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Related Experiment Video

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Quantitative Analysis of Cell Edge Dynamics during Cell Spreading

Quantitative Analysis of Cell Edge Dynamics during Cell Spreading

Published on: May 22, 2021

Mathematical analysis of topological and random m-order spread models.

Jung-Chao Ban^1,2, Jyy-I Hong³, Yu-Liang Wu⁴

¹Department of Mathematical Sciences, National Chengchi University, Taipei, 11605, Taiwan, ROC.

Journal of Mathematical Biology

|February 2, 2023

Summary

This study compares deterministic and random models for spreading processes. It explains why certain propagation patterns occur more frequently in one model than the other, supported by numerical evidence.

Keywords:

Random spread model Spread rate Topological spread model Transition model n-spread rate

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Area of Science:

Complex Systems
Mathematical Modeling

Background:

Spreading processes are ubiquitous in nature and technology.
Understanding the dynamics of these processes is crucial for prediction and control.
Deterministic and random models offer different perspectives on propagation patterns.

Purpose of the Study:

To analyze and compare two distinct models for spreading processes: one deterministic and one random.
To investigate the spread rate of propagation patterns within each model.
To explain observed differences in pattern frequency between the two models.

Main Methods:

Utilizing substitution dynamical systems to model deterministic spreading.
Employing branching processes to model random spreading.
Encoding propagation patterns for quantitative analysis.

Main Results:

Quantified the spread rate for various patterns in both deterministic and random models.
Identified key factors contributing to the higher frequency of certain patterns in one model over the other.
Demonstrated a significant difference in pattern prevalence between the deterministic and random approaches.

Conclusions:

The choice of model (deterministic vs. random) significantly impacts the dynamics and observed frequencies of spreading patterns.
Substitution dynamical systems and branching processes provide complementary frameworks for analyzing complex spreading phenomena.
Numerical evidence supports the theoretical comparison of the two spreading models.