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Nonlocal models in biology and life sciences: Sources, developments, and applications.

Swadesh Pal1, Roderick Melnik2

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Nonlocal mathematical models are crucial for understanding complex biological systems where local models fall short. This review explores their diverse applications in biology, from population dynamics to neurodegenerative diseases and nanotechnology.

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Active matter and AICell biology, genomics, and populations dynamicsEpidemiology and immunologyHealth sciences and innovative technologiesNetwork coupling and integrationNonequilibrium phenomena and processesNonlocal interactions in time and spaceNonlocal modelsNonlocal processes and phenomenaPattern formationsSmart and intelligent systems

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Area of Science:

  • Biophysics
  • Mathematical Biology
  • Life Sciences

Background:

  • Mathematical modeling is essential for understanding biophysical mechanisms in developmental biology.
  • Local models often fail to capture essential dynamics in biological systems.
  • Nonlocal models address interactions occurring over a range of distances.

Purpose of the Study:

  • To review different nonlocal mathematical models applied to biology and life sciences.
  • To discuss the sources, developments, and applications of these models.
  • To highlight emerging trends and future directions in nonlocal modeling.

Main Methods:

  • Systematic discussion of pattern formation conditions in population dynamics.
  • Analysis of nonlocal interactions on networks, including brain dynamics.
  • Exploration of nonlocal continuum models for nanotechnology and peridynamics.

Main Results:

  • Nonlocal models are vital for understanding cell-cell adhesion, disease spread, and neural networks.
  • Applications include modeling neurodegenerative diseases, cancer stem cells, and avascular tumors.
  • Nonlocal continuum models and peridynamics are applicable to nanoscale interactions and biomedical engineering.

Conclusions:

  • Nonlocal mathematical models offer a powerful framework for complex biological phenomena.
  • Their applications span diverse fields from population dynamics to advanced bioengineering.
  • Continued development promises deeper insights into biological systems and novel technological solutions.