Stabilization in a chemotaxis model for virus infection

Bellomo, Nicola; Tao, Youshan

doi:10.3934/dcdss.2020006

Cited by 37 publications

(30 citation statements)

References 34 publications

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“…Solving Eqs. (30)- (34), then there exists a CHIKV-free equilibrium Ω 0 = (s 0 , 0, 0, 0, x 0 ), where s 0 = ξ and x 0 = λ m . From Eqs.…”

Section: Resultsmentioning

confidence: 99%

“…The syndrome of chikungunya includes: fever, headache, severe joint and muscle pain, rash, fatigue, and nausea. The basic mathematical model of within-host virus dynamics was proposed by [15] and has been extended in several works (see, e.g., [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]). Wang and Liu [35] have proposed and studied the following within-host CHIKV dynamics model which contains four compartments, uninfected-monocytes (s), infected monocytes (y), free CHIKV particles (p), and antibodies (x):…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global properties of saturated chikungunya virus dynamics models with cellular infection and delays

2019

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This paper studies the global properties of chikungunya virus (CHIKV) dynamics models with both CHIKV-to-monocytes and infected-to-monocyte transmissions. We assume that the infection rate of modeling CHIKV infection is given by saturated mass action. The effect of antibody immune response on the virus dynamics is modeled. The models included three types of time delays, discrete or distributed. The first type of delay is the time between CHIKV entry an uninfected monocyte to be latently infected monocyte. The second time delay is the time between CHIKV entry an uninfected monocyte and the emission of immature CHIKV. The third time delay represents the CHIKV's maturation time. Lyapunov method is utilized and LaSalle's invariance principle is applied to address the global stability of equilibria. The model is numerically simulated to support theoretical results.

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“…Solving Eqs. (30)- (34), then there exists a CHIKV-free equilibrium Ω 0 = (s 0 , 0, 0, 0, x 0 ), where s 0 = ξ and x 0 = λ m . From Eqs.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global properties of saturated chikungunya virus dynamics models with cellular infection and delays

2019

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“…In Table 1, we have calculated the values of R 0 and R 1 and equilibria Figure 2. The simulation of trajectories of system (52)-(56) for Case (2).…”

Section: Case(2) Effect Of the Latencymentioning

confidence: 99%

“…During the last decades, diverse mathematical models have been developed to describe the within-host dynamics of many human viruses such as human immunodeficiency virus (HIV) [2,[4][5][6][7]12,16,20,22,31,36,38,[40][41][42]52], hepatitis B virus (HBV) [3,47], hepatitis C virus (HCV) [37,39,28], human T-cell leukaemia virus (HTLV) [30,51], chikungunya virus (CHIKV) [18,45] and so on. A proper model of virus dynamics could provide insights of a better understanding of the disease and clinical treatments used to fight against it.…”

Section: Introductionmentioning

confidence: 99%

Global stability of discrete virus dynamics models with humoural immunity and latency

Ełaiw

Alshaikh

2019

Journal of Biological Dynamics

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This paper studies the global stability of discrete-time viral infection models with humoural immunity. We consider both latently and actively infected cells. We study also a model with general production and clearance rates of all compartments as well as general incidence rate of infection. We use nonstandard finite difference method to discretize the continuous-time models. The positivity and boundedness of solutions of the discrete models are established. We establish by using Lyapunov method, the global stability of equilibria in terms of the basic reproduction number R 0 and the humoural immune response activation number R 1 . The results signify that the infection dies out if R 0 ≤ 1. Moreover, the infection persists with inactive immune response if R 1 ≤ 1 < R 0 and with active immune response if R 1 > 1. We illustrate our theoretical results by using numerical simulations. ARTICLE HISTORY

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“…Miao et al [6] developed an infection model consisting of five partial differential equations, time delays, and adaptive immunity. In a very recent work, Bellomo and Tao [26] studied a viral infection model with diffusion induced by chemotaxis dynamics. More recently, many works have added an explicit equation for HBV nucleocapsids to some HBV infection models.…”

mentioning

confidence: 99%

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

Ełaiw

Agha

2019

Adv Differ Equ

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This paper studies the global dynamics of a general diffusive hepatitis B virus (HBV) infection model. The model includes both enveloped viruses and DNA containing capsids. Two immune responses are recruited to attack the virus and infected hepatocytes. These are the cytotoxic T-lymphocytes (CTL) which kill the infected liver cells, and B cells which send antibodies to attack the virus. The non-negativity and boundedness of the solutions are discussed. The existence of spatially homogeneous equilibrium points is examined. The global stability of all possible equilibrium points is proved by choosing suitable Lyapunov functionals. Some numerical simulations are performed to enhance the theoretical results and present the behavior of solutions in space and time.

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Stabilization in a chemotaxis model for virus infection

Cited by 37 publications

References 34 publications

Global properties of saturated chikungunya virus dynamics models with cellular infection and delays

Global properties of saturated chikungunya virus dynamics models with cellular infection and delays

Global stability of discrete virus dynamics models with humoural immunity and latency

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

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