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Related Concept Videos

Tumor Immunotherapy01:27

Tumor Immunotherapy

652
Immunotherapy is a treatment that boosts or manipulates the immune system to fight diseases, including cancer. For instance, by stimulating an immune response through vaccinations against viruses that cause cancers, like hepatitis B virus and human papillomavirus, these diseases can be prevented. Nonetheless, some cancer cells can avoid the immune system due to their rapid mutation and division. The immune response to many cancers involves three phases: elimination, equilibrium, and escape.
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Testing Cancer Immunotherapeutics in a Humanized Mouse Model Bearing Human Tumors
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A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model.

Muhammad Salman Khan1, Maria Samreen1, Muhammad Asif Khan2

  • 1Department of Mathematics, Quaid-I-Azam University, Islamabad 44230, Pakistan.

Entropy (Basel, Switzerland)
|July 27, 2022
PubMed
Summary
This summary is machine-generated.

Researchers developed a discrete-time model for immunogenic tumors, finding Neimark-Sacker bifurcation. This study enhances understanding of tumor dynamics and bifurcation analysis in discrete systems.

Keywords:
Andronov–Hopf bifurcationNeimark–Sacker bifurcationboundednesscontrol of bifurcationexistenceimmunogenic tumors modellinearized stabilitynonstandard difference schemenumerical simulations

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Area of Science:

  • Mathematical Biology
  • Computational Biology
  • Dynamical Systems Theory

Background:

  • Immunogenic tumor models are crucial for understanding cancer immunology and developing therapies.
  • Qualitative analysis of tumor dynamics can reveal complex behaviors and potential therapeutic targets.
  • Discrete-time models offer a computationally tractable approach to studying biological systems.

Purpose of the Study:

  • To develop a dynamically consistent discrete-time model for immunogenic tumors.
  • To analyze the stability of fixed points and identify bifurcation phenomena.
  • To compare the dynamical behavior of the discrete model with its continuous counterpart.

Main Methods:

  • A nonstandard difference scheme was employed to discretize the continuous immunogenic tumor model.
  • Fixed point analysis was used to determine equilibrium states and their stability.
  • Bifurcation theory, specifically analyzing Hopf and Neimark-Sacker bifurcations, was applied.
  • Numerical simulations were conducted to validate theoretical findings.

Main Results:

  • A unique positive fixed point was identified in the discrete-time model.
  • The discrete model exhibits Neimark-Sacker bifurcation at the positive fixed point.
  • The continuous model exhibits Hopf bifurcation at its corresponding positive fixed point.
  • Period-doubling bifurcations were found to be absent in the discrete-time model.

Conclusions:

  • The discrete-time immunogenic tumor model accurately captures key dynamical properties, including bifurcations.
  • Neimark-Sacker bifurcation in the discrete model offers insights into complex tumor growth patterns.
  • The study highlights differences in bifurcation behavior between continuous and discrete dynamical systems in tumor modeling.