The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.

Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon

Department of Information Systems College of Computers and Information Science King Saud University Riyadh Saudi Arabia

Department of Mathematics City University of Science and Information Technology Peshawar KP 25000 Pakistan

Department of Mathematics College of Natural and Computational Sciences Debre Berhan University 445 Debre Berhan Ethiopia

Department of Mathematics University of Peshawar Peshawar KP 25000 Pakistan

IS Department College of Education King Saud University Riyadh Saudi Arabia

IT4Innovations VSB Technical University of Ostrava Ostrava Czech Republic

School of Mathematics and Data Sciences Changji University Changji Xinjiang 831100 People's Republic of China

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