scholarly journals Global Stability of HIV-1 Infection Model with Two Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Miao ◽  
Xamxinur Abdurahman ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Immune Response ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Infection Model ◽  
Global Dynamics ◽  
Response Model ◽  
Delay Differential ◽  
Ctl Immune Response ◽  
Hiv 1

We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. Our model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium, and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria of the CTL immune response model has been studied.

scholarly journals Global Dynamics of a Delayed HIV-1 Infection Model with CTL Immune Response

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Yunfei Li ◽  
Rui Xu ◽  
Zhe Li ◽  
Shuxue Mao
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Ctl Immune Response ◽  
Hiv 1

A delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable.

scholarly journals Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Abdoul Samba Ndongo ◽  
Hamad Talibi Alaoui
Keyword(s):  
Incidence Rate ◽  
Viral Entry ◽  
Disease Transmission ◽  
Transmission Function ◽  
Infection Model ◽  
Global Dynamics ◽  
General Incidence Rate ◽  
Delay Differential ◽  
Hiv 1 ◽  
Intracellular Delays

In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T,V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R0 and R1 which depends on the delays.

scholarly journals Optimal Control of a Time Delayed HIV-1 Infection Model

2019 ◽  
Vol 12 (2) ◽  
pp. 506-518
Author(s):  
Nigar Ali ◽  
Muhammad Ikhlaq Chohan ◽  
Gul Zaman
Keyword(s):  
Optimal Control ◽  
Delay Differential Equations ◽  
Control Function ◽  
Infection Model ◽  
Virus Concentration ◽  
Hiv Infection Model ◽  
Delay Differential ◽  
Objective Functional ◽  
Theoretical Results ◽  
Hiv 1

In this paper, an optimal control problem of HIV infection model of delay differential equations is taken into account. Then we set a control function which represents the efficiency of reverse transcriptase inhibitors. Objective functional is constructed to minimize the virus concentration as well as treatment costs.Adjoint system is derived using Pontryagins Maximum Principle. Optimality system is calculated and numerical simulation is carried out to illustrate the theoretical results. Finally, conclusion is drawn

scholarly journals Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Haibin Wang ◽  
Rui Xu
Keyword(s):  
Immune Response ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Latently Infected ◽  
Infected Cells ◽  
Ctl Immune Response ◽  
Hiv 1

An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infectionR0≤1; if the basic reproduction ratio for viral infectionR0>1and the basic reproduction ratio for CTL immune responseR1≤1, the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune responseR1>1, the global stability of the CTL-activated infection equilibrium is also derived when the time delayτ=0. Numerical simulations are carried out to illustrate the main results.

scholarly journals Global dynamics of a two-strain HIV infection model with intracellular delay

2020 ◽  
Vol 99 (99) ◽  
pp. 1-13
Author(s):  
Jin Xu
Keyword(s):  
Delay Differential Equations ◽  
Critical Case ◽  
Infection Model ◽  
Target Cells ◽  
Global Dynamics ◽  
Hiv Virus ◽  
Reproduction Numbers ◽  
Discrete Delays ◽  
Hiv Infection Model ◽  
Delay Differential

In this paper, we formulate mathematical model to describe the interaction of two strains of HIV virus and the target cells within a host. Model is in the form of a delay differential equations with a two discrete delays to account for the average time for replication for the two strains. The model dynamical turns to be generically determined by two composite parameters R1 and R2, the basic reproduction numbers for strain 1 and strain 2 in the absence of the other strain, in the sense that except for the critical case R1 = R2 > 1, the solutions are proved to converge to the corresponding equilibrium globally. The method used is Lyapunov functionals.

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