Nigar Ali

Asymptotic behavior of HIV-1 epidemic model with infinite distributed intracellular delays

In this study, asymptotic analysis of an HIV-1 epidemic model with distributed intracellular delays is proposed. One delay term represents the latent period which is the time when the target cells are contacted by the virus particles and the time the contacted cells become actively infected and the second delay term represents the virus production period which is the time when the new virions are created within the cell and are released from the cell. The infection free equilibrium and the chronic-infection equilibrium have been shown to be locally asymptotically stable by using Rouths Hurwiths criterion and general theory of delay differential equations. Similarly, by using Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction ratio is less than unity, then the infection-free equilibrium is globally asymptotically stable, and if the basic reproduction ratio is greater than unity, the chronic-infection equilibrium is globally asymptotically stable. Finally, numerical results with conclusion are discussed.

The Effects of Time Lag and Cure Rate on the Global Dynamics of HIV-1 Model

In this research article, a new mathematical model of delayed differential equations is developed which discusses the interaction among CD4 T cells, human immunodeficiency virus (HIV), and recombinant virus with cure rate. The model has two distributed intracellular delays. These delays denote the time needed for the infection of a cell. The dynamics of the model are completely described by the basic reproduction numbers represented by R0, R1, and R2. It is shown that if R0 < 1, then the infection-free equilibrium is locally as well as globally stable. Similarly, it is proved that the recombinant absent equilibrium is locally as well as globally asymptotically stable if 1 < R0 < R1. Finally, numerical simulations are presented to illustrate our theoretical results. Our obtained results show that intracellular delay and cure rate have a positive role in the reduction of infected cells and the increasing of uninfected cells due to which the infection is reduced.

Optimal control strategy of HIV-1 epidemic model for recombinant virus

In this work, an optimal control strategy is developed to eliminate the spread of HIV-1. To do this, two control variables are used such as the efficaciousness of drug therapy in reducing the infection of new cells and decreasing the production of new viruses. Existence for the optimal control pair is accomplished and the Pontryagins Maximum Principle is used to characterize these optimal controls. Objective functional is constituted to minimize the densities of infected cells and free virus and to maximize the density of healthy cells. The optimality system is derived and solved numerically.

Stability analysis of delay integro-differential equations of HIV-1 infection model

Abstract In this paper, the analysis of an HIV-1 epidemic model is presented by incorporating a distributed intracellular delay. The delay term represents the latent period between the time that the target cells are contacted by the virus and the time the virions penetrated into the cells. To understand the analysis of our proposed model, the Rouths–Hurwiz criterion and general theory of delay differential equations are used. It is shown that the infection free equilibrium and the chronic-infection equilibrium are locally as well as globally asymptotically stable, under some conditions on the basic reproductive number R 0 {R_{0}} . Furthermore, the obtained results show that the value of R 0 {R_{0}} can be decreased by increasing the delay. Therefore, any drugs that can prolong the latent period will help to control the HIV-1 infection.

Mathematical analysis of delayed HIV-1 infection model for the competition of two viruses

In this research article, a new mathematical delayed human immunodeficiency virus (HIV-1) infection model with two constant intracellular delays, is investigated. The analysis of the model is thoroughly discussed by the basic reproduction numbers and . For , the infection-free equilibrium is shown to be locally as well as globally stable. Similarly, the single-infection equilibrium is proved to be locally as well as globally asymptotically stable if . Our derived results show that the incorporation of even small intracellular time delay can control the spread of HIV-1 infection and can better the quality of the life of the patient. Finally, numerical simulations are used to illustrate the derived theoretical results.