A delayed HIV-1 infection model with Beddington–DeAngelis functional response

Wang, Xia; Tao, Youde; Song, Xinyu

doi:10.1007/s11071-010-9699-1

Cited by 45 publications

(25 citation statements)

References 16 publications

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“…In [17], they proved global stability of the virus model with the incidence rate βx p v q , and they have presented a global analysis of model (1.2) by Lyapunov functions. In [18], we have studied a HIV-1 infection model with intracellular delay and Beddington-DeAngelis functional response, and obtained a necessary and sufficient condition for the global stability of the infectionfree equilibrium and give some sufficient conditions for the local stability of the infected equilibrium. In present paper, a class of more general HIV-1 infection model with Beddington-DeAngelis incidence rate and CTL immune response is considered.…”

Section: Discussionmentioning

confidence: 99%

Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response

2011

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In this paper, the global stability of virus dynamics model with Beddington-DeAngelis infection rate and CTL immune response is studied by constructing Lyapunov functions. We derive the basic reproduction number R 0 and the immune response reproduction number R 0 for the virus infection model, and establish that the global dynamics are completely determined by the values of R 0 . We obtain the global stabilities of the disease-free equilibrium E 0 , immunefree equilibrium E 1 and endemic equilibrium E * when R 0 ≤ 1, R 0 > 1, R 0 > 1, respectively.

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Section: Discussionmentioning

confidence: 99%

Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response

2011

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“…Studying the transmission, epidemiology and dy- namic virus of HBV infection is still a popular topic. In order to better understand the dynamics of viral infection, including HIV and HCV infection, many mathematical models have been proposed since they can provide insights into the dynamics of viral load in vivo and play a significant role in the development of a better understanding of diseases and various drug therapy strategies against them [2,6,15,17,[32][33][34][35]. In this paper, we have developed a hepatitis B virus infection model with cell-mediated immunity.…”

Section: Discussionmentioning

confidence: 99%

The importance of immune responses in a model of hepatitis B virus

2011

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In this paper, the dynamical behavior of a hepatitis B virus model with CTL immune responses is studied. Analyzing the model, we show that the virusfree equilibrium is globally asymptotically stable if the basic reproductive ratio of virus is less than one and the endemic equilibrium is locally asymptotically stable if the basic reproductive ratio is greater than one. When the basic reproductive ratio is greater than one, the system is uniformly persistent, which means the virus is endemic. Mathematical analysis and numerical simulations show that the CTL immune responses play a significant and decisive role in eradication of disease. The study and information derived from this

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“…Recently, a great deal of attention has been paid by many researchers on the Beddington-DeAngelis type response function, which has been used in the virus dynamics model (Wang et al, 2010;Huang et al, 2011;Elaiw et al, 2012), and in ecological model (Hsu et al, 2013) and their stability behaviours have been studied. Moreover, a general form of incidence rate function f (x, v) has been considered (Huang et al, 2010).…”

Section: T F X Y V V T Dx T Qy T Y T F X Y V V T P Q Y T V T Ky T Umentioning

confidence: 99%

Stability properties of a delayed HIV model with nonlinear functional response and absorption effect

Pradeep¹,

Ma²,

Guo³

2015

J. Natn. Sci. Foundation Sri Lanka

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This study investigated the impact of latent and maturation delay on the qualitative behaviour of a human immunodeficiency virus-1 (HIV-1) infection model with nonlinear functional response and absorption effect. Basic reproduction number (R 0 ), which is defined as the average number of infected cells produced by one infected cell after inserting it into a fully susceptible cell population is calculated for the proposed model. As R o (threshold) depends on the negatively exponential function of time delay, these parameters are responsible to predict the future propagation behaviour of the infection. Therefore, for smaller positive values of delay and larger positive values of infection rate, the infection becomes chronic. Besides, infection dies out with larger delays and lower infection rates. To make the model biologically more sensible, we used the functional form of response function that plays an important role rather than the bilinear response function. Existence of equilibria and stability behaviour of the proposed model totally depend on R o . Local stability properties of both infection free and chronic infection equilibria are established by utilising the characteristic equation. As it is crucially important to study the global behaviour at equilibria rather than the local behaviour, we used the method of Liapunov functional. By constructing suitable Liapunov functionals and applying LaSalle's invariance principle for delay differential equations, we established that infection free equilibrium is globally asymptotically stable if R 0 ≤ 1, which biologically means that infection dies out. Moreover, sufficient condition is derived for global stability of chronic infection equilibrium if R 0 > 1 , which biologically means that infection becomes chronic. Numerical simulations are given to illustrate the theoretical results.

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A delayed HIV-1 infection model with Beddington–DeAngelis functional response

Cited by 45 publications

References 16 publications

Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response

Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response

The importance of immune responses in a model of hepatitis B virus

Stability properties of a delayed HIV model with nonlinear functional response and absorption effect

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