthermore, optimal control theory is applied to discover the optimal drug adjustment as an input control of the system therapies in order to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin's maximum principle. Numerical simulations are presented to validate our theoretical results.

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Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Cited by 4 publications

References 41 publications

Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth

Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth

Dynamics of an Intra-host Diffusive Pathogen Infection Model

Optimal Control Analysis of a Mathematical Model for Breast Cancer

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