Abstract
This paper mainly investigates the effect of the lévy jumps on the stochastic HIV infection model with cytotoxic T lymphocytes (CTLs) immune response. First, we prove that there is a unique global positive solution in any population dynamics, then we find sufficient conditions for the extinction of the disease. For proofing the persistence in mean, a special Lyapunov function be established, we obtain that if the infected CD4+ T-cells and virus particles will persistence in mean. Finally, numerical simulations are carried out to illustrate the theoretical results.
Highlights
IntroductionAIDS (acquired immunodeficiency syndrome) is caused by the human immunodeficiency virus (HIV)
acquired immunodeficiency syndrome (AIDS) is caused by the human immunodeficiency virus (HIV)
This paper mainly investigates the effect of the lévy jumps on the stochastic HIV infection model with cytotoxic T lymphocytes (CTLs) immune response
Summary
AIDS (acquired immunodeficiency syndrome) is caused by the human immunodeficiency virus (HIV). The progress of HIV infection has several different stages, including the early stage of infection, the clinical latency stage, stage of immune system becomes damaged, and the final stage that HIV progresses to acquired immunodeficiency syndrome (AIDS)-a fatal disease, for the life threatening effect of HIV that motivated numerous research to study HIV infection in different ways [1]. HIV is a retrovirus that attacks the body’s immune system, CD4+ T-cells are the primary target cells of HIV infection [2]. CD4+ T-cells play a central role in immune regulation, their depletion has a wide range of deleterious effects on the functioning of the entire immune system and leads to the immunodeficiency of AIDS [3].
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