Search

• By utilizing some novel and non-standard analytical techniques, a new extinction theorem of an higher-order perturbed multistage AIDS model is given. • We demonstrate that this new theorem is stronger and much more general than its homologue existing in the recent literature. • Some simulations are provided in order to bear out our theoretical results. The principal purpose of this paper is to improve the extinction sufficient conditions of the higher-order perturbed multi-stage AIDS/HIV model proposed by Liu and Jiang in [1]. First, and by utilizing some novel and non-standard analytical techniques, we give a new extinction theorem of the said AIDS model. Then, we demonstrate that this new theorem is stronger and much more general than its homologue existing in [1]. Finally, we provide some simulations in order to bear out our theoretical results and clarify the impact of the adopted mathematical techniques on the findings. [ABSTRACT FROM AUTHOR]

Direct cell-to-cell transmission of HIV-1 is proved to be a more efficient means of virus infection than virus-to-cell transmission. In this paper, we incorporate both virus-to-cell and cell-to-cell transmissions into an HIV-1 virus model, which also contains intracellular delay and humoral immunity. By analyzing the characteristic equations, the local stability of feasible equilibria is established. By using Lyapunov functionals and LaSalle’s invariance principle, it is verified that global threshold dynamics of the model can be explicitly described by immune-inactivated reproduction rate and immune-activated reproduction rate. Numerical simulations are carried out to illustrate the corresponding theoretical results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study the threshold dynamics of an HIV-1 viral infection model with cell-mediated immune responses and direct cell-to-cell transmission mechanism. The model demonstrates global threshold dynamics with respect to the reproductive numbers for viral infection ℜ 0 and for CTL immune response ℜ 1 . The proofs of main results come from suitable uses of analyzing the characteristic equation and constructing Lyapunov functionals. Specifically, if ℜ 0 < 1, the infection-free equilibrium E 0 is locally and globally asymptotically stable, and the viruses are cleared. If ℜ 1 < 1 < ℜ 0 , the CTL-inactivated equilibrium E 1 is locally and globally asymptotically stable, and the infection becomes chronic but without persistent CTLs response. If ℜ 1 > 1, the CTL-activated equilibrium E 2 is locally and globally asymptotically stable, and the infection is chronic with persistent CTLs response. Numerical simulations are performed to support our results. [ABSTRACT FROM AUTHOR]

• Two numerical methods are developed for solving the fractional-order HIV-1 infection model of CD4 + T-cells. • Two method (Bessel matrix method and Bessel quasilinearization method) are based on the novel Bessel polynomials. • Error and convergence analysis are studied. • Numerical applications and comparisons show that methods are effective. • In the comparison of the two methods used, the Bessel-QLM method gives better results. In this paper, two numerical methods based on the novel Bessel polynomials are developed to solve the fractional-order HIV-1 infection model of CD 4 + T-cells considering the impact of antiviral drug treatment. In first of these methods, by using the Bessel polynomial and collocation points, we transform the HIV problem into a system of nonlinear algebraic equations. And this method, which is the method of direct solution is called as Bessel matrix method. The second method, which is called the Bessel-QLM method converts firstly HIV problem to a sequence of linear equations by using the technique of quasilinearization and then the reduced problem is solved by the direct Bessel matrix method. Error and convergence analysis are studied for the Bessel method. Finally, the applications are made on the numerical examples and also the numerical results are compared with the results of other available techniques. It is observed from applications that the presented results are better than the results of other existing methods and also the Bessel-QLM method is more efficient than the direct Bessel method. [ABSTRACT FROM AUTHOR]

Based on some important biological meanings, we propose a class of HIV infection models incorporating both classical cell-free virus diffusion and direct cell-to-cell transmission. According to recent studies, the direct cell-to-cell transfer of HIV is a significantly more efficient mode of retroviral dissemination. In the first part of our analysis, we show that our model possesses non-negative solutions. Then, we derive sufficient conditions for the asymptotic stability of equilibriums. The analytical solutions are verified by simulation results. At the end of the paper, some important conclusions are given. [ABSTRACT FROM AUTHOR]

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78 , 1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the dynamics of a five-dimensional virus model with immune responses and an intracellular delay which describes the interactions of the HIV virus, CD4 cells and CTLs within host, which is an improvement of some existing models by incorporating (i) two distributed kernels reflecting the variance of time for virus to invade into cells and the variance of time for invaded virions to reproduce within cells; (ii) a nonlinear incidence function f for virus infections, and (iii) antibody responses, which are implemented by the functioning of immunocompetent B lymphocytes, play a critical role in preventing and modulating infections. By constructing Lyapunov functionals and subtle estimates of the derivatives of these Lyapunov functionals, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection , for CTL immune response , for antibody immune response , for CTL immune competition and for antibody immune competition . The global stability of the model precludes the existence of Hopf bifurcation and other complex dynamical behaviors in long time. Numerical simulations are also performed in order to illustrate the dynamical behavior. [Copyright &y& Elsevier]

Abstract: As drug treatment allows more and more people with HIV/AIDS to live longer, the trade-off between benefits to drug treatment and potential threat infectivity individuals needs to be carefully evaluated. In this paper, we shall extend and investigate an HIV/AIDS treatment model (Cai et al., 2009) [14]. The infection force of the extended model is assumed to be of density dependent form. The resulting incidence term contains, the bilinear and the standard incidence. Mathematical analysis establishes that the global dynamics of the HIV infectious disease is completely determined by the basic reproduction number . If , the disease always dies out and the disease-free equilibrium is globally stable. If , the disease persists and the unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region. [Copyright &y& Elsevier]

Abstract: In this paper, some fundamental analysis and results are introduced for the accessibility of impulsive control systems (ICS). The main result is the characterization of accessibility for nonlinear ICS based on the ‘number of impulses’ which is required. These results naturally generalize and correct some earlier results obtained for linear ICS. The theory developed is applied to an impulsive model of the dynamics of human immunodeficiency virus (HIV) subject to medication. It is shown that HIV system fulfills the accessibility criterion. Finally, an impulsive control strategy is designed based on exact linearization to improve the response immune system of a patient of HIV. [Copyright &y& Elsevier]

Abstract: This paper presents a mathematical model which is in the form of a system of ordinary differential equations. These equations describe the dynamics of the immune system, human immunodeficiency virus (HIV), and drug-resistant mutants. We derive optimal treatment strategies for the HIV infection by formulating and then analyzing an optimal control problem with a structured treatment interruptions (STI) control approach. The continuous optimal treatment strategy is found by solving the corresponding optimality system. Moreover, using a direct search approach, a suboptimal STI in therapy is also obtained. We demonstrate, by numerical simulation, that the optimal treatment strategies reduce the mutant virus particles and increase the uninfected CD4+ T-cell count. [Copyright &y& Elsevier]