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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Exploring the Dynamics of a Model for HIV Infection Featuring Dual Time Delays

Journal of Applied Nonlinear Dynamics 14(3) (2025) 575--604 | DOI:10.5890/JAND.2025.09.007

Sangeeta Kumari$^1$, Parimita Roy$^2$

$^1$ Department of Mathematics, School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore-64112, Tamilnadu, India

$^2$ Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India

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Abstract

Mathematical models have significantly contributed by showing how virological synapses are created to enable cell-to-cell transmission. To replicate the crowding effect of Human Immunodeficiency Virus (HIV), this study, motivated by previous studies, attempts to develop a new compartmental epidemic model with two delays and nonlinear incidence rates. The first delay occurs between the time the virus enters the body and the beginning of HIV latency. The second delay occurs when infected cells must produce virions. We thoroughly investigated the local stability of the model's stable states using the delay differential equation stability theory and calculated the basic reproductive number ($R_0$). Numerical simulations were also conducted to assess the relative contributions of the two delayed viral transmission modes, investigate the effects of time delays and other factors on disease dynamics, and assess the effects of time delays on disease dynamics. We used the Partial Rank Correlation Coefficient (PRCC) to do a global sensitivity analysis and identify the most sensitive parameters affecting $R_0$, providing information on potential ways to slow down the progression of the HIV disease. We offered an extensive numerical analysis for our deterministic and delay models, including bifurcations and time series. Our simulation indicates that to keep the system predictable, we should control the time delay, $\tau_1$, which stands for the interval between viral entry into an uninfected target cell and the generation of an active target cell. In addition to outlining basic management measures, the current study demonstrates the complex dynamics of two delayed HIV models.

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