https://doi.org/10.1140/epjp/s13360-023-04734-3
Regular Article
Dynamics of a delayed cytokine-enhanced diffusive HIV model with a general incidence and CTL immune response
School of Mathematics and Statistics, Central South University, 410083, Changsha, Hunan, China
Received:
23
September
2023
Accepted:
22
November
2023
Published online:
6
December
2023
In this paper, a new HIV CD4
T cells reaction-diffusion model has been introduced, which aims to explore the joint impact of cell-free infection, cytokine-enhanced viral infection, CTL immune response and time delay. Our results show that inflammatory cytokine infection, time delay and reaction-diffusion play an important role in HIV model and can not be ignored. First, we investigate the existence and nonnegativity of the solution of the model. Then, we obtain the existence of three equilibria namely infection-free equilibrium 
, immune-free equilibrium 
and immunity-inactivated equilibrium 
respectively. Next, two threshold parameters 
(basic reproduction number) and 
(immune response reproduction number) are defined, which determine the dynamic behavior of the model. Using Lyapunov functionals and LaSalle’s invariance principle, we show that is globally asymptotically stable when 
; If 
, the model is uniformly persistent and is globally asymptotically stable when 
; is globally asymptotically stable when and 
. Finally, a special case is given to show the global attractiveness of the three equilibria by numerical simulation.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
