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Related Concept Videos

Immunodeficiency Diseases01:25

Immunodeficiency Diseases

Immunodeficiency disorders are conditions in which the immune system's ability to fight infectious disease and cancer is compromised or entirely absent. The immune system comprises a complex network of cells, tissues, and organs that work together to protect the body from potentially harmful invaders. When this system is deficient or not functioning properly, it leaves the body susceptible to infections, diseases, or other complications.
There are three main causes of immunodeficiency disorders...
Immune Response Against Viral Pathogens01:29

Immune Response Against Viral Pathogens

The immune system's response to viral infections is a complex and coordinated process involving natural killer (NK) cells, T cell-mediated responses, and antibody-mediated responses.
NK Cells
NK cells are a crucial part of our innate immune system, acting as the first line of defense against viral infections. These cells can recognize and kill infected cells without prior exposure to the virus, effectively slowing down the spread of infection. Additionally, NK cells produce proinflammatory...

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Updated: May 21, 2026

Humanized NOD/SCID/IL2r&#947;null (hu-NSG) Mouse Model for HIV Replication and Latency Studies
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Dynamic analysis of an HIV stochastic time-delay differential equations incorporating two infection pathways and CTL

Yan Wang1, Jingze Ma1, Qiuyue Dong1

  • 1College of Science, China University of Petroleum (East China), Qingdao, 266580, Shandong, China.

Journal of Mathematical Biology
|May 20, 2026
PubMed
Summary

This study introduces a mathematical model for viral dynamics, showing that cytotoxic T-lymphocyte (CTL) immunity uses environmental randomness more effectively than B-cell immunity to clear viruses.

Keywords:
CTL immune responseCell-cell transmissionHIV infectionStationary Markov processStochastic differential equation

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Published on: September 25, 2018

Area of Science:

  • Mathematical Biology
  • Immunology
  • Stochastic Processes

Background:

  • Viral infections involve complex interactions between virus, host cells, and immune responses.
  • Cell-to-cell transmission and immune system dynamics, including T-cell responses, are crucial for viral control.
  • Stochasticity and time delays significantly influence the behavior of biological systems.

Purpose of the Study:

  • To develop and analyze a novel five-dimensional stochastic time-delay differential equation model for viral dynamics.
  • To investigate the impact of cytotoxic T-lymphocyte (CTL) immune response on viral clearance.
  • To explore the role of random perturbations and cell-cell transmission in viral dynamics.

Main Methods:

  • Formulation of a five-dimensional stochastic time-delay differential equation model.
  • Transformation of the model into an eight-dimensional stochastic differential equation.
  • Application of Lyapunov functions to establish the existence of stationary Markov processes.
  • Utilizing spectral radius analysis and the law of large numbers for extinction criteria.
  • Conducting numerical simulations to analyze model behavior and parameter impacts.

Main Results:

  • Demonstrated the existence of a unique global positive solution for the model.
  • Established conditions for a stationary Markov process based on the stochastic CTL-activated reproduction number.
  • Derived a critical condition for virus extinction.
  • Numerical simulations revealed the influence of random perturbations, cell-cell transmission, and time delays on viral load and T-cell counts.
  • Quantified viral clearance probabilities, showing CTL-mediated immunity's efficient use of stochasticity.

Conclusions:

  • The developed stochastic model provides insights into viral dynamics and immune responses.
  • CTL-mediated immunity is more effective in leveraging environmental stochasticity for accelerated viral clearance compared to B-cell mechanisms.
  • Time delays and cell-cell transmission play significant roles in shaping viral load and T-cell dynamics.