Dynamic Behavior of a General Stochastic HIV Model with Virus-to-Cell Infection, Cell-to-Cell Transmission, Immune Response and Distributed Delays

• Published in: Journal of nonlinear science Vol. 33; no. 5
• Main Authors: Wang, Yan, Lu, Minmin, Jiang, Daqing
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-10-2023; Springer Nature B.V
• Subjects: Analysis; Classical Mechanics; Differential equations; Economic Theory/Quantitative Economics/Mathematical Methods; HIV; Human immunodeficiency virus; Immune system; Liapunov functions; Markov processes; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical models; Mathematics; Mathematics and Statistics; Noise levels; Perturbation; Theoretical; Stationary Markov process; 60H10; 92D30; Immune response; Cell-to-cell transmission; 37H30; Distributed delay; Stochastic differential equation
• ISSN: 0938-8974; 1432-1467
• DOI: 10.1007/s00332-023-09955-5

In this paper, we construct a general four-dimensional delayed HIV infection model with virus-to-cell infection, cell-to-cell transmission, CTL immune response and parameter perturbations. By substitution, the four-dimensional delayed stochastic differential equations can be transformed into a degenerate eight-dimensional stochastic differential equations. The existence of the global positive solution of the system is obtained rigorously. By constructing appropriate Lyapunov functions, the existence of a stationary Markov process is derived when the stochastic reproduction number
R
0
s
is greater than one. Finally, we investigate the effects of noise level and the cell-to-cell transmission on the dynamic behavior of the model. Our model is a general model of the existing stochastic virus infection model, and the theoretical results improve and generalize the existing conclusion.