Abstract
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.
Highlights
Human immunodeficiency virus (HIV) is a virus that causes the condition of acquired immunodeficiency syndrome (AIDS)
We present the dynamical behavior of the proposed model and show how delays and cure rate influence stability
We prove the wellposedness of the proposed model and study the effect of delay and cure rate in controlling HIV-1
Summary
Human immunodeficiency virus (HIV) is a virus that causes the condition of acquired immunodeficiency syndrome (AIDS). [4] extended the basic model of HIV-1 infection to fourdimensional ordinary differential equation model, where latent period for the infected cells is included and a portion of these cells is reverted to the uninfected class. This improvement makes the use of nonlinear stability methods nontrivial. Genetic engineering offers an alternative approach, featuring modification of a viral genome to produce recombinant capable of controlling infections by other viruses [11] This method has been used to modify rhabdoviruses, including the rabies and the vesicular stomatitis viruses (VSV), making them capable of infecting and killing cells previously attacked by HIV-1.
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